Network Polarization

391

Introduction

Over the last two decades, dyadic studies ofconflict have generated a wealth of findings(Bremer, 2000). Yet most propositionsderived from systemic theories of worldpolitics received little or no empiricalsupport (Bueno de Mesquita, 2003; Buenode Mesquita & Lalman, 1988; Bennett &Stam, 2004; Moul, 1993). More impor-tantly, meaningful findings at the dyadic andmonadic levels of analysis failed to generalizeto the systemic level (Maoz, 2001; Maoz etal., 2003).

On the other hand, recent applications ofsocial networks analysis to world politics

(Maoz et al., 2005) show considerablepromise for a broader understanding ofsystem-related processes. Maoz’s (2001)network explanation of the democratic peacefocuses on the relationship between theregime of states and the regime structure oftheir environment, revealing cross-levellinkages between democracy and peace.Maoz et al. (2003) showed that – in contrastto previous investigations – there exists across-level linkage between status inconsis-tency and conflict.

The present study offers a new conceptionof systemic polarization and interdepen-dence as properties of system structure. Theeffect of system polarity on conflict has beena central issue in systemic theories of worldpolitics. However, there is no consensus onhow system polarity affects conflict (e.g.

© 2006 Journal of Peace Research,vol. 43, no. 4, 2006, pp. 391–411Sage Publications (London, Thousand Oaks, CA and New Delhi) http://jpr.sagepub.comDOI 10.1177/0022343306065720

Network Polarization, Network Interdependence,and International Conflict, 1816–2002*

ZEEV MAOZ

Department of Political Science, University of California, Davis

This study examines the effect of polarization and interdependence on systemic conflict. It argues thatboth polarization and interdependence must be conceptualized in terms of different types of relationsamong states and that different relationships would reflect varied levels of polarization and inter-dependence. Accordingly, this study develops general measures of network polarization and inter-dependence that allow measurement of these concepts over a wide array of international relations.Hypotheses are deduced from the realist and liberal paradigms about how alliance polarization, tradepolarization, and cultural polarization affect systemic conflict. Likewise, hypotheses are deduced regard-ing the expected effects of strategic and economic interdependence on conflict. These hypotheses aretested using data on alliance, trade, linguistic, and religious networks over the period 1816–2002. Thefindings suggest that alliance polarization and strategic interdependence increase the amount ofsystemic conflict, while trade polarization and economic interdependence have a dampening effect onthe amount of conflict in the international system. The theoretical implications of these results arediscussed.

* Replication data are posted at http://psfaculty.ucdavis.edu/zmaoz/datasets.htm and http://www.prio.no/jpr/datasets. Correspondence: [email protected].

Moul, 1993; Wayman & Morgan, 1991).The liberal paradigm emphasizes the effectsof interdependence on war and peace, yet westill lack empirical evidence connectingdifferent types of interdependence to conflictand peace at the systemic level. Accordingly,I explore the following issues:

(1) Can we conceive of polarity and polar-ization in relational terms? If so, candifferent aspects of systemic polarizationhave different effects on conflict andpeace?

(2) Can we conceive of different dimensionsof interdependence among states? Howdo different aspects of interdependenceaffect conflict in the internationalsystem?

Polarization, Interdependence, andSystemic Conflict

Polarization and ConflictThe concept of polarity is a cornerstone ofsystemic theories of international politics(Wayman & Morgan, 1991; Waltz, 1979;Geller & Singer, 1998; Bueno de Mesquita,2003). However, there is no agreement on(a) how to operationalize it and (b) how itaffects systemic conflict. Typical notions ofpolarity focused on two principal character-istics: the distribution of capabilities – typi-cally, over the subset of major powers – andthe pattern of alliances in the internationalsystem. Two rival hypotheses link polarity toconflict. One argument – associated withstructural realism – is that polarization tendsto stabilize the system because each blocdeters the other from attacking (e.g. Waltz,1979; Mearsheimer, 1990). As the systembecomes increasingly heterogeneous, thelikelihood of conflict due to opportunismand miscalculation increases. Others (e.g.Deutsch & Singer, 1964) argue that multi-polarity increases the chances of peacebecause it expands the interaction oppor-

tunities for states, allowing them to use moreflexibility in dealing with capability dispari-ties through diplomacy and alignment ratherthan through war.

The ‘parity promotes conflict’ thesis –associated with the power transitionapproach (Organski & Kugler, 1980; Kugler& Lemke, 1997) – contends that when thesystem leader is challenged by a contenderfor system leadership, the probability ofconflict increases. This is conditioned bystates’ satisfaction with the status quo. Theempirical evidence on polarity and conflict isdecidedly mixed (Geller & Singer, 1998;Bueno de Mesquita, 2003). Most empiricalstudies suggest that polarity – howevermeasured – does not appear to have apowerful effect on the amount of conflict inthe international system (Moul, 1993).

Studies of polarity and conflict shareseveral problems. First, they offer a relativelynarrow definition of polarity; central aspectsof international relations are not reflected inexisting measures. Polarity is measured by thedistribution of capabilities or by the structureof alliances. But if we conceive of structure asthe manner in which units are organized interms of their attributes and relations, thendifferent attributes or different relations mayyield different levels of polarity. For example,economic polarization – measured by thestructure of international trade flows – orcultural polarization – the kind discussed inthe ‘clash of civilization’ thesis (Huntington,1996) – may have important implications forpeace and war in the system.

Second, strategic polarization may beoffset by another type of polarization – forexample, low economic polarization.Alternatively, the effect of one dimension ofpolarization may be compounded by anotherdimension. Using single indices of polariza-tion to predict conflict may oversimplify theeffect of polarization of conflict.

Third, most studies focus on the great-power system. This causes severe selection

journal o f PE AC E RE S E A RC H volume 43 / number 4 / july 2006392

bias, because the definition of a great poweris quite arbitrary, and because it ignores sig-nificant variations in the structure of theinternational system due to the number,alignment patterns, and interaction amongminor powers.

From this discussion, it follows that onecould deduce two diametrically opposedhypotheses regarding the effect of strategicpolarization – conceptualized in terms of thestructure of alliances and the distribution ofcapabilities – on systemic conflict:

H1: The higher the degree of alliancepolarization, the greater the amount ofconflict in the international system.

H1a: The higher the degree of alliancepolarization, the lower the amount ofconflict in the international system.

H2: The more centralized the distributionof capabilities in the internationalsystem, the greater the amount ofconflict.

H2a: The more centralized the distributionof capabilities in the internationalsystem, the lower the amount ofconflict.

Even ardent realists consider trade to bean important element of economic powerand, thus, a key element of national power(Mearsheimer, 2001). Hence, the structureof trade relations may have an importanteffect on international conflict. In contrast toalliance polarization, which indicates agrowing hostility between blocs, trade polar-ization may indicate a growing level of in-bloc trading and a reduced level of tradebetween blocs. Therefore, trade polarizationis expected to reduce conflict because blocsare independent of each other and inter-dependent within them.1 It follows that

H3: The higher the degree of trade polar-ization, the lower the amount ofconflict in the international system.

The polarization of the internationalsystem may be defined in cultural terms. Thecultural composition of states may definetheir world-views and their definitions offriends and foes (Maoz et al., 2004). Theextent to which the system is polarized incultural – or civilizational – terms may primeit to intercivilizational conflict (Huntington,1993, 1996). Tests of this hypothesis do notsupport Huntington’s speculation (Hender-son, 1998; Henderson & Tucker, 2001;Russett, Oneal & Cox, 2000; Henderson,2004). However, these tests are dyadicwhereas Huntington’s hypothesis is systemicin nature. Specifically, cultural polarizationsuggests that the system is organized alongcultural ‘fault lines’. These divides may spillover into international tensions.2 Thus,

H4: The higher the degree of cultural polar-ization of the international system, thehigher the amount of conflict in it.

Interdependence and Systemic ConflictThe concept of interdependence is typicallyassociated with economic relations (Keohane& Nye, 1977). The ideas about economicinterdependence and peace go as far back asAdam Smith and August Comte (Harkabi,1991; Gat, 2006). The concept is alsoespoused by neoliberal scholars (Oneal &Russett, 1999; Russett & Oneal, 2001).

The neoliberal school suggests thateconomic interdependence reduces the like-lihood and magnitude of conflict at both thedyadic and systemic levels.3 High inter-dependence tends to generate widespread

Zeev Maoz NE T WO R K PO L A R I Z AT I O N A N D IN T E R D E PE N D E N C E 393

1 Trade polarization is not equivalent to economic inter-dependence. More on this point below.

2 Huntington (1996, 2000) claims that intercivilizationalconflict applies only to the post-Cold War era. However,Russett, Oneal & Cox (2000: 611–612) argue for tests ofthe cultural polarization thesis over a broader time-frame,because intercivilizational divides do not emerge in amoment and are not likely to be brief and abrupt.3 A notable exception to this argument is Barbieri (2002).

effect on the system when economic disrup-tions occur. Under high interdependence,conflict-related disruptions of trade arecollectively costly. When states are relativelyself-reliant, and trade does not make for amajor part of their national income, the costof conflict is reduced and the temptation toresolve conflicts of interests through the useof force may be higher. This implies that

H5: The higher the level of trade inter-dependence, the lower the level ofconflict in the international system.

Economic interdependence, however, isjust one way in which states depend on eachother. Strategic reliance creates another formof interdependence. Alliances representstates’ choice to pool capabilities in order todeal with common threats. By formingalliances, states become dependent on eachother’s capabilities and become increasinglydependent on others’ decisions (Morrow,1991). The extent of this dependence isbased on the type of alliance and on the levelof capabilities each alliance partner brings tothe common pool. When many states areallied with each other, increased strategicinterdependence tends to increase the extentof systemic conflict, because states may dragtheir allies or be dragged by them intoconflict through a chain-ganging process(Christensen & Snyder, 1990).4 Thus,

H6: The higher the level of strategic inter-dependence, the more conflict theinternational system will experience.

In the next section, I offer a new concep-tion of systemic polarization.

An Index of Network Polarization

One of the common ‘measurement’ strategiesof polarity avoids actual measurement of theterm. Instead, scholars label different periods– on the basis of historians’ judgments – interms of a specific type of polarity (e.g. multi-polarity for the 1816–1905 period, bipolar-ity for the 1945–90 period, unipolarity in thepost-Cold War period, etc.).5 Nonetheless,there exist quite a few measures of polarity(Wayman & Morgan, 1991; Moul, 1993).One approach views polarity as the extent ofinequality in the distribution of capabilitiesin the system (e.g. Ray & Singer, 1973; Hopf,1991). Other approaches focus on thealliance configuration of major powers.

The proliferation of measures of polaritymay suggest that yet another measure wouldcompound the overwhelming array ofmeasures that exist across a wide variety ofdisciplines. Yet, there are good reasons tooffer a new measure of polarization.

(1) Most existing measures presuppose agiven division of the system into groups,blocs, or cliques. In many cases,however, the division into groups andthe membership in these groups isexogenous. This is theoretically andmethodologically problematic. An en-dogenous procedure defining groupsand group membership as a result of thestructure of relations among actors mayprove superior to the existing measures.

(2) Most measures treat bloc membership asmutually exclusive (e.g. Bueno deMesquita, 1975: 199). In real life,however, some states may not be in anygroup, while others may be in multiplegroups. Assigning states to mutuallyexclusive blocs ignores complex relation-ships in the system, an importantproperty of polarization.


4 Christensen & Snyder argue that chain-ganging is morelikely when states value offensive capabilities over defensiveones. When the opposite is true, states turn to buck-passing. However, credibility costs suggest that strategicinterdependence may have a positive effect on conflict,regardless of the offensive/defensive balance.

5 See, for example, Brecher (1993), Brecher & Wilkenfeld(1997), and Cornwell & Colaresi (2002).

(3) As noted, we need a more generalmeasure that will allow for differentdimensions of system structure, such aseconomic or cultural polarization.

Most measures of polarization share twocommon features. First, they agree on whatconstitutes maximum polarization. Considera set of units that form a given system(parties in a parliament, families in a neigh-borhood, states in the international system)that is characterized by a given relationship(voting together, sending children to variousschools, having international alliances). Themaximum level of polarization is bipolarity:a state of affairs wherein half of the units areall clustered together in one bloc, the otherhalf are also clustered together in a com-pletely distinct bloc, and there are nobystanders, that is, units that do not belongto either bloc.

Second, existing measures are largelysilent on what constitutes minimum polar-ization. Does minimum polarization occurwhen no ties exist between any two units?Does minimum polarization occur whenthere exist only dyadic ties betweenmembers, but no larger groupings? Or, do weobserve minimum polarization when allmembers are bound together in one grandnetwork, alliance, clique, or coalition, andnobody is excluded?

Several ideas about the concept of polar-ization follow from this discussion.6 First,polarization is about how units interact with,or relate to, one another. Second, the conceptsuggests a summary description of how thesystem is organized in terms of the groupingof members. Third, implicit in this dis-cussion is the notion that polarization isindependent of the number of membersmaking up the system, but not of thenumber of blocs, cliques, or other groupings.

Specifically, maximum polarization can beobtained only with two blocs that aremutually exclusive in terms of the membersmaking up each bloc. Any other configura-tion of units and blocs is less than themaximum.

The measurement of polarization andinterdependence is grounded in socialnetwork analysis.7 A social network iscomposed of a set of units and a rule thatdefines whether or in what way any two unitsare related to each other. For example, analliance network consists of a set of states anda rule stating: state i is/is not an ally of statej. A trade network consists of a set of statesand a rule stating ‘the amount of exportsgoing from state i to state j ’. Social networkscan be represented by graphs or by matrices.Here, I use matrix algebra to measure polar-ization and interdependence. Networkpolarization, like other general networkproperties, is defined as

(1)

where the subscript T indicates a givennetwork.

Network polarization is a product of twoconcepts: Node Polarization (NPOL) andClique Overlap Index (COI) (Maoz, 2005a).In order to illustrate these concepts, considera hypothetical alliance configuration of fivestates. This configuration is represented by a5 � 5 matrix. Each entry sij denotes thepresence (1) or absence (0) of an alliancebetween states i and j.8 This is represented inTable I.

In order to measure polarization, wefirst derive the clique structure from this

Network propertyActual level of property Netwo

=| rrk

Maximum level of property NetworkT

T|


6 A more elaborate discussion of polarization bringing inconcepts and measures from economics and other politicalscience subfields is in Maoz (2005a).

7 A discussion of social networks analysis is beyond thescope of the present study. The most comprehensive intro-duction to this approach is Wasserman & Faust (1997).Maoz et al. (2005) discuss applications of this approach tointernational relations.8 Note that the diagonal is composed of scores of 1,meaning that each state is allied with itself.

sociomatrix. A clique is a subset of 1 . . . Nunits (in our case, states) that forms a closednetwork, that is, in which each unit has adirect tie to every other unit (Wasserman &Faust, 1997: 254).9 Two cliques cm, cl mustdiffer with respect to at least one member; noclique is a proper subset of another clique.This hypothetical alliance configurationyields three cliques: BCE, AC, AD. Theclique affiliation matrix (CA) is an n � mmatrix where rows represent units (states)and columns represent cliques. Each entrycaik is 1 if unit i is a member of clique k and0 otherwise. The clique affiliation matrixof this alliance configuration is given inTable II.

Note that cliques are not equivalent toalliances. Alliances can be subsets of cliques,but the clique structure may be differentfrom the alliances that exist in the system. Ifstate i has bilateral alliances with j and k, andj and k also have a bilateral alliance, we havea clique ijk although each of its componentalliances is strictly dyadic.

Node polarization reflects the relationshipbetween the states that form a clique andthose that do not. It first measures for eachclique the squared difference between allmembers of the network. Thus, for N unitsin the network, we have a total of N(N – 1)/2

pairwise comparisons. Since all pairwisecomparisons between members of a givenclique sum up to [s(s – 1)/2](1 – 1)2 = 0, andall pairwise comparison between units thatare not members of that clique sum also to[(N – s)(N – s – 1)/2](0 – 0)2 = 0, the onlynon-zero comparisons are the s(N – s)(1 – 0)2

= s(N – s). This sum is given by the bottomrow in Table II. Second, we sum across thesum of squared differences, and the numberis given by the rightmost column of thetable. Third, we divide the sum of differencesby the maximum possible sum of differencesfor a network of size N. This maximumdepends on whether N is odd or even. Foreven N, we have maxd = k(N/2)2, and for oddNs we have maxd = k(N2 – 1)/4. Thus, thenode polarization measure is given by

NPOL = for even N and (2)

NPOL = for odd N. (3)

NPOL ranges from 0 to 1. NPOL = 0 isobtained if all states form a single clique, and1 when the cliques are uniformly distributedsuch that half (or N/2 – 1 members for oddNs) are in each of the cliques. When no tiesexist in the network (e.g. when there are noalliances), then NPOL = 4(N – 1)/N2 for

4

11

2

s N s

k N

i ii

k

( )

( )

−

−=∑

41

2

s N s

kN

i ii

k

( )−=∑


9 The convention in social network analysis is to deal withcliques of size 3, . . ,N, but in our case we consider cliquesof size 1–2. Cliques of size 1 assume that a unit that hasno ties to any other unit is tied to itself. In our case, a stateis said to be aligned with itself even if it has no other allies.Cliques of size 2 are dyads and in our case represent bi-lateral alliances.

Table I. A Hypothetical Sociomatrix (S) ofAlliance Commitments

A B C D E

A 1 0 1 1 0B 0 1 1 0 1C 1 1 1 0 1D 1 0 0 1 0E 0 1 1 0 0

Table II. A Clique Affiliation (CA) Matrix ofAlliances

I II III Σs(N–s)

A 0 1 1B 1 0 0C 1 1 0D 0 0 1E 1 0 0

No. states in clique (s) 3 2 2s(N–s) 6 6 6 18

even N and NPOL = 4/(N + 1) for odd N.Note that NPOL derived from Table II is1.0.

Node polarization is not sufficient tocapture polarization, because it does notaccount for membership overlap acrosscliques. In order to do that, consider theClique-by-Clique Overlap (CCO) matrixthat is obtained by multiplying the transposeof CA (CA') by CA (CCO = CA' � CA).This matrix is given in Table III.

Entries in the CCO matrix are definedsuch that ccoij denotes the number of statesthat cliques i and j share in common.Diagonal entries ccoii reflect the number ofmembers in each of the cliques. A measureof clique overlap reflects the actual member-ship overlap across cliques divided by thetotal sum of possible clique overlap.

COI = (4)

The numerator of the expression inEquation (4) reflects the actual extent ofmembership overlap across cliques. Thedenominator reflects the maximum possiblemembership overlap across k cliques. Sincetwo cliques must have at least one differentmember, then the maximum possible overlapbetween cliques i and j must be (ccojj – 1).Since each clique has ccojj members, it canoverlap that number of times with othercliques. Thus, the denominator reflects whatis the maximum overlap in a matrix of

dimension k, in which the diagonal denotesthe distribution of members over cliques. Inour example, COI = 2/4 = 0.5.

Finally, network polarization is defined asNPI (i.e. Network Polarization Index) =NPOL � (1 – COI ). Thus, we have

NPI =

(5)

for even N

and

NPI =

(6)

for odd N.

Maximum network polarization isobtained when the system is strictly bipolar– divided into two cliques with half of theunits in each and no overlap between thecliques. Zero polarization obtains if all unitsare members of one clique (NPOL = 0). Wealso get zero polarization when there ismaximum overlap among the cliques. Whenno two units in the system are connected,then COI = 0 and NPI = NPOL = 4(N –1)/N2 for even N and 4/(N + 1) for odd N.10

With small Ns, no ties among units implieshigh polarization.11 However, polarization

4

111

2

s N s

k N

ccoi i

i

k

ijj i

( )

( )

−

−

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

−= =∑

++=

−

=

∑∑

∑ −

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

11

1

2

1

k

i

k

jj jjj

k

cco cco( )

4

112

1s N s

kN

ccoi i

i

k

ijj i

k

( )−⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

−= = +∑ ∑

ii

k

jj jjj

k

cco cco

=

−

=

∑

∑ −

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

1

1

2

1( )

cco

cco cco

ijj i

k

i

k

jj jjj

k

= +=

−

=

∑∑

∑ −

11

1

2

1( )


10 Actually, in completely disconnected networks, thedenominator is 0 and COI is undefined. However, sincethe numerator is also 0, we can set COI to 0 without lossof generality.11 Actually, maximum polarization can be observed alsowith a completely disconnected network of size N = 3, butthis is a unique exception to the strict bipolarity property.

Table III. The Clique-by-Clique Overlap (CCO)Matrix

Clique I II III

I 3 1 0II 1 2 1III 0 1 2

decreases significantly with the increase indisconnected networks.

The NPI has several properties:

(1) NPI is not sensitive to the size of thenetwork.

(2) NPI is sensitive to the number of cliquesin the network. NPI = 1 only with k =2 (or k = 3 and N = 3). For any othervalue of k, NPI < 1.

(3) Clique structures define NPI scores.Two networks of the same size and withthe same number of cliques can haveentirely different NPI scores. Small per-turbations in clique affiliation and/or inclique overlap have an immediate effecton NPI.

(4) NPI encompasses all levels of associ-ations between and among members ofthe network: monadic, dyadic, triadic,quadratic, etc.

(5) The key limitations of NPI, as is the casewith all clique-based measures ofnetwork structure, are fourfold: (i) It islimited to symmetric relations; asym-metric relations have to be symmetrizedin some manner (e.g. Wasserman &Faust, 1997: 273–276). (ii) It is limitedto binary sociomatrices; non-binarymatrices must be binarized according tosome rule. (iii) It does not account forcohesion within cliques. (iv) It does notaccount for distances between cliques.

The latter limitations can be overcome byweighting the CA matrix by some attributeindex that defines clique cohesion and cliqueposition on some space (Maoz, 2005a).

An Index of NetworkInterdependence

In a system that entails different relation-ships, such as alliances, trade, or politicalcoordination, interdependence among stateson these relationships is an important struc-

tural feature. Rosseau’s depiction of the stateof nature as an ideal setting is marred byinterdependence (Hinsley, 1963). The StagHunt metaphor (Jervis, 1978) captures thesecurity dilemma in world politics. Inter-dependence creates potential for bothcooperation and friction. Hence, it isimportant to examine how interdependenceaffects conflict and cooperation in thesystem.

Hoff & Ward (2004) estimate networkdependence as a function of the structure ofrelations in the network. I take a differentapproach, using actual relations to measureinterdependence directly. I illustrate this viaalliance data.

Interdependence represents the extent towhich a change in the relationship betweentwo units affects other units in the system. Ifstates i, j, and k have a relationship (e.g. areallied with each other), and if one of themchanges its behavior in a manner thatconcerns this relationship (e.g. i gets into warwith another state l ), this is likely to affectthe other states ( j and k). If i and j are relatedbut neither of them has a relationship withk, then a change in i ’s condition will affectonly j but not k. There may also exist indirectinterdependence. State i has an alliance withj and j has an alliance with k, but i does nothave a direct alliance with k. If state i getsinto a war, then the likelihood of k alsogetting involved in war depends on j ’sdecision to help i. Here, i ’s dependence on k(and k’s dependence on i ) goes through theirrelationship with j.

Consider the level of commitmentsentailed in a given type of alliance. First, Iassume that a state’s commitment to itself(self-defense) is higher than its commitmentto any other state. Absolute commitment isassigned a score of 1. Second, the level ofcommitment of one state to another dependson the type of alliance that such states mayhave. I assign a defense pact a level of com-mitment of 0.75, a non-aggression pact is


assigned a commitment level of 0.5, and anentente is assigned a commitment level of0.25.12 I specify an alliance sociomatrix for agiven year t. At is an nt � nt symmetricalmatrix where nt denotes the number of statesin year t, and aij = aji ∀ i, j∈At. Each entryaij is 0 if states i and j have no alliance, orassumes the appropriate commitment scoreif they have an alliance of a given type.

Dependence of a state on its ally is basedon (1) the degree of commitment entailed inthe alliance treaty and (2) the capabilitiesinvolved in the alliance. The degree of com-mitment is denoted by the commitmentscore of the alliance. However, since alliancesare typically a device for pooling resourcesfor a common cause, strategic dependence isa function of the extent to which an ally addsto one’s capabilities. Thus, alliance inter-dependence is a function of the capabilitiesof its members, weighted by the level ofcommitment expressed in the alliance treaty.For example, suppose state A with a capabil-ity score of 0.3 signs a defense pact with stateB that has a capability score of 0.05. State Ais now dependent on state B at a level of 0.05� 0.75 = 0.0375, but state B depends onstate A at a level of 0.3 � 0.75 = 0.225.

Formally, let At be an n � n alliance com-mitment matrix. Let Mt be an n � ndiagonal matrix with diagonal entries miirepresenting the composite index of nationalcapability (CINC) of state i and non-diagonal entries are all set to 0. I define adirect alliance dependence matrix as theproduct of the alliance and capabilitymatrices, ADt

1 = AtMt. Note that each entryad1

ij in matrix ADt1 represents the extent to

which state i depends on the capabilities ofstate j (weighted by their alliance reliabilityscore). This does not equal the extent of jdependence on the (weighted) capabilities ofi. This matrix is illustrated in Table IV.

Matrix ADt1 represents the first-order (or

direct) alliance dependence of each state oneach other state. Yet, first-order dependencedoes not reflect indirect dependencies. Notethat state A is not directly aligned with stateE, but it has a second order (ally of my ally)alliance with E because B – A’s direct ally –had a non-aggression pact with E. Thus, if Aand B get in war with state D, they can counton E (taking into account less-than-perfectreliability) not to attack any of them. So weneed to account for both direct and indirectdependence between units. To measuresecond-order dependence, we raise matrixADt

1 to the second power such that ADt2 =

ADt1 � ADt

1. This is given in Table V.Note that states A and C did not have a

direct alliance; thus, the entry in row A andcolumn C in matrix ADt

1 was 0. However,both had alliance ties to state B. This makesnow for a second-order dependency of ad2

ac


12 Obviously, this is an arbitrary figure. Yet, it relies onstudies assessing the empirical reliability of alliance types(Leeds, 2003).

Table IV. Weighted Alliance/Capabilities Matrix

A B C D E

A 0 0.75 0 0.25 0B 0.75 0 0 0 0.5C 0 0 0 0.75 0D 0.25 0 0.75 0 0E 0 0.5 0 0 0

Alliance (At)

A B C D E

A 0.2 0 0 0 0B 0 0.25 0 0 0C 0 0 0.1 0 0D 0 0 0 0.3 0E 0 0 0 0 0.15

Capabilities (Mt)

A B C D E

A 0 0.1875 0 0.075 0B 0.15 0 0 0 0.075C 0 0 0 0.225 0D 0.05 0 0.075 0 0E 0 0.125 0 0 0

Alliance dependence (ADt1)

= 0.006 and ad2ca = 0.011, for the second-

order dependence of a on c and of c on a,respectively. Continuing along these lines,we can calculate the third- fourth- . . . n – 1degree of dependence by successively raisingthe first-order dependence matrix to thethird, fourth . . ., n – 1 power. The overalldependence in any system of N states is

therefore given by AD = ADi + M. We add

the diagonal capability matrix to the reacha-bility matrix (the reachability matrix is thesum of all first, . . . n – 1 dependencematrices). This allows us to express the levelof self-dependence in the system. The ADtmatrix reflects the dependence of any twostates in the system on each other. Table VIshows the overall alliance dependence in thesystem.

The level of interdependence in thesystem is measured as follows. First, I calcu-late the row total dependence scores as adi. =

adij, and the total column dependence

score as ad.i = adij. The total row depen-

dence indicates the weighted alliance-capability of each state, considering both itsown capabilities and the capabilities of itsallies weighted by their alliance commit-ments. For example, state A has only 0.2 ofthe system’s capabilities on its own, but –taking into account the type of direct andindirect alliances it has with other states andthe capabilities of its direct and indirect allies– it now relies on 48.6% of the system’s capa-bilities. State D was the single most powerfulstate in the system, but now declines to thirdplace in terms of weighted capability alliancerank. The total column dependence suggeststhe extent to which other states in the systemare dependent on a given state. Here, forexample, we see that the level of dependenceon state C is greater than the dependence ofthe system on states A and B.

Next, we measure the net dependence of agiven state on other states in the system(excluding self-dependence), using di. = (adi.– adii)/adi.. Likewise, the dependence ofother states on any given state is measured byd.i = (ad.i – adii)/ad.i. This is given in therightmost column and the bottom row of thematrix in Table VI. Finally, the overall strate-gic interdependence in the system isobtained by averaging the d.i row (d

–.i =

d.ij) and di. (d–

i. = di.j) column of the

matrix and averaging the two resultingaverages. This is given in the bottom right

1

1n

j

n

=∑1

1n

j

n

=∑

i

n

=∑

1

j

n

=∑

1

i

n

=

−

∑1

1


Table V. Second-Order Alliance/CapabilityDependence

A B C D E

A 0.000 0.000 0.006 0.000 0.014B 0.000 0.000 0.000 0.011 0.000C 0.011 0.000 0.000 0.000 0.000D 0.000 0.009 0.000 0.000 0.000E 0.019 0.000 0.000 0.000 0.000

Second-order alliance dependence (ADt2)

Table VI. Overall Alliance Dependence (ADt) in the System

A B C D E Sum row Total dep. (di.)

A 0.200 0.188 0.006 0.077 0.015 0.486 0.588B 0.151 0.250 0.001 0.012 0.077 0.491 0.491C 0.011 0.002 0.100 0.225 0.000 0.339 0.705D 0.051 0.010 0.075 0.300 0.001 0.436 0.313E 0.019 0.125 0.000 0.001 0.150 0.295 0.492

Sum column 0.433 0.575 0.182 0.615 0.242 Averages 0.518Total dep. (d.i) 0.538 0.565 0.451 0.512 0.381 0.489 0.504

quadrant of Table VI. The bottom right(boldface) number reflects the overall level ofinterdependence (ID) in the system in termsof alliance ties.

The ID score has several attractivefeatures.

(1) It is based on both the attributes of theunits and the ties between them. In ourexample, the attributes are capabilities;the ties are alliance reliability scores.

(2) It reflects both dependence due to directrelations and dependence due to indirectrelations.

(3) It is applicable to both binary and ratiolevel data.

(4) It applies to both symmetrical and asym-metrical relations.

(5) It provides unit-level and dyadicmeasures of dependence as well asoverall system interdependence measures.The unit level measures are the di. andd.i scores that measure the extent towhich any unit in the network dependsupon other units, as well as the extent towhich all other units depend on thefocal unit. The directed dyadic measures(the adij entries of the ADt matrix)reflect the extent to which each state idepends on state j. Finally, the systemicinterdependence reflects the averagedependence of each state on any otherstate in the system.

(6) ID is continuous and standardized sothat it is insensitive to the number ofunits and the manner in which they aregrouped or organized, allowing system-atic comparison of states, dyads, andsystems over time and across space.

With these measures, we can now proceedto a test of the hypotheses specified above.

Research Design

Spatial–Temporal Domain and DataSourcesThe data cover all states in the internationalsystem over the 1816–2001 period. Specificmeasures are based on data availability. I usedthe following data resources.

(1) Conflict data: The source for the conflict(MID and War) data is the Dyadic MIDdataset covering the 1816–2001 period(Maoz, 2005b).

(2) Alliance data: The formal alliance datasetis available from the COW2 website(http://cow2.la.ps.edu) and is docu-mented in Gibler & Sarkees (2004). Ialso use the newly released ATOPdataset (Leeds, 2005).

(3) Trade data: I use the Barbieri, Keshk &Pollins (2004) trade dataset that coversthe period 1870–1996.

(4) Capability data: I use the COW capa-bility dataset documented in Singer(1990) and available from the COW2website.

(5) Religious and linguistic data: I use theCultural Dataset that was compiled byPhil Schaffer at the University ofMichigan and is available upon request.This dataset was used by Henderson(1998, 2004) and Henderson & Tucker(2001).

(6) Regime data: I use the Polity IV dataset(Jaggers & Gurr, 1995). Data can bedownloaded from http://www.cidcm.umd.edu/inscr/polity/index.htm.

The unit of observation is a given year, andall variables are measured at the systemiclevel in a manner specified below.

Measurement of Variables

Conflict Measures I employ a number ofmeasures of the dependent variables. Imeasure the overall volume of conflict of the


system by (a) the total number of dyadicdisputes at any given year, (b) the totalnumber of war dyads at any given year, (c)the proportion of dyads engaged in MIDsat a given year = 2 � (no. of dyadicMIDs)/[N(N – 1)], where N is the numberof states in the system at a given year, and (4)the duration of conflict days in the system,measured as the sum of MID days in thesystem for that year.

NPI Measures The NPI measures are usedfor alliances, trade, religious, and linguisticpolarization. The alliance and trade measuresare obtained from respective alliance andtrade sociomatrices. For each year, an alliancesociomatrix was measured as an N � Nbinary matrix where the presence of analliance of any kind between two states isassigned a score of 1 and 0 otherwise. Tradedata were dichotomized such that, when thedollar amount of exports of state i to jexceeded 5% of the total exports of theformer entry, tij = 1, and 0 otherwise. Cliqueextraction, clique affiliation, and cliqueoverlap matrices were calculated according tothe algorithms specified above.

NPI indices for religious and linguisticpolarity require an extra step, owing to theaffiliational nature of the data. I use thereligious and linguistic affiliation matricesfrom previous studies (Maoz et al., 2003,2004). I illustrate the procedure with thereligious affiliation data. For each decade, areligious affiliation matrix (RAt) is an n � mmatrix with the n states in the system and mcolumns representing all religions in thesystem. Each entry raik is the proportion ofstate i’s population subscribing to religion k.I generate an n � n sociomatrix of religioussimilarity RSt by multiplying RAt by its trans-pose: RSt = RAt � RA't. Each entry rsij denotesthe joint proportion of the populations ofstates i and j that share the same religiousaffiliation, regardless of type of religion. Thediagonal entries rsii are replaced by the index

of qualitative variation obtained from row iof matrix RAt. This denotes the degree ofreligious diversity of state i. Matrix RSt isdichotomized such that each entry rsij > 0.05receives a score of 1 and entries rsij ≤ 0.05receive a score of 0. The remainder of themeasurement of NPI is the same as foralliances and trade. Linguistic polarization ismeasured in the same manner, starting witha linguistic affiliation matrix LAt, convertingit into a linguistic similarity sociomatrix LStand dichotomizing it by setting lsij > 0.05 to1, and 0 otherwise.

Measures of Trade and Alliance Inter-dependence Alliance interdependence ismeasured exactly as explained in the exampleabove.13 Trade interdependence starts with arow-standardized trade sociomatrix Tt withentries tij reflecting the share of state i ’sexports going to state j. Diagonal entries inthe standardized trade matrix are set to theproportion of trade to the state’s GDP. Allsubsequent steps in the process of measuringtrade interdependence are identical to themeasurement of alliance dependence.

Control Variables In previous inquiriesapplying social network analysis to system-level processes (Maoz, 2001; Maoz et al.,2005), I used a number of control variablesto test the effect of network characteristics onsystemic conflict. Some of these controls arenow incorporated into the measures ofdependence. Here, I add two control vari-ables typically used by system analysts. Thefirst is the capability concentration index


13 For alliance interdependence, I used the ATOP codes ofalliance commitments (with defense = 0.75, offensivealliance = 0.65, non-aggression = 0.5, neutrality = 0.3,consultation = 0.2, and shared obligations = 0.1). Multiplealliance commitment scores are aggregated and the com-mitment score of a given dyad for a given year is measuredas the sum of commitment scores divided by 2.5 (themaximum possible commitment score that could beobtained if two states had a defense, offense, . . . , sharedobligation alliance in the same year).

(CAPCON ), which is defined (Ray & Singer,1973) as

CAPCON = (7)

where cinc is the composite capability indexof state i (i ’s share of the system’s capabili-ties), and N is the number of states in thesystem.

Second, I apply Moul’s (1993) modifica-tion of the Wayman (1985; Wayman &Morgan, 1991) polarity index. This index isa ratio of the number of major power alliancegroups divided by the number of majorpowers. Moul modified this index by thelower possible limit (strict bipolarity), whichis 2/m (where m is the number of majorpowers). These variables represent possibleconfounding effects of other forms ofpolarization.

Third, following Maoz (2001; cf. Maoz etal., 2005), I use the proportion of demo-cratic states in politically relevant (contigu-ity) cliques in the system to measure the levelof network democratization. All indepen-dent and control variables (except thenumber of dyads) are lagged one year back.

EstimationThe number of MIDs/wars in the systemand their duration are discrete event-countsvariables. Therefore, I use Poisson regressionwith first-order correction for autocorrela-tion when applying these variables. In orderto take account of the possible effect of thesize of the system on the frequency of MIDsand wars, I control for the number of dyadsin the system. I also use simple time-seriesregression with correction for autocorrela-tion and overdispersion to estimate the ratio-level dependent variables (proportion ofMIDs).

Results

The degree of polarization in the system overtime is presented in Figure 1, which showsseveral trends. First, all indices of polariza-tion – with the exception of religious polar-ization – decline over time. In contrast toconventional wisdom about alliances, wherepolarity was said to be at its highest levelsduring the Cold War era, our measures showthat this era is remarkably less polarized thanthe early and mid-19th century – the so-called balance of power era. This trend ofreduced polarization also declined during thepost-Cold War period. The explanation isstraightforward, considering the structure ofthe NPI index. Since the middle of the 19thcentury, a growing number of states joinedthe system that either became nonaligned orthat joined cross-cutting alliances. Thisgenerated many more alliance cliques, as wellas a higher rate of clique overlap.14

The reduced trade polarization is notsurprising. Nor is the downward trend inlinguistic polarization surprising, given thefact that new nations have joined the inter-national system with diverse sets of lan-guages. These new states in the Middle East,Asia, and Africa did not count in thelinguistic composition of the previouscolonial powers, and thus the expansion ofthe system brought about greater linguisticdiversity.

An interesting process accounts forchanges in religious polarization, whichshows a declining trend in the 19th centuryand an increase in the 20th century. Thegrowth of the international system in theearly parts of the 19th century was largelyreligiously homogenous. The Westernhemisphere was dominated by Catholicism.The large Christian population in the

cinc N

N

ii

N2

1

1

1 1

−

−=∑ /

/


14 Indeed, a time-series regression of NPOL on year andCOI on year yielded significant trend results (b = –0.001,R2 = 0.244 for NPOL and b = –0.0003, R2 = 0.156 forCOI).

Ottoman Empire and the Muslim populationin the Austro-Hungarian Empire accountedfor the declining levels of religious polariza-tion. When such states as Romania andSerbia became independent in 1878, theyeffected a sharp reduction in religious polar-ization because the religious structure ofthese new states overlapped significantly withthe Christian states in their neighborhood.The growth in polarization since the begin-ning of the 20th century is due to thegrowing organization of religious groupingsin distinct states.

The empirical analysis begins with thecorrelations among the various measures ofsystem structure. These are presented inTable VII, which reflects several findings.First, the correlation between religious andlinguistic polarization is moderate, but this isnot surprising. The distribution of differentlanguages tends to conform to the distri-bution of religious affiliations, yet linguisticgroups are far more diverse than religiousones. The high correlation between linguis-tic and alliance polarization, and the negativeand high correlations between religious andlinguistic polarization, on the one hand, andtrade polarization, on the other hand, require

some explanation. Linguistic polarization,alliance polarization, and trade polarizationall decline over time. Religious polarization,on the other hand, shows a more mixedpattern, hence displaying negative correla-tion with trade polarization and low correla-tion with alliance polarization. I deferdiscussion of the correlations involving theinterdependence variables to a later point.

Table VIII estimates the effects of the NPIindices and the control variables on systemicconflict. Alliance polarization has a robusteffect on systemic conflict. This effect ispositive for the entire period as well as for the20th century, but negative for the 19thcentury. These results are upheld when wedelete the trade variable (for which we havedata only over the 1870–1996 period withbreaks during the two world wars) and runthe analyses with the remaining variablesover the entire 1816–2001 period. Tradepolarization has also a fairly robust andnegative effect on systemic conflict.15 The


0

0.1

0.2

0.3

0.4

0.51816

1823

1830

1837

1844

1851

1858

1865

1872

1879

1886

1893

1900

1907

1914

1921

1928

1935

1942

1949

1956

1963

1970

1977

1984

1991

1998

Year

Net

wo

rk P

ola

riza

tio

n I

nd

ex

Re1NPI1 LangNPI1 TradeNPI1 CapCon AllyNPI

Figure 1. Measures of Systemic Polarization, 1816–2002

15 Because of the medium–high collinearity between tradeand other independent variables, I ran separate regressionswith trade and control variables on all dependent variables.The actual parameter estimates varied somewhat, but thesigns and statistical significance levels remained largely thesame.

high collinearity between linguistic NPI andother independent variables allowed use ofthis variable only in selected analyses. Ingeneral, linguistic NPI tended to have asignificant negative impact on the amount ofMID and war in the system when other vari-ables that were correlated with it wereremoved.

Religious polarization has an inconsistenteffect on the amount of conflict in thesystem, positively affecting the amount ofMIDs in both centuries and the amount ofwar and the duration of conflict in thesystem in the 19th century, but negativelyaffecting the amount of war and the durationof conflict in the 20th century. Thus, theeffect of religious polarization on systemicconflict is difficult to interpret. Both thosewho support the clash-of-civilization thesisand those who reject it might find somesupport in the results, and clearly moreresearch on these matters is warranted.

Among the control variables, only thedemocratic cliques variable has a dampeningeffect on the level of conflict in the system,and this effect is largely restricted to the20th century. This corroborates the resultsof Maoz (2001) on the spillover effect ofdemocratization in politically relevant net-

works on systemic conflict. The polarityindex of Moul (1993) and the capability con-centration did not have a noticeable effect onthe amount of conflict in the system.16

We now turn to the effect of interdepen-dence on systemic conflict. First, Figure 2displays the levels of strategic and economicinterdependence in the international system.The rate of strategic interdependence showssignificant fluctuations over time. The 19thcentury shows a generally declining trend ofstrategic interdependence. This is so becauseof the declining levels of commitments of themore powerful states to one another.

Coming back to the correlations concern-ing these variables in Table VIII, we noticethat strategic interdependence has a highcorrelation with trade polarization. It turnsout, however, that this correlation is, in fact,a statistical artifact: it is wiped out if weconsider temporal trends in both variables.

Levels of trade interdependence aresurprisingly low despite the overall quantumincrease in the volume of trade in the system,especially in the 20th century. However, the


16 The Wayman index had significant positive effect insome of the analyses, but it was also not robust acrossmeasures of the dependent variables.

Table VII. Correlations Among Independent Variables

Alliance/capLinguistic NPI Religious NPI Alliance NPI Trade NPI interdependence

Linguistic NPI –Religious NPI 0.591** –

(180)Alliance NPI 0.868** 0.17*** –

(180) (180)Trade NPI 0.774** –0.537** 0.697** –

(127) (127) (127)Alliance/cap –0.269** 0.299** –0.059** –0.858** –

interdependence (180) (180) (185) (127)Trade 0.129** –0.100** –0.068** 0.178* 0.009

interdependence (127) (127) (127) (127) (127)

* p < .05; ** p < .01.

journ

alof

PE

AC

ER

ES

EA

RC

Hvolum

e 43 / number 4 / july 2006

406

Table VIII. Network Polarization and International Conflict, 1816–2001

No. of MIDs per year No. of wars per year Duration of conflict

Independent variable 1870–1996 1816–1900 1901–96 1870–1996 1816–1900 1901–96 1870–1996 1816–1900 1901–96

Constant 1.514+ 1.834 6.081** –1.382 3.055 2.502* 8.857** 7.570** 10.172**(0.797) (1.696) (0.517) (1.303) (4.345) (1.180) (0.504) (2.840) (0.594)

Linguistic NPI –α 3.844* –α. –α. 1.855 –α. –α. 3.513 –α.(1.554) (5.188) (2.923)

Religious NPI 4.621** 3.984+ 5.078** 7.758** 9.548** –11.764** 0.090 4.851** –5.606**(1.001) (2.224) (1.427) (1.881) (3.232) (3.757) (1.463) (1.630) (1.597)

Trade NPI –8.923** –β. –11.373** –10.770** –β. 0.521 –12.312** –β. –6.674**(1.385) (1.172) (2.622) (2.767) (1.491) (1.576)

Alliance NPI 13.034** –17.160** 7.237* 7.884 –28.726** 17.690** 9.239** –21.826** 10.149**(2.632) (3.052) (2.988) (6.452) (6.692) (6.500) (3.547) (4.230) (3.051)

Capability concentration 2.733+ –9.738 0.421 10.173** –4.341 5.034* 6.805** –0.991 1.109(1.426) (7.926) (1.385) (2.695) (13.021) (2.396) (1.686) (9.816) (1.205)

Moul Polarity Index 0.106 0.443 –0.051 0.267+ –0.261 0.024 0.040 –0.010 –0.150+

(0.065) (0.323) (0.074) (0.149) (0.268) (0.052) (0.088) (0.052) (0.088)Democratic cliques –19.488** –1.231 –11.332** –37.051+ –148.259+ –0.020* –1.714* –0.003 –0.897*

(7.900) (36.378) (4.397) (19.138) (85.791) (0.009) (0.864) (0.017) (0.843)No. of dyads 0.000** 0.001* 0.000** –0.000 0.003** 0.000 0.000** 0.001 0.000**

(0.000) (0.000) (0.000) (0.000) (0.001) (0.000) (0.000) (0.000) (0.000)Rho1 0.759** –0.042 0.770** 0.712** 0.110 0.706** 0.811** 0.137 0.857**

Model’s statistics F = 56.77** F = 6.22** F = 34.62** F = 30.83** F = 7.45** F = 23.24** F = 55.63** F = 7.69** F = 37.71**R2 = 0.43 R2 = 0.18 R2 = 0.28 R2 = 0.21 R2 = 0.28 R2 = 0.21 R2 = 0.36 R2 = 0.42 R2 = 0.45N = 126 N = 79 N = 97 N = 126 N = 79 N = 97 N = 126 N = 79 N = 97

DW = 2.16 DW = 1.76 DW = 2.13 DW = 1.81 DW = 1.22 DW = 2.06 DW = 1.53 DW = 2.01 DW = 1.87

** p < .01; * .01 ≤ p < .05; + .05 ≤ p < .10.α Dropped due to colinearity.β Dropped due to missing data for most years.DW Durbin–Watson statistic (corrected for serial correlation).

changes in levels of trade interdependencelargely parallel changes in levels of trade as aproportion of the state’s GDP, which has notchanged very much over the course of the20th century. The fluctuations in the level ofinterdependence in the system are due pri-marily to the change in the alliance struc-tures of the major powers.

We now turn to the analysis of the effectof interdependence on systemic conflict.Alliance/capability interdependence seems tohave a relatively robust positive effect on theamount of systemic conflict. Table IX breaksdown the entire period into pre-nuclear andnuclear eras.17 The results suggest that, as thedegree of strategic interdependence in thesystem increases, so does the amount ofconflict. However, during the nuclear era,strategic interdependence reduced theamount of war and had no significant effecton the relative number of MIDs. Trade inter-dependence, on the other hand, had a robustand fairly consistent dampening effect on the

rate of conflict in the system, thus providinga system-level support to the results of neo-liberal scholars that suggest that economicinterdependence has a dampening effect ondyadic conflict (Russett & Oneal, 2001).

The effects of the control variables onconflict is the same as in the previous table.Only the size of democratic cliques has adampening effect on systemic conflict. Capa-bility concentration and the other measuresof polarity do not appear to have a consist-ent and robust effect on the level of conflictin the international system.

Conclusion

This study examines the effects of two struc-tural variables – polarization and inter-dependence – on systemic conflict. I offer anew conception that focuses on multipleaspects of systemic polarization. Differentaspects of polarization may have differenteffects on systemic conflict. This study alsoconverts theoretical notions of interdepen-dence in the system into two dimensions ofinterdependence – economic interdependence


17 I also used a century periodization, as well as a pre-nuclear and nuclear periodization on the analyses of TableIX. Results were largely similar.

Figure 2. Interdependence in the International System, 1816–2002

Trade Interdependence Alliance Interdependence

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91816

1824

1832

1840

1848

1856

1864

1872

1880

1888

1896

1904

1912

1920

1928

1936

1944

1952

1960

1968

1976

1984

1992

2000

Year

Inte

rdep

end

ence

In

dex

journ

alof

PE

AC

ER

ES

EA

RC

Hvolum

e 43 / number 4 / july 2006

408

Table IX. Interdependence and International Conflict, 1816–2001

No. of MIDs per year No. of wars per year Prop. dyadic wars per year

Pre-nuclear Nuclear Pre-nuclear Nuclear Entire 19thIndependent variable 1870–1996 1870–1945 1946–96 1870–1996 1870–1945 1946–96 period century 1900–2001

Constant 1.400* –0.724 3.241+ –2.679* –4.073 –4.589 0.249 0.514 0.402(0.660) (1.675) (1.763) (1.223) (3.609) (7.853) (0.602) (0.886) (0.670)

Trade interdependence –9.608** –0.764 –8.135* –17.614** –5.183 –36.367* –3.685* –2.695 –4.439*(2.328) (4.404) (4.076) (4.374) (8.066) (15.451) (1.714) (2.078) (2.159)

Alliance/Cap interdependence 1.664** 2.667* 1.411+ 1.887* 4.917* –6.368* 0.434 1.450** 0.859(0.473) (1.035) (0.811) (0.851) (2.546) (2.906) (0.270) (0.539) (0.648)

Capability concentration 2.070 1.245 –4.263 7.586** –6.171 5.413 –0.067 –2.194 –0.465(1.809) (3.542) (3.370) (2.944) (6.601) (10.893) (1.300) (1.924) (1.120)

Democratic cliques –0.010** 0.005 –0.029** –0.016* 0.020 –0.082* –0.153* –0.087 –0.098*(0.004) (0.006) (0.010) (0.007) (0.013) (0.034) (0.076) (0.126) (0.051)

Moul’s Polarity Index 0.228** 0.760* 0.437* 0.527** 0.959 1.060 0.075 0.131 –0.113(0.086) (0.317) (0.225) (0.197) (0.662) (0.630) (0.079) (0.160) (0.094)

No. of dyads 0.000* 0.000* 0.000* 0.000 0.000* 0.000 – – –(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

Rho 0.784** 0.782** 0.318* 0.000 0.610** 0.407** 0.660** 0.730** 0.193

Model’s statistics F = 49.67** F = 32.22** F = 5.89** F = 42.85** F = 19.11** F = 7.11** F = 3.09* F = 2.72* F = 2.97*R2 = 0.43 R2 = 0.35 R2 = 0.28 R2 = 0.24 R2 = 0.32 R2 = 0.24 R2 = 0.09 R2 = 0.10 R2 = 0.09N = 126 N = 73 N = 52 N = 126 N = 74 N = 52 N = 126 N = 75 N = 52

DW = 1.88 DW = 2.19 DW = 1.80 DW = 1.96 DW = 1.55 DW = 2.07 DW = 2.15 DW = 1.79 DW = 2.07

Trade interdependence was not included in the runs for the 19th century because of the lack of trade data for most dyads in the system and the fact that data are only available from1870 on.

and strategic interdependence. I developedmeasures of these concepts based on socialnetwork analysis and subjected thesehypotheses to empirical tests. The results ofthis study can be summarized in the follow-ing points.

(1) Trade relations appear to be an import-ant predictor of international conflict.Specifically, as trade polarization andtrade interdependence increase, the levelof conflict in the system declines. Tradepolarization indicates high levels oftrade within largely non-overlappingtrade cliques. Therefore, as expected, itdoes indeed reduce the level of conflictin the system. Trade interdependenceincreases the costs of systemic conflictand the benefits of cooperation andtherefore tends to have a consistent androbust dampening effect on systemicconflict.

(2) Alliance polarization and alliance inter-dependence tend to increase the levels ofsystemic conflict. But this effect is lessconsistent than in the case of trade. Ingeneral, alliance interdependence tendedto reduce the amount of conflict in the19th century and increase the amountof conflict in the 20th century. Allianceinterdependence tended to reduce theamount of war in the nuclear era.

(3) Religious polarization generally has apositive impact on systemic conflict, butthis effect is neither consistent norrobust. This may provide some supportfor the clash-of-civilizations argument,yet the findings here are too tentativeto suggest a definite conclusion aboutreligious polarization and systemic con-flict. Clearly, a more detailed analysis ofthese relationships may reveal interest-ing results.

(4) The measures presented herein areoriginal and appear to have an import-ant potential for capturing different

systemic attributes. But at least one ofthem – the Network Polarization Index(NPI) – needs some refinement.

The findings of the present study suggestthat systemic analyses of internationalconflict that rely on an internationalnetworks perspective offer a great deal ofinsight into a wide variety of global processesover time. Therefore, further inquiry intothese and other matters from a systemicperspective appears to have great potentialfor international relations theory.

References

Barbieri, Katherine, 2002. The Liberal Illusion:Does Trade Promote Peace? Ann Arbor, MI:University of Michigan Press.

Barbieri, Katherine; Omar Keshk & BrianPollins, 2004. ‘BKP Trade Data Codebook’(http://psweb.sbs.ohio-state.edu/faculty/bpollins/data/bkp_trade_0.9_readme.pdf ).

Bennett, Scott & Alan Stam, 2004. The Behav-ioral Origins of War. Ann Arbor, MI: Uni-versity of Michigan Press.

Brecher, Michael, 1993. Crises in World Politics.New York: Pergamon.

Brecher, Michael & Jonathan Wilkenfeld, 1997.A Study of Crisis. Ann Arbor, MI: Universityof Michigan Press.

Bremer, Stuart, 2000. ‘Who Fights Whom,When, and Why?’, in John A. Vasquez, ed.,What Do We Know About War? Lanham, MD:Rowman & Littlefield (23–36).

Bueno de Mesquita, Bruce, 1975. ‘MeasuringSystemic Polarity’, Journal of Conflict Resolu-tion 19(2): 187–216.

Bueno de Mesquita, Bruce, 2003. ‘Realism’sLogic and Evidence: When Is a TheoryFalsified?’, in John A. Vasquez & ColinElman, eds, Realism and the Balancing ofPower. Upper Saddle River, NJ: Prentice Hall(166–199).

Bueno de Mesquita, Bruce & David Lalman,1988. ‘Systemic and Dyadic Explanations ofWar’, World Politics 41(1): 1–20.

Christensen, Thomas J. & Jack Snyder, 1990.


‘Chain Gangs and Passed Bucks: PredictingAlliance Patterns in Multipolarity’, Inter-national Organization 51(1): 65–98.

Cornwell, David & Michael Colaresi, 2002.‘Holy Trinities, Rivalry Termination, andConflict’, International Interactions 28(4):325–353.

Deutsch, Karl W. & J. David Singer, 1964.‘Multi-Polar Power Systems and InternationalStability’, World Politics 16(3): 390–406.

Gat, Azar, 2006. War in Human Civilization.Oxford: Oxford University Press.

Geller, Daniel S. & J. David Singer, 1998.Nations at War: A Scientific Study of Inter-national Conflict. Cambridge: CambridgeUniversity Press.

Gibler, Douglas M. & Meredith Reid Sarkees,2004. ‘Measuring Alliances: The Correlates ofWar Formal Alliance Dataset, 1816–2000’,Journal of Peace Research 41(2): 211–222.

Harkabi, Yehoshafat, 1991. War and Strategy (inHebrew). Tel Aviv: Ma’arachot.

Henderson, Errol A., 1998. ‘The DemocraticPeace Through the Lens of Culture’, Inter-national Studies Quarterly 42(3): 461–484.

Henderson, Errol A., 2004. ‘Mistaken Identity:Testing the Clash of Civilization Thesis inLight of Democratic Peace Claims’, BritishJournal of Political Science 34(2): 539–563.

Henderson, Errol A. & Richard Tucker, 2001.‘Clear and Present Strangers: The Clash ofCivilizations and International Conflict’,International Studies Quarterly 45(2):317–338.

Hinsley, Francis H., 1963. Power and the Pursuitof Peace. Cambridge: Cambridge UniversityPress.

Hoff, Peter D. & Michael D. Ward, 2004.‘Modeling Dependencies in InternationalRelations Networks’, Political Analysis 12(2):160–175.

Hopf, Tedd, 1991. ‘Polarity, the Offense–DefenseBalance, and War’, American Political ScienceReview 85(2): 475–493.

Huntington, Samuel, 1993. ‘The Clash of Civi-lizations?’, Foreign Affairs 72(3): 22–49.

Huntington, Samuel, 1996. The Clash of Civi-lizations and the Remaking of World Order.New York: Simon and Schuster.

Huntington, Samuel, 2000. ‘Try Again: A Reply

to Russett, Oneal & Cox’, Journal of PeaceResearch 37(5): 609–610.

Jaggers, Keith & Ted Robert Gurr, 1995.‘Tracking Democracy’s Third Wave with ThePOLITY III Data’, Journal of Peace Research32(4): 453–468.

Jervis, Robert, 1978. ‘Cooperation Under theSecurity Dilemma’, World Politics 30(2):167–214.

Keohane, Robert O. & Joseph Nye, 1977. Powerand Interdependence. Englewood Cliffs, NJ:Prentice Hall.

Kugler, Jacek & Douglas Lemke, eds, 1997. Parityand War. Ann Arbor, MI: University ofMichigan Press.

Leeds, Brett Ashley, 2003. ‘Alliance Reliability inTimes of War: Explaining State Decisions toViolate Treaties’, International Organization57(4): 801–827.

Leeds, Brett Ashley, 2005. Alliance Treaty Obli-gations and Provisions Dataset. Rice Uni-versity (http://www.ruf.rice.edu/~leeds).

Maoz, Zeev, 2001. ‘Democratic Networks: Con-necting National, Dyadic, and Systemic Levelsof Analysis in the Study of Democracy andWar’, in Zeev Maoz & Azar Gat, eds, War ina Changing World. Ann Arbor, MI: Universityof Michigan Press (143–182).

Maoz, Zeev, 2005a. ‘An Index of Network Polar-ization’. Mimeo. University of California, Davis.

Maoz, Zeev, 2005b. Dyadic MID Dataset(version 2.0). (http://psfaculty.ucdavis.edu/zmaoz/dyadmid.html).

Maoz, Zeev; Lesley G. Terris, Ranan D.Kuperman & Ilan Talmud, 2003. ‘NetworkCentrality and National Conflict Behavior,1816–2000: A Study of National Attributes,Relational Attributes and Conflict’, paper pre-sented at the annual meeting of the PeaceScience Society (International), Ann Arbor,MI, 14–16 November.

Maoz, Zeev; Lesley G. Terris, Ranan D.Kuperman & Ilan Talmud, 2004. ‘The Enemyof My Enemy: What Exactly Is It?’, paper pre-sented at the Annual Meeting of the AmericanPolitical Science Association, Chicago, IL, 1–3September.

Maoz, Zeev; Lesley G. Terris, Ranan D.Kuperman & Ilan Talmud, 2005. ‘Inter-national Relations: A Network Approach’, in


Alex Mintz & Bruce Russett, eds, New Direc-tions for International Relations. Lanham, MD:Lexington (35–64).

Mearsheimer, John J., 1990. ‘Back to the Future:Instability in Europe After the Cold War’,International Security 15(1): 5–56.

Mearsheimer, John J., 2001. The Tragedy of GreatPower Politics. New York: Norton.

Morrow, James D., 1991. ‘Alliances and Asym-metry: An Alternative to the Capability Aggre-gation Model of Alliances’, American Journalof Political Science 35(4): 904–933.

Moul, William B., 1993. ‘Polarization, Poly-nomials, and War’, Journal of Conflict Resolu-tion 37(4): 735–748.

Oneal, John & Bruce Russett, 1999. ‘Assessingthe Liberal Peace with Alternative Specifica-tions: Trade Still Reduces Conflict’, Journal ofPeace Research 36(4): 423–442.

Organski, A. F. K. & Jacek Kugler, 1980. The WarLedger. Chicago, IL: University of ChicagoPress.

Ray, James Lee & J. David Singer, 1973.‘Measuring the Concentration of Power in theInternational System’, Sociological Methodsand Research 1(4): 403–437.

Russett, Bruce & John Oneal, 2001. Triangulat-ing Peace: Democracy, Interdependence, andInternational Organization. New York:Norton.

Russett, Bruce M.; John R. Oneal & MichaeleneCox, 2000. ‘Clash of Civilizations, or Realismand Liberalism Déjà Vu? Some Evidence’,Journal of Peace Research 37(5): 583–608.

Singer, J. David, 1990. ‘Reconstructing the Cor-relates of War Data Set on Material Capabili-ties of States, 1816–1985’, in J. David Singer& Paul F. Diehl, eds, Measuring the Correlatesof War. Ann Arbor, MI: University ofMichigan Press (53–68).

Waltz, Kenneth N., 1979. Theory of InternationalPolitics. New York: McGraw Hill.

Wasserman, Stanley & Katherine Faust, 1997.Social Network Analysis: Methods and Appli-cations, 2nd edn. Cambridge: Cambridge Uni-versity Press.

Wayman, Frank W., 1985. ‘Bipolarity, Multi-polarity and the Threat of War’, in Alan NedSabrosky, ed., Polarity and War: The ChangingStructure of International Conflict. Boulder,CO: Westview (93–111).

Wayman, Frank W. & T. Clifton Morgan, 1991.‘Measuring Polarity and Polarization’, in PaulF. Diehl & J. David Singer, eds, Measuring theCorrelates of War. Ann Arbor, MI: Universityof Michigan Press (139–158).

ZEEV MAOZ, b. 1951, PhD in PoliticalScience (University of Michigan, 1981). Pro-fessor of Political Science, University of Cali-fornia, Davis (2004– ). Author of six booksand over 75 articles on international politics,strategy, and decisionmaking. Most recentbook: Defending the Holy Land: A CriticalAnalysis of Israel’s Security and Foreign Policy(University of Michigan Press, 2006).


Documents

Network Polarization