dynamic network analysis: some recent developments

Iscom 2004-2005 (April 4) drw• Overview: Networks, Scaling and a Complexity approach to Social Change.• Reconstructing Scientific Dialogue

– Example: Multiple Approaches to Temporal Scaling (Population, Economic Capital)

• Models: Baseline, Applied Simulation, Longitudinal Data and Dynamical Models– Example:Agent Behavior; Applied Ramifications

• A Baseline Model for Agent-Based Network Evolution: Ring Cohesion– General Theory– Network scaling - q-Exponentials– Feedback and Feedforward– Simulating trade– Simulating kinship– Simulating intercorporate networks– Strong Tie Small Worlds

• Medieval to Modern (European Early Renaissance intercity network, 1175-1500)– Dynamics, e.g. Climate change as semiinteractive / semiexogenous– Industries and Lattices– GIS overlay– Network overlays (e.g., Royals and alliance dynamics)

• Biotech– AJS– CMOT– Management Science

• Ring Cohesion : Kinship ,e.g, Greek Gods– MSH [1]– MSH [2]– Generalized Computational machinery, Pajek

• Not discussed: Nord-Pas-de-Calais industrial elite networks through time– Fractal network geography of social networks

focus on network dynamics in empirical and simulated data

differentiate network models of temporal processes according to several distinctions• 1.     Baseline models, applied simulation models and empirical models.

• 2.     Long-term data is not a longitudinal dataset and a longitudinal dataset does not constitute a dynamic, or a dynamical view of a process. Longitudinal implies that long-term data are cast into a framework for valid and linked comparison (e.g., tracking the same elements through time) and measuring change as well as static variables. Dynamical implies a model of the process generating change, or, for that matter, statis (e.g., self-canceling changes for a process at equilibrium).

• 3. Nondegenerate and degenerate network dynamics. The difference can be illustrated by the relation of two variables in the phase space of the phenomena, whether simulated or observed. In the degenerate case the two variables e, z are related in a way that does not predict a change variable ż from the state variables by some function ż = f(e,z). In a fully nondegenerate case such predictions can be made for both change variables. Similarly for larger sets of variables. In a simple Lotka-Voltera model for e chasing z and z chasing e, in a predator/prey model, for example, ż = f(e,z) and ė = f(e,z).

Models• Baseline, Applied Simulation (trade; biotech; marriage; other networks), Longitudinal

Data and Dynamical Models– Baseline example:Agent behavior by node <s> in network N, modifying N

P(N´) = P(<s>|N, S, SP) x

(P(<s,t Є N>|s, N, S, SP) + P(<s,t ¢ N>)) i.e. P(t Є N) + (1-P(t ¢ N)

asynchronous update of N´ for selected <s>

selection of agent <s> proportional to degree kα of s.

selection of traversal of the agent’s token to <t> at an integer distance d from <s> proportional to dβ, with d > 1. [agent tries to find a target via a token]

selection of each intermediate v from prior u in s-t path proportional to vγ.

Probability of network N´ within a class of networks formed from an existing N by addition of a new edge from target node <t> to agent <s> either within N or adding t to N, conditioned on structural properties of N in the set S, e.g., S={K,D,V}=degrees k of <i>, distances d of <s,t> and traversal properties of s,…,u,v,…,t, adding exponential influence parameters on S in set SP ={kα,dβ,vγ},

In this example the interaction variables and their influence parameters SP ={kα,dβ,vγ} correspond to activity of an agent ~ kα, the potency ~

dβ of the agent’s (token) communication and the strategy ~ vγ used in token traversal, in which γ > 0 depends on the intelligence of average nodes in the network as intermediaries in the transmission of tokens in search of targets.

Interpretations: In general, an agent sustains itself by a search, first, for a potential target t or partner with whom feedback is established within an existing network, and, failing that, with a new partner t

Field properties: we look as distributions that asymptotically converge as the asynchronous iterations ∞. The convergent field processes are brought back to make conceptual comparisons with

processes observed through time in smaller networks.

Models, baseline Example:Agent Behavior by node <s> within network N

A selected agent s sustains itself by a search, first, for a potential target t or partner with whom feedback is established within an existing network, and, failing that, by recruiting and connecting to a new node t that serves as a resource

activity of an agent ~ kα, potency ~ dβ of the agent’s (token) communication strategy ~ vγ used in token traversal, in which > 0 depends on the average

intelligence of average nodes in the network as intermediaries in the transmission of tokens in search of targets.

– Applied Ramifications: Interpretations in specific examples,1 Interorganization ties in the biotech industry2 Evolution of city networks in the Early European Renaissance3 Emergence of coherent social units (class, ethnicity, industry cores and

scaffolds), including processes such as marriage

P(N´) = P(<s>|N, S, SP) x

(P(<s,t Є N>|s, N, S, SP) + P(<s,t ¢ N>))consolidation novelty

Models, baseline Example:Agent Behavior by node <s> within network N

α=0 γ=0

Distance decay β =1.3

α=0 γ=1

α=1 γ=1 α=1 γ=0

N=250

Edges weighted by traversals forming

feedback cycles

Lower (α=1), clustered

Right (γ=1), etched routesLeft (γ=0), more novelty

α=0 γ=0 α=0 γ=1

α=1 γ=1 α=1 γ=0

N=250

Nodes weighted by

degree

Right (γ=1) ~ road circuitss

Lower (α=1) ~ airline hubs

Distance decay β =1.3Left (γ=0) ~ fewer cycles

networks and scalingq-entropy (C. Tsallis) provides an accounting system for potential and kinetic energies

for both independent q=1 and nonindependent q≠1 interactions. Cycle formation is produced by nonindependent probabilities: a final <v,u> link to complete a cycle depends on a preexisting u-v path. For a baseline network model of agency, with continuous probabilities, ought to have distributions that are q-entropic and scale-free in q-entropic (log-q-log) measures.

Conjecture: Network dynamics will satisfy the laws of thermodynamics measured by q-entropy, i.e., the study of the inter-relation between heat, work and internal energy of a system, for independent and nonindependent interactions, 0 When two systems are in thermal equilibrium with a third body (like a thermometer), they are also in thermal equilibrium (identical q-entropies) with each other1 Energy can be changed from one form to another (heat, work and internal energy), but it cannot be created or destroyed 2 In all energy exchanges, if no energy enters or leaves the system, the potential energy of the state will always be less than that of the initial state (q-entropy nondecr)3 The entropy of a perfect crystal at 0° K is zero

For many self-organizing systems, adaptive feedback (selection / intention) takes place through cycle formation, while feed-forward occurs through storage (etching) of traversal frequency as potential energy or information source for future dynamics.

Theory of Ring Cohesion provides a structural accounting system for decomposing feedback into agent-based behavioral generators

Simulations:

For α=1, β and γ make little difference, but as α 0 the log-log scale-free degree distributions almost always shift to q-exponential.

In a generalized q-log-log scale these are all scale-free.

q=1.08

q=1.20

q=1.65

q=1.16

q=1.42

q=2.90

q=1.16

q=1.31

q=1.85

q=1.21

q=1.38

q=2.10

Simulations: All these distributions fit the q-exponential. For a given γ, α and β make little difference to the q-exponential, but as γ 0, the distributions shift to a decreasing concentration potential. γ 1 has greater concentration potential

from growth models to dynamicsa more general model incorporates decline along with

growth

S = (k, d, dist, Ai,j and Aj,i) has added structural measures

and the associated influence parameters expand to

SP = (α, β, γ, δ, ε) where α, β, γ are defined as before (for

k,d,v) and two new influence parameters govern the probability bias on the deletion of a node or an edge:

selection of agent <s> for deletion proportional to degree kα of s, with δ pos. or neg; alternatively, age specific mortality.

selection of edge <u,v> for deletion proportional to reciprocal edge

weight (Auv * Avu)ε, ε pos. or neg.

This model is capable of (mild) oscillatory dynamics that can be amplified by cascade effects such as produced by structural cohesion (meso-level network effects)

Feedback and feed forward• Feedback is represented explicitely in the network agent model:

suggests that a replicator dynamic might weight the replicative success of agents by the number of incoming feedback cycles.

• The non-feedback edges, however, represent new resources or sources of novelty.

• What is required for novelty to generate innovation, however, is consolidation/reorganization. Replicator dynamics (RD) might incorporate– RD = f (feedback inputs, new ties, pairwise reciprocity resulting from

traversals, independent of agent objectives, nonindependent cycles such as generalized reciprocity, and emergent higher order organization). Ways in which directedness, e.g., may get washed out.

Higher order interactions• Why needed? The dynamic oscillations and

tipping points of observed network interactions (trade, biotech, social networks) are more exaggerated than the more continuous network evolution models that add decay in small perturbations. Are these random exogenous shocks or endogenous network processes?

• Statistical analysis of new tie formation shows that structurally cohesive aggregates have effects independent of the micro attribute predictions

dynamic role of structural cohesion• A hierarchical embedded structuration with potentials for

intersections and organizations-in-fields crossovers.• Biotech: structural cohesion provides the measure of level of

multiconnectivity in a cohesive core with a new tie and novelty/consolidation dynamics.

• Marriage networks that define social class, ethnicity, wealth and knowledge transition show similar patterns, as do trade networks.

• The consolidation processes of interaction in which significant reorganization accomodates innovation are likely to occur within structurally cohesive emergent units, e.g., David Lane’s recursive “new attributions of functionality” and “forming new attributions.” Bootstrapping proceses (Anderson 1972).

• As cohesive level goes up, by definition, size at that level goes down in an intensifying shrinkage of reorganization. Cohesive intensification in and of itself is thus also likely to be exclusionary and potentially stultifying to further innovation.

Higher order interactions: how do cohesive units emerge?

• Here is where feed-forward processes operate on networks, because the etchings of traversal frequencies create a mechanism for information storage that influences future behavior through agent perceptions (perceivable structures)

• Do these provide the endogenous network processes needed to understand the dynamic oscillations and tipping points of observed network interactions (trade, biotech, social networks) that are more exaggerated than the more continuous network evolution models that add decay in small perturbations.

Cohesive nodes (gold and red) in an expanded exchange network and further road identification (red=3-cohesive) shows a second cohesive accumulation center further to the east -- again, such cohesion supported the creation of wealth among merchants and merchant cities, with states supported by indirect taxation and loans.

Now Northern Europe is represented (and the locations are geographic): the main Hanseatic League port of Lubeck had about 1/6th the trade of Genoa, 1/5th that of Venice.

Red 3-components

Middle East and its 3-core not sampled

Betweenness Centralities in the banking network (Net 6)Betweenness centrality in the trade network ought to predict accumulation of mercantile wealth. Genoa has greatest wealth, as predicted. On September 7th 1298 Genoa defeated the Venetian fleet in battle.

Size of nodes adjusted to indicate differences in betweenness centrality of trading cities

(Net 7) Flow centrality (how much total network flow is reduced with removal of a node) predicts something entirely different: the potential for profit-making on trade flows. It necessarily reflects flow velocities central to the organizational transformations undergone in different cities, as Spufford argues.

This type of centrality is conceptually very difference and distributes very differently than betweenness and strategic centers like Venice or Genoa, which are relatively low in flow centrality.

(database now expanded to 299 cities)

(Net3) Productivities are overlapping, crosscutting and interlaced in complex ways

Note how an industrial "blue banana" construction is taking place with communications in the left column, art works in the middle and linens on the left, i.e., circulation among the NW-SE poles; while capitals show a political vacuum of smaller polities in between, and trade fairs fill in this vacuum by providing decentralized marketing institutions.

(Net3) Productivities are overlapping, crosscutting and interlaced in complex ways

(Net3) Productivities are overlapping, crosscutting and interlaced in complex ways

Engines of History

Innovation and Consolidation

PopPressure, Destruction, Cumulativity

2005Iscom_ItalyD. R. White 2005

… including power-law growth of world population.

0

500

1000

1500

2000

2500

3000

3500

-200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

And if we take the departure from the trend to define cycles of change we can begin to study other changes …

In millions, actual and trendBefore we go there, it helps to know that all power-law growth entails strong predictions from its singularity date (in this case 2030 ± 10) as the outer limit of sustained growth:

(1) It necessitates a transition before singularity

(2) It predicts cycles of diminishing length as singularity approaches

-300

-250

-200

-150

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-50

0

50

100

150

-200 -100 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

-200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

…we see cycles of population growth

Detrended World Population to 1800, in millions

Source: White et al.

Detrended as a percentage of prior population

Reconstructing Scientific Dialogue: iscom-referential

eJournal communities, e.g., Structure & Dynamics, MBS – Dialogic– Review community– Commentary, Reply, Replication

Example: Understanding Dynamics – Interaction models: classes of functions ż =f(a,b,c…)– Functions vs. exploring potential phase spaces– Measuremt. & experimental testing of unexplored spaces– Testing interactive dynamics vs. defects of curve fitting

Example: Multiple Approaches to Temporal Scaling – Population– Economic Capital

Example: Networks, Mesolevels, Scaffordings, etc.– Iscom issues

Engine process: Territorial States

e.g., run by inputs of popPressure and competition,

outputs of

Innovation

(increase

with size)

falling population

(innovations

conserved)

T= isolation competition transport

Internal

Conflict

(innovations)

Pop Density/Resources

P=Pop Pressure

This is Turchin's phase diagram for England, 1480-1800, for population size and sociopolitical violence as a pair of variables that drive one another interactively. Temporal movement here is clockwise (axes are reversed from the previous diagram). The dynamic is that the population reaches carrying capacity setting sociopolitical violence into play, which only recedes as population crisis leads to a collapse, leading into a new cycle.

Where you are on this phase diagram predicts where you are going; this is not true for synchronously correlated variables

‘Pressure’

‘Temperature’

English sociopolitical violence cycles don’t directly correlate but lag population cycles. Detrended English population cycles, 1100-1900, occur every 300-200 years.

Source: Turchin

Chinese phase diagram

Turchin tests statistically the interactive prediction versus the inertial prediction for England

detrended

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

Detrended Populations: World (logged) (power law) and England

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

-200 0 200 400 600 800 1000 1200 1400 1600 1800 2000

Cycles grow shorter as predicted by power-law growth.

England’s population cycles lag the World cycles, which are heavily weighted by China and India

Source: White et al.

Correlates that do not interact dynamically include:

Inflation cycles (English: David Hackett Fischer)

imitate

Detrended English Population cycles (Turchin)

Renaissance Equilibrium (begins with

economic depression)

1900

Effects of Inflation of Land on Monetization

(Relative to Carrying Capacity) Prices Inflation Demand for Peasants money rents to cities Real wages In kind payment of serfs, Elites to cities Conspicuous (low) retainers salaried laborers consumption Demand for Poverty forces more Demand for Coinage prestige goods meltdown of silver silver mining

Monetization (Velocity of Money in Exchange)

Thresholds (Variables affecting transition)

Reorganization (to handle higher velocities)

e.g., Division of labor, new techniques, road building, bridge building, new transport

Merchants/agents Governments/agents Churches/agents Elites/agents

GET TURCHIN VARIABLES

The population and sociopolitical crisis dynamic that drove Inflation also drove monetization and trade in luxury goods in the 12th-15th centuries. Inflation of land value created migration of

impoverished peasants ejected from the land, demands of money rents for parts of rural estates, and substitution of salaries for payments in land to retainers,

Engine processes

e.g., carnot cycles, run by inputs of fuel and energy,

outputs of

momentum

and exhaust;

mechanically

linked

decompression

(momentum

conserved)

T exhaust firing piston

(momentum)

compression

P

Engine process: Biotech

e.g., run by inputs of cohesion and novelty,

outputs of

innovation &

distribution

outside recruitment (novelty)

(innovation

conserved)

T= internal production couplings

Intra distribution

Org. (innovation)

Exchanges

cohesion

P= Cohesive Consolidation of Field

Flip these back and forth for sense of dynamics

Cumulative ties, Biotech

New ties, Biotech

New ties/Partner

versus

Core cohesion

(Biotech) time lags 1 & 2 yrs

Phase Diagram:0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1989 1991 1993 1995 1997 1999

Cores get more

cohesive ( smaller) with time;

“high metabolism”

“more compact”

Geoff’s scaling laws

New ties to partners ratio

Percent organizations in top k-component (4, 5, 6)

Interactive dynamics between innovation and consolidation (new ties dense cores)

1992 Core

Reinforcement

(1990)

Tree Ties

(New ties for 1989)

Tree Ties

(1991) Lots of

Tree Ties

Expanded Core Reinforcement

1992 Core

Reinforcement

Expanded Core Reinforcement

Densified Core Reinforcement

Densified Core and

Tree Ties

Tree TiesDensified Core Reinforcement

Visually, we see in these last slides over 12 years a repetitive or cyclical dynamic with 3-year cycleing:

new tie tree formation (reachout) for two years running,

but in the third year of each cycle –

new ties regroup to consolidate cohesion in the core.

Core reinforcement ratchets up to expanded core and then densified core. These are the same patterns shown in the statistical analysis.

Field processes

• After a field influx of recruitment novelty (absorbed into cohesive production) and new recruitment falls to a minimum, it still takes one year for the field to reorganize a more cohesive core

• Takes two years for positive effects of a more cohesive core to decay so as to require influx of novelty through recruitment

nPart newEntrants e-new year e-new/nPart new/100Entrants Cohesion %HiCohesive

672 29 362 1989 0.53869 0.12483 0.066 7.2

747 28 379 1990 0.507363 0.13536 0.063 7.2

792 18 379 1991 0.478535 0.21056 0.060 7.8

800 31 429 1992 0.53625 0.13839 0.025 2.9

873 35 520 1993 0.595647 0.14857 0.120 12.3

938 35 508 1994 0.541578 0.14514 0.130 13.7

985 24 543 1995 0.551269 0.22625 0.050 6.6

1058 34 737 1996 0.696597 0.21676 0.070 9.1

1172 14 696 1997 0.593857 0.49714 0.090 10.6

1313 13 957 1998 0.728865 0.73615 0.060 6.0

1332 12 1000 1999 0.750751 0.83333 0.055 5.5

estimated estimated

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1989 1991 1993 1995 1997 1999

e-new/nPart

e-new/100Entrants

Cohesion

Phase transition to a condensed hi metabolism core

From phase transitions to Geoff’s scaling laws?

• The new animals (corporate cores emergent megacorporations)

• Encode elements of more dispersed lower-density systems (e.g., territorial)

• But now shrunk into a condensed and ‘high metabolism’ form

• Higher ‘productivities’• From bigger brutes to smaller powerhouses?• One, but not the only way to evolve

Now look at R&D: Biotech

e.g., run by inputs of cohesion and novelty,

outputs of

innovation &

distribution

outside recruitment (novelty)

(innovation

conserved)

T= internal production couplings

Intra distribution

Org. (innovation)

Exchanges

cohesion

P= Cohesive Consolidation of Field

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1989 1991 1993 1995 1997 1999

R&D Should hit along with shifts of consolidation because these are noticeable and create excitement, and diffusion out of the core is maximum.

New ties to partners ratio

Percent organizations in top k-component (4, 5, 6)

Interactive dynamics between innovation and consolidation (new ties dense cores)

Now look at R&D (incomplete)• Look at whether the fluctuations in R&D ties match the predictions

or fit in some other way into the dynamics (R&D/Finance data below for 3 years prior to date shown. VC siphoned off to eComm with internet bubble that started in 1995.

• Need the yearly data

0.000000

0.100000

0.200000

0.300000

0.400000

0.500000

0.600000

0.700000

0.800000

1989 1991 1993 1995 1997 1999

e-new/nPart

Cohesion

R&Dties

FinancePartners

structural cohesion in kinship

• Marriage networks that define social class, ethnicity, wealth and knowledge transition show similar patterns

Greek Gods: Census Graphs

Complex census graph for the self-organizing middle eastern network with a maternal cluster (MBD) and a paternal cluster (FBD)

Engine processes

e.g., carnot cycles, run by inputs of fuel and energy,

outputs of

exhaust

decompression

T exhaust firing

compression

P

Specificity and stability in topology of protein networks

Sergei Maslov, Kim Sneppen Science, 296, 910-913 (2002)

Specificity and stability in topology of protein networks

Sergei Maslov, Kim Sneppen Science, 296, 910-913 (2002)