Network-Aware Customer Value in Telecommunication SocialNetworks

Dymitr Ruta, Przemysław Kazienko and Piotr Brodka

Abstract— The exponential growth of interactions in the net-worked society becomes gradually a reality. Social networksthrive and expand rapidly across many different interactionplatforms delivered by modern telecommunication and internetservices. The role and the impact of individuals on network in-teractions is increasingly important although rather complex anddifficult to analyse in the realistic dynamic network environment.The goal of this paper is to look into the key structural changesin social networks: addition and removal of nodes and propose amethodology for temporal modelling of network response to thesechanges in order to assess the true network impact of the addedor removed node. We propose to use the time series of the firstorder neighbourhood interaction as the key dynamic measure ofthe impact of individual node on its local network’s interaction.The proposed methodology is supported with some preliminaryexperimental results carried out on real voice telecommunicationnetwork over customer acquisition and churn events and it laysground for the new network-aware estimation of customer value.

I. INTRODUCTION

Social networks are one of possible representations ofhuman communities, in which people interact and get intorelationships with one another. These relationships typicallygrown on friendship, family bonds, cooperation, locality areusually very complex and engage our feelings, emotions, likesand dislikes, etc. Simultaneously, social networks evolve: theychange their structure; new communities arise while the othersdisappear; some relationships reinforce while other fade [16].

In the real world, people depend on each other. Our choicesand behaviour also influence behaviour of the others [6]. Itis the crucial concept of recommender networks [17] andplays an important role in marketing [15], in which peoplespread information and opinion about products through mu-tual, personal contacts. Ability to predict changes and theirconsequences is crucial in every business. For that reason,dynamic analysis within the customer network especially inthe telecommunication social network is very important. Gen-eral concept of dynamic social network analysis was presentedin [1]. In order to forecast such changes and investigatethe evolution of social networks even physics and molecularmodelling can be utilised [9]. In some other approaches,clustering [5], statistical analysis and visualisations [1] or

Dymitr Ruta, BT Innovate, Intelligent Systems Research Centre, Adas-tral Park, Orion MLB, PP10H, Martlesham Heath IP53RE, UK (phone:+441473605491; fax: +441473623683; email: dymitr.ruta@bt.com).

Przemysław Kazienko, Wrocław University of Technology, Institute ofComputer Science, Wyb. Wyspianskiego 27, 50-370 Wrocław, Poland (email:przemyslaw.kazienko@pwr.wroc.pl)

Piotr Brodka,Wrocław University of Technology, Institute of ComputerScience, Wyb. Wyspianskiego 27, 50-370 Wrocław, Poland (email: pi-otr.brodka@pwr.wroc.pl)

multi agent systems [2], [19] are used to get an insight intonetwork dynamics. Daspupta et al. tried to predict churnbased on the analysis of relationship strength in the mobiletelecommunication social network [4], whereas Gopal andMeher used standard regression to estimate the timing of churnand tenure for the same domain [8].

In this work we try to address the problem of customervalue within the context of dynamic telecommunication so-cial network. A traditional value model based on individualinteractions measurement is appended by additional dynamicnetwork value component measured as a fraction of the valueof network neighbourhood interactions implicitly stimulatedby the presence of a customer-node in question. We alsoexploit the structural changes within the network like customeracquisition and churn to estimate this additional networkcomponent of the complete customer value and discuss itsdynamics following these events.

The remainder of this paper is organised as follows. The fol-lowing section introduces telecommunication social networkand discuss some aspects of its internal structure, relationshipsand the significance of node addition and removal. The nextsection focusses on individual and group value measureswithin TSN followed with a discussion of the neighbourhoodvalue dynamics. Section V presents the proposed process ofsocial value analysis supported by experimental results carriedout over real social network data presented in the next section.Finally conclusions and recommendations for future work areformulated in the closing section

II. TELECOMMUNICATION SOCIAL NETWORK (TSN)

Let us consider a group of customers interacting with eachother by means of a variety of telecommunication technologieslike voice calls (including residential, mobile and VOIP),SMS, email etc, provided by a telecom service provider. Eachsuch customer builds relationships with other customer-nodesand thereby establishes his local social network of customerswith whom he interacted at least once during his lifetime.

Formally a telecommunication social network can be de-fined as the tuple TSN = (M, R) that consists of thefinite set of members (customers, nodes) M and the set ofrelationships R that connect pairs of distinct members: R =rij = (xi, xj) : xi, xj ∈ M, i 6= j. Note that relationships inTSN are directed, i.e. rij 6= rji.

A. Subnetwork structure

In addition to the multiple communication platforms in-dividual nodes in the network may belong to significantlydifferent types of customers, like for example business and

residential, that may drive the interactions for completelydifferent reasons and purposes. On top of that individualmembers may join into organised groups and have theirown separate social identity that could interact with otherindividuals or groups of different types. It is therefore verydifficult or even impossible to analyse a complete socialnetwork with a complex nested substructure across multipledimensions. The reality of the social network implies that forthe complexity or accessibility reasons we can only analysecertain subnetwork of the complete TSN.

In the subsequent analysis we will consider a simplifiedmodel of the TSN where each customer-node is a singleentity that can neither be divided nor form groups and isidentified by its contact number. Moreover we will consideronly a single dimension or platform of interaction relatedto voice communication over landline telephone network.The reason for that is not only simplicity but also variousaccessibility and confidentiality issues when attempting toanalyse social network of the same customers but based onthe data coming from different service providers. As to thedifferent types of customers we will consider residential andbusiness subnetworks ignoring their mutual impact.

B. Strength of relationships

Relationships within telecommunication social network aretypically being established through multiple interactions be-tween a pair of nodes although each time different node mayinitialise the interaction. There are many ways to measure thestrength of such relationship but in principle it should involvetwo elements: the frequency and durations of interactions.Given interactions between a pair of nodes xi and xj wherei, j ∈ {1, ..,M} and i 6= j the interaction frequency measureRF

ij can be defined in a normalised form as:

RFij =

Fij∑k 6=i Fik

=F (xi → xj)∑

k 6=i F (xi → xk)(1)

where Fij is a frequency function counting the number ofinteractions between nodes xi and xj initialised by node xi

within a fixed time interval. The measure RFij reflects the

commitment of the node xj within node xi’s interactions.Similarly the interaction duration measure Rij

T is defined by:

RTij =

Tij∑k 6=i Tik

=T (xi → xj)∑

k 6=i T (xi → xk)(2)

where Tij is the total duration of interactions between nodesxi and xj initialised by node xi within a fixed time interval.

C. Node addition and removal

In the fixed social network interactions as well as alldynamic characteristics of the network and its nodes tendto converge to the stable values determined by the networkequilibrium. Any structural change of the network damagesthis equilibrium and causes the network to evolve towardsfinding the new stable state. This equilibrium is distorted ifa structural change occurs. From the business point of viewit is important to stimulate and prolong the changes that

generate new or boost existing interactions while trying toprevent from or limit the damages of changes that terminate ordeteriorate interactions. While theoretically one can considerall sorts of exotic network changes, in principle there aretwo basic changes of node addition and removal which aredirectly corresponding to the well known business processesof customer acquisition and customer churn.

Today’s highly competitive global telecommunication mar-ket reports steady decline in a growth rate due to maturity. Atthe same time there are huge pressures on telecom companiesto make healthy profits and increase their market shares. Oneof the major issues in such environment is on one handthe ability to attract new customers and on the other handprevent from churn known as a process of losing a customerto a competitor. Recent estimates suggest that churn ratesin the telecom industry could be anything between 25% to50% [7] and given the acquisition rates are similar thereis a massive turnover of customers through the company’sTSN. Moreover on average it costs around $400 to acquirea genuinely new customer which takes years to recoup [7].These huge acquisition costs are estimated to be between 5 to8 times higher than it is to retain the existing customer [21].Statistics also show that most of churns occur early in thecustomer lifetime whereas loyal long-lived customers generatethe most value. These loyal customers also tend to be betterconnected with other customers in the network and losingthem may lead to further negative effects of churn propagationor drop in interaction activity of other connected customers.Given these facts it makes therefore every economic senseto have a highly selective strategy to predict and preventfrom customer churn [18] along with the strategy to attractnew customers particularly showing signs of strong socialconnectivity.

This work, however, is not concerned with churn predictionnor scoring for acquiring valuable customers. What it is tryingto deliver is the preliminary intelligence about how the inter-action value streams generated by particular customers changeas a result of these structural changes in the social network.Given that customer churn is a reverse process of customeracquisition and that unlike before customer acquisition, theinteraction data are available for analysis before the churnthe focus will be directed towards modelling the impact ofcustomer churn only. The main concern of this analysis is toexploit network changes like customer churn to try to evaluatethe true, network-aware customer value measured not only indirect customer interactions but also in the stimulated value ofdirectly and indirectly connected customers that becomes onlyapparent when we compare them with the value exerted fromthe same neighbour-customers before the customer joined orafter he churned. Accordingly we try to devise a generic modelof social value of a customer and propose the methodologyto evaluate it along with dynamic characteristics.

III. THE CONCEPT OF VALUE IN TSNSince the acquisition each customer generates a dynamic

value stream consisting of a value of his outbound calls aswell as value added network component stemming from the

fact that his presence drives inbound calls from his neighbours.As a consequence of the latter one may also argue thatoutbound interactions themselves are to a degree driven bythe presence of other nodes and hence the total value of anode should involve a combination of interactions upon thegiven node balanced between his ability to initialise and attractinteractions with other nodes.

A. Individual node’s value measures

Social network analysis (SNA) uses a number of measuresor metrics to characterise each node’s profile and importancewith respect to its interaction with the network. Amongthose there are few common structure measures reflectingthe centrality rate of the node: centrality degree (C) andsocial position (S). Centrality degree, being just the numberof links to the other nodes [3], is the simplest and the mostintuitive measure. For the undirected graphs, centrality simplymeasures the number of edges connected to the single node,whereas for the directed graph, it can be divided into indegree(C) - for edges directed to the given node, and outdegree (C)- for edges, directed from the given node [20].

In our telecommunication social network each node caninitialise outbound and take inbound interactions. Hence fora given relationship strength function R ∈ {RF , RT } bothcentrality in- and outdegrees can be simply defined by:

C(R, xi) =∑

j 6=i

Rij C(R, xi) =∑

j 6=i

Rji (3)

For the frequency based relationship strength RF the valueof C(RF , xi) equals to the number of all inbound andfor C(RF , xi) all outbound interactions of the member xi

whereas C(RT , xi) and C(RT , xi) simply calculate the totaltime the node xi spends on all inbound and outbound in-teractions respectively. Similarly, one can define the centralitydegree measure for any other relationship strength in inbound,outbound or combined versions.

The above measures are actually well aligned with thebusiness value that the service providers charge the users forthe interactions. In fact telecommunication bills are a directfunction of the frequency C(RF , xi) and duration C(RT , xi)of interactions initialised by the node. The value of all inboundinteractions to the given node xi is at the moment not beingattributed and hence not being charged to the node xi but israther related to the other nodes that initialise the interaction.

Social value of a network node can also be expressed inother way that is directly linked to both the importance ofconnected neighbour nodes and the strength of their rela-tionships. In other words, social value of the node may bedescribed by the value of its neighbours and by the fact howimportant this particular member is for its neighbours [10].Social position S(xi) is a measure proposed and developed in[10], [11]. It can be used to calculate the importance of everysingle member of the network in an iterative way:

S(n+1)i = S(n+1)(xi) = (1− ε) + ε

∑

j 6=i

S(n)j Qji (4)

where S(k)i is a social position of node xi after kth iteration,

ε ∈ (0, 1) is a fixed coefficient, Qij is the commitmentfunction expressing the strength of the relation from xi toxj . The constant ε represents the openness of node’s socialposition on external interactions, such that high ε means thatthe social position is highly influenced by other nodes whilelow ε means the social position is static with weak influenceof other nodes [11], [12]. The convergence of S

(n)i as defined

in (4) was proven regardless of initial values S(0)i in [13].

The importance of the node xi described by social positionSi (Si = limn→∞ S

(n)i ) depends on the social positions of

the neighbourhood and the strength of relationships directedto xi from its neighbours. More precisely, xi’s social positionis inherited from its neighbours’ activity directed to xi andthe level of inheritance strictly depends on the strength ofthis activity. Commitment function Qij expresses the activitystrength of node xi absorbed by node xj . Subject to additionalrequirements this function can be assigned to the relationshipstrength measures as defined in Section II-B i.e. Qji = RF

ji

or Qji = RTji. The only situation that requires adjustment

is when the node xi has no outbound connections to anyother node in TSN, but there are other nodes with inboundconnections to xi. In this case the commitment function Qij

should be equally distributed among all incoming neighboursxj [11]. Note that for all but isolated nodes:

∀xi,i=1,..,M

∑

yj ,j=1,..,M

Qij = 1 (5)

Many other measures known from SNA and describingsingle node’s interaction with the network can be used toreflect social value of the node in the direct and wider networkcontext. Three of such measures Ci, Ci and Si were utilisedin this paper. In the experimental section we focus more onvariations of the centrality degree measures due to their directlink with a business value of customer interactions.

B. Group and neighbourhood valueThe previous section was dedicated to measuring individual

node’s value in a wider or local network context. Here wetake a more global look at the social value of a group ofnodes and specifically focus on the special groups that sharethe same neighbour node. Before we do that let us formaliseindividual value of a node xi built upon the relationships withother nodes from the set M as V M (xi) or shortly V M

i (Forexample V M

i = Si, C(R, xi), C(R, xi)).Now given a group of nodes G ⊂ M , the social value of

group G is some form of the sum of individual value measureV M

i of all members that belong to this group xi ∈ G. Incase of measures built on direction-sensitive interactions likeout- or indegree centrality (C, C) the groups social valuebecomes a direct sum of all individual social values of thegroup member:

V MG =

∑

xi∈G

V Mi V M

G =∑

xi∈G

V Mi (6)

For social value measures insensitive to the direction ofrelationship like the full centrality degree C = C + C the

problem with the summing is that the same interaction fromcertain node xi to xj would be counted twice: once as anoutbound interaction from xi to xj contributing to V M

i andthe second time as an inbound interaction to xj from xi

contributing to V Mj . In this case single pairwise interactions

among nodes that are both in group G need to be excludedfrom the sum of individual member’s social value measureswhich can be formally defined as:

V MG = V M

G + V MG − V G

G − V GG (7)

Once we defined both variations of the group social value letus now consider a group of nodes that are directly connectedto the given node xi and call such a group the 1st orderneighbourhood of the node xi denoted by N1(xi) = N1

i anddepicted in Fig. 1. The same way one can define the higherorder neighbourhoods Nk

i which would include all nodes thatcan be connected by at most k edges to the given node xi. Itis important to note that the neighbourhoods of any order donot include the node xi.

If we then assume that the impact of individual nodes onthe 2nd and higher order neighbourhood values is negligiblethen we can finally define a simplified but complete socialvalue model for individual customer-node xi as:

Vi = α0 + α1vMi + α2v

Mi + α3v

MN + α4v

MN (8)

where α0 stands for fixed subscription value, α1 and α2 arethe fractions of outbound and inbound interactions attributedto node xi and α3 and α4 stand for the fractions of outboundand inbound neighbourhood values that are driven by node xi.

Depending on the nature of interactions the values αparameters may take different perhaps very surprising values.While the first three components can be fairly simply eval-uated from the interaction data the contributions to isolatedneighbourhood values are virtually impossible to evaluatefrom the normal network interactions data. These additionalneighbourhood contributions can only be isolated after thestructural change of the network when the node is added(customer acquisition) or removed (customer churn) from thenetwork as described in Section II-C. A customer that churnssuddenly disappears from the network which immediatelycancels the first three components of his overall social valueVi. His neighbourhood however continues to interact andit is expected that the impact of churned customer on hisneighbourhood value will gradually fade to 0. By measuringthe neighbourhood value before and after the churn we canpotentially estimate the magnitude of this impact. The sameapplies to the new customer that suddenly appears in thenetwork and stimulates a change in his neighbourhood value.In the subsequent analysis we will look closer into theimpact of node addition and removal on the dynamics of theneighbourhood value.

IV. DYNAMICS OF NEIGHBOURHOOD VALUE

Let us now consider dynamic aspects of customer valueas defined in Eq. (8). From the dynamic perspective there

Fig. 1. A customer with his 1-order neighbourhood

are three distinct periods that feature significantly differentpatterns of value dynamics: customer acquisition, customermaturity and customer churn. Customer acquisition and aperiod directly following it can be characterised by growingindividual inbound and outbound value streams and sharplygrowing neighbourhood along with rather slowly growingimpact of newly established customer on their neighbourhoodvalues. The second significant period of maturity starts whenall individual customer dynamics saturate to the network av-erage trends i.e. when expansion of customer neighbourhoodand growth of interaction value can be comparable to thenetwork-wide average rates. This period called service usagecontinues for the rest of customer lifetime and is typicallycharacterised by the small variability of value streams, andsaturated dynamic variables at near-zero rates of change. Thisperiod is rather uninteresting from the dynamic point of viewand customer value can be modelled by a fixed annual rates ofvalue streams. Customer churn shakes the dynamics of socialvalue again by reducing the individual node value streams tozero and stimulating change in the neighbourhood value.

Lets assume that a customer xi in his maturity periodgenerates a constant value stream of Vi(t) = α(t)vi(t) asdefined in (8). The objective is now to solve this socialvalue equation within the introduced periods of acquisition,maturity and churn. For simplicity we can assume that α0 isa known fixed subscription amount equal to 0. The α1 andα2 parameters depend on the pricing structure of a serviceprovider, yet given most companies charge only for outboundinteraction the value of α1 is expected to be close to 1whereas a value of α2 close to 0 and they both shouldnot change much in time. Situation is quite different forneighbourhood value contributions as clearly α3 and α4 are0 or near 0 during acquisition then are expected to climbup to the maximum levels during the maturity and graduallydecay back to 0 following customer churn as depicted in Fig.2. The presented graph is only a reflection of an educatedguess supported by some observations and there is plentyof unknowns associated with it. Could the neighbourhoodvalue contibutions α3 and/or α4 take negative values, or inother words could the presence of a customer be detrimentalto the neighbourhood’s interactions? Is the churn process adirect reversal of acquisition in terms of neighbourhood valuedynamics? How to distinguish between a genuine changes

in value trend and the value changes caused by a customerchurn or acquisition? We will try to address some of thesechallenging questions in the experimental section.

Acquisition Maturity Churn

t

α3, α4

αmax

Fig. 2. Expected evolution of the influence of individual customer on hisneighbourhood value along 3 stages of customer lifetime

V. THE PROCESS OF CUSTOMER VALUE ANALYSIS

As mentioned before the analysis of customer value in-volves at least two distinct elements. First is a direct mea-surement of inbound and outbound interactions of a particularnode and second is estimation of a wider impact on neighbour-hood interaction that exclude interactions to the given node.The value of inbound and outbound interactions is immedi-ately available from the interaction data while the value ofthe impact on neighbourhood interactions is only implicit. Infact it is unclear to which degree the interactions made bycustomer neighbours are driven by the customer presence, orin other words it is not clear if under customer absence hisneighbours would interact less, redirect interactions to othercustomers or perhaps even get stimulated to grow their ownneighbourhoods and as a result interact more.

Structural changes within social network like customerchurn or acquisition give a realistic opportunity to isolate andestimate their impact on neighbourhood value stream and ex-plore its dynamics over time. By comparing the social value ofcustomer neighbourhood before and after the churn or beforeand after acquisition one can truly estimate his social valueby measuring the change in neighbourhood value triggered bythe churn or acquisition events. Such experimental scenario isillustrated in Fig. 3 for customer churn.

As mentioned in previous section the major differencein the two elements of the customer value model lies inthe value dynamics following customer acquisition or churn.While the value of direct interactions with a given node startsimmediately after a customer joins the network and terminatescompletely after he churns, the value of neighbourhoods growsslowly after acquisition and decays gradually after churn untilthe new equilibrium is achieved.

Another issue related to such analysis is that it mightbe very difficult to extract a direct impact of particularcustomer’s churn on his neighbourhood value as there maybe many other concurrent drivers of value dynamics likeother customers’ churn, acquisition, customer geographicalmoves and other significant network events. From the globalperspective, all these additional processes impacting on socialvalue dynamics happen continuously anyway and are part ofthe ongoing network value fluctuations; hence their impact

should be statistically similar before and after the churn oracquisition event. For simplicity we can therefore clean thenetwork throughout the analysis period by removing nodesthat were added or removed during the analysis period. Incase of a significant imbalance between newly acquired andchurn customers we may suspect an acquisition or churnpropagation affect which then has to be taken into account asan additional value impact. Typically one can expect increasedacquisition rate following an acquisition of a socially strongcustomer or increased churn rate after a key customer-nodeleft the network. Note that the process of analysing the impactof churn on social value dynamics is directly reverse tothe process of analysing the impact of customer acquisitionalthough the actual characteristics of the value dynamics areundoubtedly different. A diagram illustrating such process isshown in Fig. 4.

Fig. 3. The neighbourhood of churning customer

Fig. 4. Process of analysis of social neighbourhood for churning and acquiredcustomers

The first part of this process is the identification of re-lationships in social network which allows establishing theneighbourhood of any particular customer. The next step isfinding customers for which we want to analyse the socialvalue dynamics, and those would be the customers who churnor are acquired preferable during the middle part of the periodthe analysis is conducted for. Then the key part involvesestablishing the neighbourhoods of such customers (prior- forchurn and post- for acquisition) and measure the time seriesof their total business values from before the event until thepoint after the event for which the neighbourhood value timeseries attains again stationarity. Note that as illustrated inFig. 1 and 3, the value of churned or acquired customer isexcluded from the neighbourhood value both before and afterthe churn/acquisition event and thus social value of a customeris a measure of customers ability to drive business value fromthe rest of the social network.

VI. EXPERIMENTS

The experiments were carried out on the real telecommuni-cation social network TSN over voice interactions among busi-ness and residential customers of a telecom service provider.In order to monitor both inbound and outbound interactionsthe network was scaled down to interactions involving hun-dreds of thousands of business and residential customers froma particular geographical region. Even for such a reduced setthe interactions with the external networks involved severalmillions of nodes and hundreds of millions of calls over 1moth. We have split the analysis into 3 parallel trails involvingall internal and external interactions, then only internal interac-tions among the members of the selected regional subnetworkand finally internal interactions among residential customersonly. Fig. 5 illustrates relative differences between neighbour-hood sizes of the analysed networks for both inbound andoutbound interactions and outbound only.

Fig. 5. Average neighbourhood size of the churning node compared to thenetwork-wide average neighbourhood size. customers

Since the available data covered the period of only 1 monthwe have further split it into three 10-day slots. The second slotwas used to identify newly acquired and churning customers,the first one to extract their neighbourhoods and calculateneighbourhood values before the change event and the lastslot to evaluate neighbourhood values after the event. Toavoid contamination the nodes acquired or churned in thefirst and last slot were removed from the analysis and theneighbourhood values were detrended. Due to lack of spaceand the symmetry the presented results are shown only forcustomer churn.

Social position and centrality degrees introduced in SectionIII were used to evaluate individual node values and theirneighbourhood values in the first and third slots for bothnumber and duration of calls. Fig 6 shows the average relativevalue of the churning node in the first pre-churn period fordifferent subnets and relationship measures. Clearly residentialnodes are the least interacting among themselves prior tochurn. Interesting and perhaps not surprising the relativestrength of inbound interactions compared to outbound. Thechurning node seems to be engaged in much greater inter-action with the external network than with internal networkserved by the same service provider and in terms of durationof interactions this disproportion grows up to 15 times forresidential customers.

Fig. 6. Average value of the churning node in the pre-churn time slot relatedto the network-wide average value. customers

More interesting results are presented in Fig. 7 whichshows the relative average change of the neighbourhood valueof the churning node that occurred after the node’s churncompared to the pre-churn period. Internal communicationamong residential neighbours reported around 7% drop inthe number of calls yet their oubound calls duration grewby on average 8%. The neighbourhoods seemed to receiveabout 11% more calls from the whole network after the churnyet returned about 15% less calls to it. Business neighboursseemed to be rather unaffected by the customers churn actuallyincreasing their inbound and outbound traffic measured bothin the numbers and duration of calls.

Fig. 7. The change in the churning neighbourhood value recorded betweenpre-churn and post-churn time slots related to the churning neighbourhoodvalue in the pre-churn period

Fig. 8 presents average social positions of the churningand regular nodes along with the average social positionswithin their neighbourhoods. Due to the requirement of thecompleteness of network interaction only figures for internalnetwork and separately for internal residential customers’network are presented. Interestingly the social position ofthe churning residential node turned out to be about 40%lower than the social position of a regular node, while forbusiness customers it drops even further prior to churn. Theneighbourhoods of the churning and regular nodes for bothbusiness and residential customer networks seem to havesimilar social position levels prior to customer churn.

Fig. 9 shows the change in social position of the churningnode’s neighbourhood after the churn event compared to thepre-churn period. The average social position of churner’sneighbourhood within residential network fell by 23% afterthe churn event compared to regular nodes, while withinthe whole internal network the neighbourhood social position

Fig. 8. Comparison of social position measures for churning and regularnode along with their typical neighbours.

drops by 11%, which gives further evidence of the drop in theactivity of the churning node’s neighbourhood after the churn.

Fig. 9. Average change in social position among churning node’s neighbour-hood between pre-churn and post-churn period related to the average socialposition of a regular node.

VII. CONCLUSIONS

People influence one another and this principle can beused to analyse and extend the concept of customer value intelecommunication social networks. Current value models aretypically linked to the measurement of outbound interactionof each node. They ignore the fact that inbound interactionis partially driven by the presence and relationship with ofinteraction party and they completely ignore the implicit valueof neighbourhood interactions stimulated by the node withoutactually taking part in these interactions. An updated customervalue model is here proposed which appends the value ofdirect customer interactions with the network value addedcomponent exerted from the neighbourhood interactions. Amethodology for estimating the missing network value hasbeen proposed and it is based on measuring the change inneighbourhood values after the node addition or removalfrom the network corresponding to customer acquisition andchurn. The preliminary experiments carried out on a real TSNinteracting over 1 month revealed that churning customersinfluence their neighbourhoods. Neighbourhood value mea-sures expressed by both social position and centrality degreesdropped significantly after the churn particularly within res-idential subnetwork. Also individual value measures of thechurning node indicated a significantly reduced social positionand also decaying particularly outbound interaction intensityprior to the churn event.

However, additional studies on larger data sets stretchingalong longer periods are necessary to build a dynamic profileof the social value change until the new equilibrium and toevaluate the rest of parameters in the introduced social valuemodel. Once these observations are validated and formallydescribed the next step could be to try to predict the magni-tude of the change in network’s activity based on the localproperties of the node that triggers the change.

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