Hussain, Dil Muhammad Akbar

Typisk analytisk foranstaltninger i grafteori gerne grad centralitet, betweenness og nærhed centralities er meget almindelige og har lang tradition for deres vellykkede brug. Men modellering af skjult, terrorister eller kriminelle netværk gennem sociale grafer ikke rigtig give den hierarkiske struktur af sådanne netværk, fordi disse net er sammensat af ledere og tilhængere. I denne korte papir, vi undersøge lille verden net ved at beregne først Bayes posteriori sandsynlighed som derefter bruges til at beregne entropi af nettet. Den beregnede sandsynlighed og entropi distribution yderligere udnyttet til at forudsige den kommandostruktur af nettet.Nøgleord: Social Networks Analyse, Bayes Teorem, entropi, hierarkisk struktur

    Aalborg UniversitetPredicting Hierarchical Structure in Small World Social NetworksHussain, Dil muhammed AkbarPublished in:International Multi Conference of Engineering and Computer Scientists on Data Mining and Applications.Publication date:2009Document VersionPublisher's PDF, also known as Version of recordLink to publication from Aalborg UniversityCitation for published version (APA):Hussain, D. M. A. (2009). Predicting Hierarchical Structure in Small World Social Networks. In S. I. Ao, O.Castillo, C. Douglas, D. D. Feng, & J-A. Lee (Eds.), International Multi Conference of Engineering and ComputerScientists on Data Mining and Applications. (pp. 690). IAENG, International Association of Engineers.General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            ? Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            ? You may not further distribute the material or use it for any profit-making activity or commercial gain            ? You may freely distribute the URL identifying the publication in the public portal ?Take down policyIf you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access tothe work immediately and investigate your claim.Downloaded from vbn.aau.dk on: May 01, 2017Predicting Hierarchical Structure in Small WorldSocial NetworksD. M. Akbar Hussain, Member IAENG ∗Abstract—Typical analytical measures in graph the-ory like degree centrality, betweenness and closenesscentralities are very common and have long historyof their successful use. However, modeling of covert,terrorist or criminal networks through social graphsdo not really provide the hierarchical structure ofsuch networks because these networks are composedof leaders and followers. In this short paper we in-vestigate small world networks by computing first theBayes posteriori probability which is then used to cal-culate the entropy of the network. The computedprobability and entropy distribution further utilizedin predicting the command structure of the network.Keywords: Social Networks Analysis, Bayes Theorem,Entropy, Hierarchical Structure1 IntroductionDrug dealers, terrorist and covert networks are typically,represented through social graphs. Since 9-11 terrorist at-tacks a great deal of research is taking place ﬁrstly to un-derstand the dynamics of these terrorist networks (anal-ysis) and secondly, developing methods to either destabi-lize or disintegrate these networks. Insight visualizationof any social network typically focuses on the character-istics of the network structure. Social Network Analy-sis is a mathematical method for ’connecting the dots’,SNA allows us to map and measure complex relation-ships/connections between human groups, animals, com-puters or other information/knowledge processing enti-ties and organizations [1]. These relationships can revealunknown information about these dots and the networkitself. Jacob Moreno invented ”Sociometry” which is thebasis of SNA, utilized ”sociograms” to discover leadersand map indirect connections in 1934 [2].The two basic elements of SNA are connections andnodes. Connections are ties between individuals orgroups and nodes are the individuals or groups involvedin the network. There are diﬀerent dynamics of so-cial networking for example Kin-based (father, husband),Role-based (oﬃce), Interactions (chatting) and Aﬃlia-tions (clubs etc). Analysts have applied SNA in manyﬁelds to reveal hidden informal links between nodes [3].∗Date of the manuscript submission: 15 January, 2009 AalborgUniversity Esbjerg, Niels Bohrs Vej 8, 6700 Esbjerg Denmark Tel:+45 99 40 77 Email: akbar@aaue.dkFor example in businesses SNA have been used to an-alyze email patterns to determine which employees areoverloaded, similarly, law enforcement and national se-curity organizations are using various method of SNA toidentify important nodes and connections of terrorist or-ganizations [4].2 Method & ResultsGiven any network where the nodes/agents are individ-uals, groups, organizations etc., a number of networkmeasures such as centrality or cut-points are usedto locate critical/important nodes/agents. Typically,social network analysis try to identify the followingcharacteristics:• Important individual, event, place or group.• Dependency of individual nodes.• Leader-Follower identiﬁcation.• Bonding between nodes.• Vulnerabilities identiﬁcation.• Key players in the network.• Potential threat from the network.• Eﬃciency of overall networkNetworks visualization is semantically presented in theform of a graph in which the nodes represent entities andthe arcs represent relationship among nodes. Classiﬁca-tion of nodes and its distinctiveness is a challenging task,many traditional social network measures and the infor-mation processing network measures can help in reveal-ing importance and vulnerabilities of the nodes/agents inthe network [5, 6, 7, 8]. Application of existing tools onthese complex socio-technical networks/systems is verydemanding to winkle out the required information. Mostof the measures and tools work best when the data is com-plete; i.e., when the information is inclusive about the in-teraction among the nodes. However, the diﬃculty is thatcovert and terrorist networks are typically distributedacross many boundaries for example from cities or coun-tries and data about them is never complete-correct ata certain instant of time. Normally, a sampled snapshotdata is available some of the links may be intentionallyhidden. Also data is collected from multiple sources forexample news (print/tv), open source Internet data, se-curity agencies, etc., and at diﬀerent time instants. Inaddition inclusive and correct information may be pro-hibitive because of secrecy. Obviously, there could beother diﬃculties but even these provide little guidancefor what to expect when analyzing these complex socio-technical systems with the developed tools.Figure 1: Small World Random Network ExampleIn this paper we are analyzing small world social net-works systematically to compute Bayes posterior prob-ability and then entropy of the network is determinedby extracting each time a single node to reveal its posi-tion in the network structure. For the implementationof our proposed framework we have selected a 30 nodesmall world network as shown in ﬁgure 1, after the com-putation of Bayes probability and entropy the networkis re-structured based on the distribution of probabilityand entropy and it can be seen in ﬁgure 2 that it has ahierarchical structure approximately consistent with theimportance of nodes.3 ConclusionThe standard statistical solution for SNA has been ma-tured for long time now and used in the studying socialbehavior however, elucidating the pattern of connectionsin social structure is very challenging and the conven-tional social network analysis may not be enough to re-veal the structural pattern of nodes. The real world so-cial networks including small world networks have varyingcomplexity. The purpose of this paper is to investigateand locate the command structure in such networks. TheFigure 2: Hierarchical Structure of Nodesidea of using such model is based on the underlying as-sumption philosophy of Bayesian Posterior Probabilitythat uncertainty and degree of belief can be measured asprobability. The initial investigation shows that it is pos-sible to predict the command structure, however, theseare preliminary results and one may not draw a solidconclusion from these investigation. In our future workwe would like to extend this framework for more com-plexed and well known network structures available asopen source for the consistency of our proposed hypothe-ses.References[1] Valdis Krebs:. Connecting the dots, tracking twoidentiﬁed terrorists, 2002.[2] Jacob Levy Moreno:. Sociometry, experimentalmethod and the science of society, an approach to anew political orientation, 1951, published by beaconhouse.[3] Cory Kutcher:. Social network analysis - linking for-eign terrorist organizations, 2008.[4] Dil M. Akbar Hussain:. Destabilization of terroristnetworks through argument driven hypothesis model,journal of software, vol. 2, no. 6, pages 22 - 29, 2007.[5] Bavelas A:. A mathematical model for group struc-tures, human organization 7, pages 16 - 30, 1948.[6] Shaw M. E:. Group structure and the behaviour ofindividuals in small groups, journal of psychology, vol.38, pages 139 - 149, 1954.[7] Scott J:. Social networks analysis. 2nd edition, sagepublications, london, 2003.[8] Newman M. E. J:. A measure of betweenness central-ity based on random walks, cond-mat/0309045, 2003.

Predicting Hierarchical Structure in Small World Social Networks

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Predicting Hierarchical Structure in Small World Social Networks

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