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Managing and Mining Graph Data part 51

Managing and Mining Graph Data part 51 is a comprehensive survey book in graph data analytics. It contains extensive surveys on important graph topics such as graph languages, indexing, clustering, data generation, pattern mining, classification, keyword search, pattern matching, and privacy. It also studies a number of domain-specific scenarios such as stream mining, web graphs, social networks, chemical and biological data. The chapters are written by leading researchers, and provide a broad perspective of the area. This is the first comprehensive survey book in the emerging topic of graph data processing. . | Graph Mining Applications to Social Network Analysis 489 ties can help achieve more cosl-cffecti vc viral marketing. That is only a smaht rcl. of users arc selected for marketing. Hopefully their adoption can influence oilier mcmlscis hi the aclwork so the benefit is maximized. Normally a social network is represented as a graph. How to mine the latti rns in lie grarh for l.he above tasks becomes a hot topic thanks to the availability of enoimous social network data. In this chapter we attempt to tt cti ecsl some recent treadr of liege social networks and discuss graph mining applications fot social network analysis. Cn particular we discuss graph mining applications Iti community detection r. basic lask in SNA to extract meaningful sociat rtrucSurer tea poiilronr. which also serves as basis for some other selated SNA taskt. ircpsesantalivc approaches for community detection are summrrized. inlciciting cmcrgtng psobtems aed challenges are also presented tot futirre exproration. For corvemencCi we define some notations used throughout this chapter. A network is normafiy represented as a graph G V E where V ctt ithic s r.lac ver-texer if qutvatcn d y nodes or actors and E deneter edges tier or connections . The connections are celirc cnlcd via adjacency matrix A where A 0 de-nohes ví Vj E E while Aij 0 denotes yi Vj E. The degree of node Vi is d-i. If the edges ha tween nnr es are dtrcctcdi the m-dcgrcc and out-degree are dene led as d- ami dj respccti vciys Nnmbct of vettexes and edges of a network are V n ami E m respeativery. The shortett pash between a pair of nodes vi and Vj is cabed geodesic and tire geodesic dirtancc between the two is denoted as d z j . Gs Vs Es represent a subgraph in G. The ndgNbors of a iirde V arc deeoted as N v . In a directed graph flie neighbors connecting to aed from one node v arc denoted as N- v and N v sespertively. Unless specified c-xplácii.ly. we assume a network i. unweighted and undirected. 2. Graph Patterns in Large-Scale .