Managing and Mining Graph Data part 31 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. . | A Survey of Clustering Algorithms for Graph Data 2885 Here NumConstrainedPaths e i j refers to the number of global shortest paths between i and j which pass through e and NumShortPaths i j refers to the number of shortest paths between i and j. Note that the value of NumConstrainedPaths e i j ma a be t if none of the shortest paths between i and j contain e. The algorithm rankc the edges by order of their beiweannnse ind and sicldcs flic edge with the highest score. The betweenness coefficients ate recompuaed and die ptoees- is repeated. The set of connected comeoncntt after deletion form the natural clusters. A variety of termination-criteria fegt fixing number rtf connected components can lie used tn conjunction with the algorithm. A key isauc is the ciricicnt olctcrmi nation rat edge-betweenness centrality. The number of paths heiween any pair of nodes can be exponentially large and ii would teem that the computation of the betweenness measure would be a key hottienccki tt has been shown tn 36 that the network structure index ctn also he used in order So csiimatc cdsciectwccnncss centrality effectively by paiawise node sampling. The Spectral Clustering Method liig s techniques ate often used in multi-dimensional data in order to deSennine rhe underlying ttr rrelation structure in the data. It is natural to c ucation as to wheiher euch techniques can alio be used for the more general casa of graph dtrtt . It iurnt out that thti is indeed possible with the use of a mettiod called spectral clustering. In spectral clusteritig meihodi we innice ute of the node-node adjacency matrix of flee graph. It at tt graph con tai ning n nodei let. us aesurnc that we have a n x n adjacency mainXi in which the entry i j coirespond its the weight of the edge ectwecn the nodes i and j. Thia essen tiaiiy coarasponds to the similarity beiween nodes i and j. This enlry ii denoted by Wij and the corresponding matiix is denoted by W. This mairix is .
