TAILIEUCHUNG - Managing and Mining Graph Data part 12

Managing and Mining Graph Data part 12 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 Laws and Generators SH of neid-world graphs. Generalized random graph models extend the basic random graph model to allow arbitsary degree distributions. Given a degree distribution we can rai d coun 1 assign a degree to each node of the graph so as to match the given distribuOion. Edges are formed by randomly linking two nodes till no node has extra degrees left. We describe two differenh modeli below the PLRG moOel and the Exponential Cutoffs model. TOese diSfer only in the degree distortions used the rest of the graphgeneration process reiiKiins itie tame. The graphs thus created can in gen-eeal include eeif-graphe and multigraphs huvlng multiple edges between two nodes . The PLRG model Ono of the obvious moUifications to the Erdos-Renyi model in to chanue the degree dtstribution from Poinson to power-law. One such model is the Power-Law Random Geaph PLRG model of Aiello et al. 3 a similar model is the Power Law Out Degree PLOD model of Palmer and Sioffan 72 i. There are two parameters a agd 5. The number of nodes of giegree k in givtn by ea k. By consti ucbon. the degree distribution is specifically a power law Pk a k where 5 in tie power-law exponent. The authors show thet graphs generated by ihis model can have several possible properties based oniy on the value of 5. When 5 1 the gaanh is almost 1111 11. connected. For 1 5 2 a giant componeng exists and smaller componenSs are of size 0 1 . For 2 5 50 the giant component exinte and rhe smaller components are of size O log N . At 5 50 the smaller component are of size O log N log log N . For 5 50 sso gtant component exests. Thut foc the gtant component we have a phase transition at 5 50 there ts also a. change tn the size of the smaller components tt 5 2. The Exponential cutoffs model Another generalized random graph model is due to Newman et al. i9 . Here the probability that a node has k edges is gtven by pk Ck-7 e-k K where C y ttcd n aie conn3ants. This model hes a .

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