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Managing and Mining Graph Data part 13

Managing and Mining Graph Data part 13 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 1001 l.hc array uni iortnly at random and the node ntorcd in that cell can be considered to have been chose n under prcicrcnl.ial attachment. This re quires 0 1 time for each iteration and O N rime to generate tire entire graph however it needt extra sfttuec ao store the edge list. This technique can he easily extended fo the case when the preferential at-tachmcnt nqualion involves a constant fl ruch as P v a k v fl iter the GI iP msdeli It the constant fl is a negative integer say. fl 1 as tn the AB inodclji vee can handle this easily by adding fl cniriss for every existing node into ihe array. Hocvcvcri Il tiris ia not the casCi the method needs to be modified rightlyi with some probability a the node is chorcn according to the simple pactcrcntial attachment equation like in the BA model . With probability 1 a it is chosen unhoomls at aaxdom trom the net of existing nodes. For each iteration. thy value of a can hit choset co ihaS the final effect is that of choosing nodes recording ice tho modified preferential attachment equation. Summary of Preferential Attachment Models. All yrefirential attachment models test die idea than tire rich fet richer high-degree nodes attract more cdecti or OtighfPageRank nodes attract more edges and so on. This simple paoceso atong with ahe idea if network growth over time automatically leads to tie power-law degree dtstrlhntionr seen in many real-world graphs. Ar such there models mate tt veiy hnaortas t contribution to the field of graph miningi Stitt most of these mohels appear to tuffer from some limitations lor oxamplc. they do not accm to generate any community structure in the goapha they neneaaiet Also apart trona the wook of Pennock et al. 75 little cltort has gone mto itnsl ng reasons tor oicviat ons from power-law behaviors lor notne grapha. It appeart thai we need Co considcr additional processes to undenstond and mode such characteristics. 3.3 Optimization-based generators Mosl. of tht