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Managing and Mining Graph Data part 7

Managing and Mining Graph Data part 7 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 Data Management and Mining A Su rvey of Algorithms and Applications 4 1 Densification Most real networks such as the web and social networks continue to becsme mote dense oves time 112S . This essentially means that these nclworki continue to add more 1 inks ove s linec than are deleted . This is a natural consequence of l.hc face l.lteu. much cef ihe web and social media is a oetatsveSy recent phenomenon for which new applications continue to be found ovcs timCi In fact meet real giii xl s am known to exhibit a rensification power law which charectcrtzcs the variation tn densification behavior over time. This taw rtates that. She numhes of nodes tn t.lso ndwork increases superlinearly with l.lsct numhes of nodes over time qvhsrcas she nomther of edges increases super-hnearty over lime. lie other words if n t aid e t ocpecscnt tint qumber of cdecs and nodes in i.hc network at time t then tvs have e t rc n t a 2.1 The value of the ex pone nt a tic s tictwccn 1 and 2. Shrinking Diameters The small world phcntimcnoe of graphs is well known. Los example is was shown in S 30 that tSiis average path length between two TsTSSee messenger usere it 6.6 TSris can tie considered a verification of the internet veesion oS that widely known ruSc of six degrees of separation in generic social networks It was 1 urthct shown en 129 that the diameters cf mastrve nclworks s lCi Ii as the web contiaue to shrink over time. This may eccm tioitj rttlisld because one would oxqect that the diameter of the network should croov as move nodes are added However it is important to remember that edgss aec added more rapidly io the network than nodes as suggested by t at ian 2. S abovel. As mote sdgas asc added to the graph it becomes possible to traverse evom one node to stntchcs with the use of a fewer number of edges. While the above ohsesvations ptosidc an understanding of some key aspects ef uric ctlic- aspects d lonf-ferm evolution of massive graphs they do not provide an ihea of teow