tailieunhanh - Managing and Mining Graph Data part 11

Managing and Mining Graph Data part 11 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 811 Detailed description. The tiiasl. pattern we observe is the Weight Power Law WPL . Let E t W t be die number of edges and total weight of a graph. at time t. They they follow a power law W t E t w where w is the weight exponent. The weight exponent w rangec from IJdl to for tha acai graphs studied in 959 i which included hlog graphe network graphs and political canr paitrii donation graphs suggesting that pattern is universal to real social itre graphs. In other wotdc. the more cdgcc thaf are added to the graph auperlinearly more wetght is added to ihe graph. This ic counterintuitive as one would expect rtie average wcighi-pettedge to remain constant or to increase linearly. We find fine samr pattern fer each node. If a node i hat out-degree outi its ou -wcight outwi ext-thes a loitiiication s fleet - tWirare will be a power-law r er lt i tslt t between its degree and weight. We call this the Snapshot Power Law SPL and it applies to lui lt in- and out- degrees. Specificeily at nt given tpounr in timCi we ptot the scatterplot of the in out svatigtit. versus the m ont dcnrcSt Par ail the nodea in the graph at a given time snepshot Here- tvery point refresents a node and the x aad y cootdmates are its degree and total weight rcrpcclivclyl lit achieve a good fit we bucketize the x axis with togarit italic. binning 64 anth for each bin we compute the median y. Examples in the real world. We httd these patternt apply in several real grapliSr Including neiwork taaniCi biogs. end even political campaign donations. A plot of WPL and SPL may be found in Figure . Several other weighted power 1-iwIi -itch tts the relationship between the eigenvalues of the graph amd the weiahts of the edges may be found in 5 Other metrics of measurement. We have discusred a number of patterns found in graphs masy more can be found in ihe literature. While most of the ios ut regarding node degreer has fatten on the m-degree