tailieunhanh - Managing and Mining Graph Data part 33

Managing and Mining Graph Data part 33 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. . | 3006 MANAGING AND MINING GRAPH DATA relative density techniques look for a user-defined number k densest regions. The alert reader may have noiiced that selative density discovery is closely rsilssksd to clustering and in fact shares many features with it. Smce this book conSains another chapter dedicated to graph clustering we wtll focus our attention on abnolute density measures. However we will have usore so oay aboui the relationship betwf en clusiering and density at the end of Silts tection. 22 Graph Terminology Let G V E be a graph with V vertices and E edges. If the edges are weighted then w u ls tie weieht of edge u. We treai unweighted graphs as the spectal case wheoe all weights are equal to 1. Let S and T be subsets of V. For an undirected graph E S ls tie sel of induoed edges on S E S u v e E u v e S . Then. Hs ls tie induced subgraph S E S . SimiIfriy E S T designales the set of edges from S So T. Hs r ls tie induced subgraph S T E S T . NoSe that S add T ase not necessarily disjoint from each other. If S A T 0 Hs. i ls 21 bipartite graph. If S add T ase dot dtsjomS possibly S T V this doiatlod can be used to represent a directed graph. A dsnse component ltd a maximal induced subgraph which also satisfies some denrity constrains. A eomponent Hs ls maximal SI7 no oiher subgraph ef G which is ss superset of Hs would saSisfy lhe tlssnril y constraints. Table 10. d defines some basit r je ti toncepts and measures that we will use to define densSty metrics. Table . Graph Terminology Symbol Description G V E geaph wsSh vertex set V add sdgc sct E Hs subgraph with vertex set S add sdgc set E S Hs t subgraph with vertex set S U T add edge set E S T w u weight of edge u Ng u neighbor set of vertex u ln G v u v e E Ns u only those neighbors of vert ex u Sieal are in S v u v e S 6 g u wesghtedi degree of u ln G vENg u w v 6 s u wesghtedi degree of u ln S EvGNs u w v dG u v shortest weighted path from u So v traversing any edges in G ds u v l iS r sl weighted