tailieunhanh - Managing and Mining Graph Data part 34

Managing and Mining Graph Data part 34 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. . | 3116 MANAGING AND MINING GRAPH DATA Figure . Illustrative example of shingles in the upper part links to some oilier web pages in the lower part. We can describe each upper tvch pege vertex by the Itst of lower web pages to which it links. In order to pi it tome vertices into the same group we have to measure the simil aei ty of tin ve dices which de no tes tcr what extent they share common neighbor With liter help xf shinglingi fox each vertex in the upper part we can generate conslantisiee shingles to describe in oudinks its neighbors in the lower part . As shown in Figure the outlinks to the lower part are converted to shingles s1 s2 s3 s4. Since the nize of shieetcs can be significantly smeller ihax the original datar much computational cost can be saved in terms ef and space. In the paper Gibson et ah itepc employ the shingling algorithm for convert ne donse component into constant-ssze shingles. The algorithm is a twQiStxp ptoccdurc. Step 1 ie recursive shiegiingi where the goal is to exact some sutisstr of vertices where die vertices in each subset share many common neighbors. Figure iiXi-istraics the tccursivc shingling process for a geaph T V is the oudinks of vertices V . Aitci the iirti. thmgling process lor each vcrlcx v E Vi its ouhllnks T v ate converted into e constant size of 1x1 shingles v . Then we can transpose the mapping relation E0 to E1 so that each shingle in v cotreseondt to a set of vcetictst which share this shingle. In other words. a new bipartite graph is constructed where each vertex in one Survey of Algorithms for Dense Subgraph Discovery 317 Figure . Recursive Shingling Step part represents one shiegte. and each vertex in another part is the original vertex. If there is a edge from shingle v to vertex v v is me of the shingles for v s outlinke ginc-atcd hy shingling. From now on V is considered as T V . Foilowsng hhe iamc procesiutCi we apply shingling on V and T V . After the second