PDF-Represen ting Graph Metrics with ew est Edges T

F eder A Mey erson R Mot ani L OCallaghan and R anigrah CarnegieMellon Univ ersit y and Stanford Univ ersit Abstract e are giv en a graph with edge w eigh ts that represen ts the metric on the v ertices in whic h the distance b et een t. e the smallest subset such that has no directed cycles Let be the number of unordered pairs of vertices of which are not adjacent We prove that every directed graph whose shortest directed cycle has length at l east 4 satis64257es c r where is an a Here are represen ting this as 2D problem but in general it can an dimensional problem oin ts are represen ted their co ordinates or this problem co ordinates eing in tegral on mak uc of di57355erence though will assume that ha real co ordinates 11 Why graph clustering is useful?. Distance matrices are graphs .  as useful as any other clustering. Identification of communities in social networks. Webpage clustering for better data management of web data. by . Matchings. . Tobias . Mömke. and Ola Svensson. KTH Royal Institute of Technology. Sweden. Travelling Salesman Problem. Given . . n. . cities . distance. . d(u,v. ) . between . c. ities. . Murali. Mani, . Mohamad. . Alawa. , . Arunlal. . Kalyanasundaram. University of Michigan, Flint. Presented at IDEAS 2011.. Provenance Metadata. Data about origins of data. Applications:. Check whether data item is valid – in health records. Motivating Graph . Packings. . and Coverings of Non-Complete Graphs . “Old Bob” Gardner Math Department Seminar January 27, 2012. Complete Graphs:. Comparing Samples. Note. . Suppose you have a collection of . Why graph clustering is useful?. Distance matrices are graphs .  as useful as any other clustering. Identification of communities in social networks. Webpage clustering for better data management of web data. Grigory. . Yaroslavtsev. . Penn State + AT&T Labs - Research (intern). Joint work with . Berman (PSU). , . Bhattacharyya (MIT). , . Makarychev. (IBM). , . Raskhodnikova. (PSU). Directed. Spanner Problem. Teorier om ting över tid: idag. Introduktion (tre inkompatibla intuitioner). Endurantism. Perdurantism. Exdurantism. Teorier om tid vs. teorier om ting över tid. Identitet över tid?. Tre sinsemellan inkompatibla intuitioner:. Bipartite Matching. Alexandra Stefan. Flow Network. A . flow network. is a . directed. graph G = (V,E) in which each edge, (. u,v. ) has a . non-negative capacity, c(. u,v. ) ≥ 0. , and for any pair of vertices (. . Intro problem- 3 houses and 3 utilities.  K. 3,3. problem: Can 3 houses be connected to 3 utilities so that no 2 lines cross?. Similarly, can an isomorphic version of K. 3,3. be drawn in the plane so that no two edges cross?. Outline. Link Analysis Concepts. Metrics for Analyzing Networks. PageRank. HITS. Link Prediction. 2. Link Analysis Concepts. Link. A relationship between two entities. Network or Graph. A collection of entities and links between them. Distance matrices are graphs .  as useful as any other clustering. Identification of communities in social networks. Webpage clustering for better data management of web data. Outline. Min s-t cut problem. Adjacency List. Adjacency-Matrix. Pointers/memory for each node (actually a form of adjacency list). Adjacency List. List of pointers for each vertex. Undirected Adjacency List. Adjacency List. The sum of the lengths of the adjacency lists is 2|E| in an undirected graph, and |E| in a directed graph..