PDF-The K clique Densest Subgraph Problem

10 HoweverfrequentlythedensestsubgraphproblemfailsindetectinglargenearcliquesinnetworksInthisworkweintroducethecliquedensestsubgraphproblem2Thisgeneralizesthewellstudieddensestsubgraphprobl. Tsourakakis Francesco Bonchi Aristides Gionis Francesco Gullo Maria A Tsiarli Carnegie Mellon University Yahoo Research Aalto University University of Pittsburgh Pittsburgh PA USA Barcelona Spain Espoo Finland Pittsbu rgh PA USA ABSTRACT Finding den Chen Rudolf Fleischer and Jian Li University of Notre Dame IN USA Email dchencsendedu Fudan University SCS and IIPL Shanghai China Email rudolffudaneducn University of Maryland College Park MD USA Email lijiancsumdedu Abstract We study approxi Longin Jan Latecki. Based on :. P. . Dupont. , J. . Callut. , G. Dooms, J.-N. . Monette. and Y. Deville.. Relevant subgraph extraction from random walks in a graph. . RR 2006-07, Catholic University of Louvain , November 2006.. Degree 10 0 10 1 10 2 10 3 10 4 10 5 10 0 10 2 10 4 10 6 Total Subgraph 1 Subgraph 2 Subgraph 3 Degree 10 0 10 1 10 2 10 3 10 4 10 5 Count of Degree 10 0 10 2 10 4 10 6 Total Subgraph 1 Subgraph 2 Sub Admin. Last assignment out today (yay!). Review topics?. E-mail me if you have others…. CS senior theses . Wed 12:30-1:30 (MBH 538). Thur. 3-4:30 (MBH 104). Run-time analysis. We’ve spent a lot of . Subgroups. Chapter 7. Feb 20, 2009. Definition of subgroups . Definition of sub-groups: “Cohesive subgroups are subsets of actors among whom there are relatively strong, direct, intense, frequent or positive ties. It formalizes the strong social groups based on the social network properties ”. , Convexity, and the quest towards Optimal Algorithms. Boaz Barak. Harvard University. Microsoft Research. Partially based on work in progress with . Sam Hopkins. , . Jon Kelner, . Pravesh Kothari. , Ankur Moitra and Aaron Potechin.. of Large Datasets. . Charalampos (Babis) E. Tsourakakis. Brown University. charalampos_tsourakakis@brown.edu. Brown University. and. Core-periphery . structure. By: Ralucca Gera, NPS. Why?. Mostly observed real networks have:. Heavy tail (. powerlaw. most probably, exponential). High clustering (high number of triangles especially in social networks, lower count otherwise). (and related problems). on Minor-Free Graphs. Hans . Bodlaender. (U Utrecht, TU Eindhoven). Jesper. . Nederlof. (TU Eindhoven). Tom van der . Zanden. (U Utrecht). 1. Subgraph Isomorphism. Given: a . Given a set of real numbers, output a sequence, . (. l. 1. , … , . l. i. , … , . l. n. ). , . where . l. i. . ≤ . l. i 1. . for . i. = . 1 … n-1 .. Naive Algorithm. For index . i. =1 .. . Longin Jan Latecki. Based on :. P. . Dupont. , J. . Callut. , G. Dooms, J.-N. . Monette. and Y. Deville.. Relevant subgraph extraction from random walks in a graph. . RR 2006-07, Catholic University of Louvain , November 2006.. (CPM). What is CPM?. Algorithm. Analysis. Conclusion. Contents. Method to find . overlapping. . communities. Based on concept:. internal edges of community likely to form cliques. Intercommunity edges unlikely to form cliques. Feb 20, 2009. Definition of subgroups . Definition of sub-groups: “Cohesive subgroups are subsets of actors among whom there are relatively strong, direct, intense, frequent or positive ties. It formalizes the strong social groups based on the social network properties ”.