Group and Community Detection in Social Networks

Group and Community Detection in Social Networks Ismael A. Ali Talk: Structured Graphs And Their Applications Fall 2014 | Kent State University iali1@kent.edu  Outline 1. Basics of Social Networks 2. Real-world problem 3. How to construct graph from real-world problem? 4. What graph theory problem getting from real- world problem? 5. Graph type of Social Networks 6. Special properties in social graph 7. How to find communities and groups in social networks? (Algorithms) 8. How to interpret graph solution back to real- world problem? 1. Basics of Social Networks  Definitions Social Network: finite set or sets of actors and the relation or relations defined on them. Actor = Node = Point = Agent: social entities such as persons, organizations, cities, etc. Tie = Link = Edge = Line = Arc: represents relationships among actors. Relation: collection of ties of a specific kind among members of a group. Attributes of Actor (nodes) - People can be queried about different features, like ( age, gender, race, socioeconomic status, place of residence, grade in school, etc. ) 2. Real-world Problem  The real-world problem is: “Finding Groups And Communities In Social Networks” Definition : Social Groups and Communities – “Two or more people , who interact with one another, share similar characteristics and attributes and collectively have a sense of unity” – Actors who have all possible ties among themselves • Social networks and the social network analysis: – Is an interdisciplinary academic field (social psychology, sociology, statistics, and graph theory) – 1930; first sociograms in the to study interpersonal relationships, by Jacob – 1950; sociograms approaches mathematically formalized – 1980; theories and methods of social networks became popular in the social and behavioral sciences – Social network analysis is now one of the major paradigms in contemporary sociology http://www.cmu.edu/joss/content/articles/volume1/Freeman.html Why to find social groups and communities? – behavior analysis – location-based interaction analysis – recommender systems development – link prediction – customer interaction and analysis & marketing – media use – Security – Social studies 3. How to Construct Graph From Real-world Problem? - Shared Attributes: Actors are grouped based on the shared attributes among them. i.e. Group of four people (Bob, Carol, Ted, and Alice) - Blue for males, red for females Bob Carol Alice Ted http://faculty.ucr.edu/~hanneman/nettext/C3_Grap - Attribute 1: "close friends”: who they regarded as close friends in the group? Bob Carol Alice Ted A directed graph of friendship ties Bob, Carol, and Ted form a "clique" (i.e. each is connected to each of theisothers) Alice a "pendant" (tied to the group by only one connection) - Attribute 2: “Spouse” Bob Carol Alice Ted A directed graph of spousal ties  4. What Graph Theory Problem Getting From Real- world Problem? • Clique problem: refers to any problem to find particular (complete) subgraphs ("cliques") in a graph, • i.e., sets of elements where each pair of elements is connected. http://sebastian.doc.gold.ac.uk  • Note: the notion of clique here dose not necessary refers to a complete subgraph, Complete Graph: there's an edge between any two node Dense Graph: number of edges is close to the maximal number of edges Sparse Graph: when it has only a few edges http://sebastian.doc.gold.ac.uk  Dense Graph Definition • A graph G = (V, E) is said to be dense if for every v ∈ V , degree(v) > n/2, where n = |V| • Density is the ratio between the number of edges |E| and the number of vertices |V|. • Density for undirected graphs: • The maximal density is 1 = complete graphs • Maximum number of edges ½ |V| (|V|−1) http://www.cc.gatech.edu/~vigoda/MCMC_Course/  Complexity of the problem • Clique problem is NP-Complete problem – k-clique problem, the input is an undirected graph and a number k, and the output is a clique of size k if one exists (or, sometimes, all cliques of size k) 5. Graph Type of Social Networks  Small-World Graph = Scale- Free Graph – most nodes are not neighbors of one another, but most nodes can be reached from every other by a small number of hops or steps. – Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes (the number of steps required) grows proportionally to the logarithm of the number of nodes N in the network, that is: Last time by: Reem http://www.lenddo.com/blog/2012/06/facebook-proves-it%E2%80%99s-a-small-world-after-all-we-are-all-connected-by- 6. Special Properties in Social Graphs • Community Structure: Real-world social graphs are found to exhibit a modular structure; with nodes forming groups, and possibly groups within groups – In a modular graph, the nodes form communities where groups of nodes in the same community are tighter connected to each other than to those nodes outside the community • Heavy-tailed Degree Distribution: – few “hubs”, – most nodes have few neighbors - The degree distribution has a power law (functional relationship) - many low degree nodes - only a few high degree nodes in real graphs • Small Diameter: also known as the ‘small-world phenomenon’ or the ‘six degrees of separation’ M. E. J. Newman and M. Girvan. Finding and evaluating community structure in networks. Physical 7. How to Find Communities nnd Groups in Social Networks? (Algorithms)  Taxonomy of Community Criteria - Community detection methods categories: • Node-Centric Community Detection – Each node in a group satisfies certain properties • Group-Centric Community Detection – Consider the connections within a group as a whole. The group has to satisfy certain properties without zooming into node-level • Network-Centric Community Detection – Partition the whole network into several disjoint sets • Hierarchy-Centric Community Detection – Construct a hierarchical structure of communities  A classification of community detection and graph clustering methods  A classification of community detection and graph clustering methods  Clique Percolation Method • (CPM) Clique is a very strict definition, unstable • Normally use cliques as a core to find larger communities • CPM is such a method to find overlapping communities – Input • A parameter k, and a network – Procedure 1. Find out all cliques of size k in a given network 2. Construct a clique graph. Two cliques are adjacent if they share k-1 nodes 3. Each connected components in the clique graph form a community 27  Example: Clique Percolation Method Step 1: Find all Cliques of size 3 {1, 2, 3}, {1, 3, 4}, {4, 5, 6}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8} 28 ep 2: Construct Clique Graph {1, 2, 3}, {1, 3, 4}, {4, 5, 6}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8} 29 ep 3: Finding Communities o cliques are adjacent if ey share k-1 nodes (i.e. k-1=2) {1, 2, 3}, {1, 3, 4}, {4, 5, 6}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8} Communities: {1, 2, 3, 4} {4, 5, 6, 7, 8} 30 8. How to Interpret Graph Solution Back to Real-life Problem? - Finding Cliques in the Social Graph of the Social Network leads to the communities and groups inside the Social Networks, based on the attributes and characteristics of actors in the communities  References • Community detection in Social Media, (2012), Symeon Papadopoulos, Yiannis Kompatsiaris, Athena Vakali, Ploutarchos Spyridonos, Data Mining and Knowledge Discovery May 2012, Volume 24, Issue 3, pp 515-554 • Community Detection in Graphs, (2010), Santo Fortunato, Complex Networks and Systems Lagrange Laboratory, ISI Foundation, Viale S. Severo 65, 10133, Torino,I-ITALY. • A Comparison of Community Detection Algorithms on Artificial Networks, (2009), Günce Keziban Orman1,2 and Vincent Labatut , Discovery Science Lecture Notes in Computer Science Volume 5808, pp 242-256 • Social Network Analysis. Methods and Applications, (2008), Wasserman, Stanley, Faust, Katherine, Cambridge, University Press • Computing Communities in Large Networks Using Random Walks, (2005), Pascal Pons and Matthieu Latapy, Computer and Information Sciences – ISCIS, Lecture Notes in Computer Science Volume 3733, 2005, pp 284-293 http://www.lifelearn.com/2013/11/5-easy-creative-ways-thank-social-