Web 2.0 Social Data Analysis

Transcription

1 Web 2.0 Social Data Analysis Ing. Jaroslav Kuchař Structure (2) Czech Technical University in Prague, Faculty of Information Technologies Software and Web Engineering

2 2 Contents Strong and Weak Ties Networks in Their Surrounding Contexts Positive and Negative Relationships

3 3 Graph Partitioning Many methods Divisive Identifying and removing the spanning links Agglomerative Glue nodes together into regions

4 4 Problems? Several bridges Which to remove first? No edge is local bridge Solution -> traffic -> shortest paths

5 5 Betweeness Shortest path - path that connects the two nodes with the shortest number of edges Betweeness total amount of flow (shortest paths) through the edge x7 =

6 6 The Girvan-Newman Method Repeat following steps as long as edges remain in graph 1. Find the edge of highest betweenness and remove from graph 2. recalculate all betweennesses

7 The Girvan-Newman Method 7

8 8 Computing Betweeness 1. Perform a breadth-first search of the graph, starting at A 2. Determine the number of shortest paths from A to each other node 3. Based on these numbers, determine the amount of flow from A to all other nodes that uses each edge.

9 1. Breadth-first search 9

10 2. Counting Paths 10

11 3. Determine the flow values 11

12 12 Clustering Algorithms try to maximize the number of edges that fall within the same cluster Indicates presence 1 A of different communities B in a network Clustering coefficient - probability - friends are friends too Neighborhood overlap - common friends/ all friends 0 D 0.33 C E 0.17 F G

13 13 Betweeness centrality The number of shortest paths that pass through a node divided by all shortest paths 0 A B C 0 D E 1 0 F G 0

14 14 Degree Centrality (in-) or (out-) degree is the number of edges that lead into or out of the node 2 A B 3 4 C 1 D E 4 1 F G 1

15 15 Closeness Centrality The mean length of all shortest paths from a node to all other nodes Measure of reach 2 A B C 2.17 D E 1.33 F G

16 16 Eigenvector Centrality A node with high eigenvector centrality is connected to other nodes with high eigenvector centrality 0.36 A Similar to Google PageRank B Who is connected to 0.54 C the most connected nodes 0.19 D E F G

17 17 Reciprocity Oriented graphs Edge in both directions The ration of the number of relations which are reciprocated over the total number of relations 2/5 = 0.4 A B C D

18 18 Density The ratio of the number of edges over the total number of possible edges Total number Undirected n(n-1)/2 Directed n(n-1) 5/6 = 0.83 A B C D

19 degree 19 Preferential Attachment The great majority of new edges are to nodes with an already high degree Nodes in descending degree Jure Leskovec, Lada Adamic, and Bernardo Huberman. The dynamics of viral marketing. ACM Transactions on the Web, 1(1), May 2007.

20 20 Homophily The principle that we tend to be similar to our friends. Plato - similarity begets friendship Aristotle - people love those who are like themselves birds of a feather flock together (racial, ethnic, age, place, occupation, affluence, interest, opinions)

21 21 Homophily: race (different colors of nodes), friendships in the middle, high schools James Moody. Race, school integration, and friendship segregation in america. American Journal of Sociology, 107(3): , November 2001.

22 22 Measuring Homophily p fraction of all = male q fraction of all = female p 2,( q 2 ) Same gender = Cross-gender = 2pq Homophily Test: If the fraction of cross-gender edges is significantly less than 2pq, then there is evidence for homophily. 5 of 18 cross-gender, p=2/3, q=1/3 2pq = 4/9 = 8/18 > 5/18

23 23 Transitivity Property of ties If there is a tie between A and B and one between B and C, in transitive network A and C will also be connected Transitivity and homophily together lead to the formation of cliques (fully connected clusters)

24 Giorgos Cheliotis 24

25 25 Affiliation Node for each person Node for each focus connect person A to focus X by an edge if A participates in X affiliation network bipartite graphs

26 Co-evolution:social-affiliation network 26

27 Triangles in a social-affiliation network 27

28 28 A Spatial Model of Segregation Markus M. Mobius and Tanya S. Rosenblat. The process of ghetto formation: Evidence from Chicago, Working paper.

29 29 The Schelling model the effect of homophily operating at a local level

30 Treshold = 3 30

31 31

32 32 Structural Balance each edge labeled with either + or The most plausible

33 33 Structural Balance Structural Balance Property: For every set of three nodes, if we consider the three edges connecting them, either all three of these edges are labeled +, or else exactly one of them is labeled +. Balance Theorem: If a labeled complete graph is balanced, then either all pairs of nodes are friends, or else the nodes can be divided into two groups, X and Y, such that every pair of nodes in X like each other, every pair of nodes in Y like each other, and everyone in X is the enemy of everyone in Y.

34 Structural Balance 34

35 35 Structural Balance Tibor Antal, Paul Krapivsky, and Sidney Redner. Social balance on networks: The dynamics of friendship and enmity. Physica D, 224(130), 2006.

36 Questions 36

37 37 Resources D. Easley, J. Kleinberg: Networks, Crowds and Markets: Reasoning About a Highly Connected World, Cambridge University Press, 2010, ISBN