Overview Agenda: A selection of concepts from Social Network - PDF document

Knowledge Management Institute 707.000 Web Science and Web Technology „Social Network Analysis“ Markus Strohmaier Univ. Ass. / Assistant Professor Knowledge Management Institute Graz University of Technology, Austria e-mail: markus.strohmaier@tugraz.at web: http://www.kmi.tugraz.at/staff/markus Markus Strohmaier 2007 1 Knowledge Management Institute Overview Agenda: A selection of concepts from Social Network Analysis • Sociometry, adjacency lists and matrices • One mode, two mode and affiliation networks • Prominence • Cliques, clans and clubs Markus Strohmaier 2007 2 1

Knowledge Management Institute Sociometry as a precursor of (social) network analysis [Wasserman Faust 1994] • J.L. Moreno, 1889 - 1974 • Psychiatrist, grew up in Vienna • Worked for Austrian Government • Driving research motivation (in the 1930‘s and 1940‘s): – Exploring the advantages of picturing interpersonal interactions using sociograms, for sets with many actors Markus Strohmaier 2007 3 Knowledge Management Institute Sociometry [Wassermann and Faust 1994] • Sociometry is the study of positive and negative relations, such as liking/disliking and friends/enemies among a set of people. t s f o r m a w e b p l e o f e x a m v e a n y o u g i C a n h i p s ? a t i o n s c h r e l u r e s u c a p t t h a t FOAF: Friend of a Friend, http://www.foaf-project.org/ XFN: X HTML F riends N etwork, http://gmpg.org/xfn/ • A social network data set consisting of people and measured affective relations between people is often referred to as sociometric. • Relational data are often presented in two-way matrices termed sociomatrices. Markus Strohmaier 2007 4 2

Knowledge Management Institute Sociometry [Wassermann and Faust 1994] • Images taken from Wasserman/Faust page 76 & 82 Solid lines dashed lines dotted lines Markus Strohmaier 2007 5 Knowledge Management Institute How can we represent (social) networks? We will discuss three basic forms: • Adjacency lists • Adjacency matrices • Incident matrices Markus Strohmaier 2007 6 3

Knowledge Management Institute Adjacency Matrix (or Sociomatrix) • Complete description of a graph • The matrix is symmetric for nondirectional graphs • A row and a column for each node • Of size g x g (g rows and g colums) Markus Strohmaier 2007 7 Knowledge Management Institute Adjacency matrices taken from http://courseweb.sp.cs.cmu.edu/~cs111/applications/ln/lecture18.html Adjacency matrix or sociomatrix Markus Strohmaier 2007 8 4

Knowledge Management Institute Adjacency lists taken from http://courseweb.sp.cs.cmu.edu/~cs111/applications/ln/lecture18.html Markus Strohmaier 2007 9 Knowledge Management Institute Incidence Matrix • (Another) complete description of a graph • Nodes indexing the rows, lines indexing the columns • g nodes and L lines, the matrix I is of size g x L • A „1“ indicates that a node n i is incident with line l j • Each column has exactly two 1‘s in it [Dotted line] [Wasserman Faust 1994] Markus Strohmaier 2007 10 5

Knowledge Management Institute Adjacency lists vs. matrices taken from http://courseweb.sp.cs.cmu.edu/~cs111/applications/ln/lecture18.html Lists Vs. Matrices (I) If the graph is sparse (there aren't many edges), then the matrix will take up a lot of space indication all of the pairs of vertices which don't have an edge between them, but the adjacency list does not have that problem , because it only keeps track of what edges are actually in the graph. On the other hand, if there are a lot of edges in the graph, or if it is fully connected, then the list has a lot of overhead because of all of the references. . Markus Strohmaier 2007 11 Knowledge Management Institute Adjacency lists vs. matrices taken from http://courseweb.sp.cs.cmu.edu/~cs111/applications/ln/lecture18.html Lists Vs. Matrices (II) If we need to look specifically at a given edge , we can go right to that spot in the matrix, but in the list we might have to traverse a long linked list before we hit the end and find out that it is not in the graph. If we need to look at all of a vertex's neighbors , if you use a matrix you will have to scan through all of the vertices which aren't neighbors as well, whereas in the list you can just scan the linked- list of neighbors. . Markus Strohmaier 2007 12 6

Knowledge Management Institute Adjacency lists vs. matrices taken from http://courseweb.sp.cs.cmu.edu/~cs111/applications/ln/lecture18.html Lists Vs. Matrices (III) If, in a directed graph, we ask the question, "Which vertices have edges leading to vertex X?", the answer is straight-forward to find in an adjacency matrix - we just walk down column X and report all of the edges that are present. But, life isn't so easy with the adjacency list - we actually have to perform a brute-force search. � So which representation you use depends on what you are trying to represent and what you plan on doing with the graph Markus Strohmaier 2007 13 Knowledge Management Institute Fundamental Concepts in SNA [Wassermann and Faust 1994] Which networks would not qualify as social • Actor networks? – Social entities – Def: Discrete individual, corporate or collective social units – Examples: people, departments, agencies Which relations would • Relational Tie not qualify as social – Social ties relations? – Examples: Evaluation of one person by another, transfer of resources, association, behavioral interaction, formal relations, biological relationships • Dyad – Emphasizes on a tie between two actors – Def: A dyad consists of two actors and a tie between them – An inherent property between two actors (not pertaining to a single one) – Analysis focuses on dyadic properties – Example: Reciprocity, trust Markus Strohmaier 2007 14 7

Knowledge Management Institute Fundamental Concepts in SNA [Wassermann and Faust 1994] • Triad – Def: A subgroup of three actors and the possible ties among them – Transitivity • If actor i „likes“ j, and j „likes“ k, then i also „likes“ k – Balance • If actor i and j like each other, they should be similar in their evaluation of some k • If actor i and j dislike each other, they shold evaluate k differently k k k � likes � likes � dislikes likes likes likes likes dislikes likes i j i j i j likes dislikes Example 1: Transitivity Example 2: Balance Example 3: Balance Markus Strohmaier 2007 15 Knowledge Management Institute Fundamental Concepts in SNA [Wassermann and Faust 1994] • Group – Def: The collection of all actors on which ties are to be measured – A bounded set (empirically, theoretically, conceptually validated) – A finite set (Analyzability) • Subgroup – Def: A subgroup of actors is any subset of actors, and all ties among them Markus Strohmaier 2007 16 8

Knowledge Management Institute Fundamental Concepts in SNA [Wassermann and Faust 1994] • Relation – The collection of ties of a specific kind among members – Example: the set of friendships among children, the set of formal diplomatic ties between nations in the world • Social Network – Def: Consists of a finite set or sets of actors and the relation or relations defined on them – Focus on relational information, rather than attributes of actors Markus Strohmaier 2007 17 Knowledge Management Institute One and Two Mode Networks • The mode of a network is the number of sets of entities on which structural variables are measured • The number of modes refers to the number of distinct kinds of social entities in a network • One-mode networks study just a single set of actors • Two mode networks focus on two sets of actors , or on one set of actors and one set of events Markus Strohmaier 2007 18 9

Knowledge Management Institute One Mode Networks • Example: One type of nodes (Person) Taken from: http://www.w3.org/2001/sw/Europe/events/foaf- galway/papers/fp/bootstrapping_the_foaf_web/ Other examples: actors, scientists, students Markus Strohmaier 2007 19 Knowledge Management Institute Two Mode Networks • Example: • Two types of nodes Type A Type B A I Can you give II B examples of two mode networks? III C IV D Examples: Examples: actors, conferences, scientists, courses, students movies, articles Markus Strohmaier 2007 20 10

Knowledge Management Institute Affiliation Networks • Affiliation networks are two-mode networks – Nodes of one type „affiliate“ with nodes of the other type (only!) • Affiliation networks consist of subsets of actors, rather than simply pairs of actors • Connections among members of one of the modes are based on linkages established through the second • Affiliation networks allow to study the dual perspectives of the actors and the events [Wasserman Faust 1994] Markus Strohmaier 2007 21 Knowledge Management Institute Is this an Affiliation Network? Why/Why not? [Newman 2003] Markus Strohmaier 2007 22 11