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# First steps in social network analysis

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Zinayida Petrushyna, Ralf Klamma

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### First steps in social network analysis

1. 1. First steps in social network Zina Petrushyna analysis Ralf Klamma Workshop Terchova, June 2009 Zinayida Petrushyna, Ralf Klamma Chair for Information Systems and Databases, RWTH Aachen University, Germany Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Joint TEL SummerSchool- June09-1
2. 2. Motivation Old theories New theory • Actual process •Knowledge is continual Zina Petrushyna Ralf Klamma • Learning happens inside • Cognitive operations are done by machines • Instructional design • Network pedagogy pedagogy Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Joint TEL SummerSchool- June09-2
3. 3. Fundamentals A network is a graph (consists of nodes and edges) L1 L2 Examples: Zina Petrushyna • People and interactions between them L1 Ralf Klamma L2 • Websites and links Teacher • Cities and traffic connections Edges are Teacher • directed/undirected L3 L3 L4 L4 • multiple • weighted/unweighted Teacher Lehrstuhl Informatik 5 Two nodes are neighbors or adjacent when one (Information Systems) Prof. Dr. M. Jarke Joint TEL edge exist between two given vertices Teacher SummerSchool- June09-3
4. 4. Fundamentals A path is a set of connected edges A length of a path is number of edges on the path Zina A distance of a path is a sum of the weights of the edges Petrushyna on the path A cycle is a path with repeated vertices Ralf Klamma A subgraph is a part of graph Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Joint TEL SummerSchool- June09-4
5. 5. Network Characteristics: Degree centrality Degree of a vertex: number of incoming and outgoing edges L1 Zina • in-degree L2 Petrushyna Ralf Klamma • out-degree Teacher • Simplest centrality measure L3 • A measure in some sense L4 shows the popularity of an actor Teacher Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Joint TEL SummerSchool- June09-5
6. 6. Network Characteristics: Closeness How far a node is from the others? Zina Petrushyna The closeness of the node i is defined as: c(i ) ≡ Ralf Klamma 1 ∑ j∈Nd (i , j ) Who are leaders? Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Joint TEL SummerSchool- June09-6
7. 7. Network Characteristics: Shortest-path Zina Petrushyna Ralf Klamma News, rumor, fad, message – does it know the ideal route? To get from one place to another more likely a message wanders around more randomly, encountering who it will. Certainly it is possible for information to flow between two individuals via a third mutual acquaintance, even when the Lehrstuhl Informatik 5 (Information Systems) two individuals in question are themselves well acquainted Prof. Dr. M. Jarke Joint TEL SummerSchool- June09-7
8. 8. Network Characteristics: Betweenness Measure for the influence an actor can exert The shortest-paths v(j, k) for each j, k and j≠k the betweenness of node i is Zina Petrushyna Ralf Klamma vi ( j, k ) bi ≡ ∑ j ≠k v( j, k ) Who controls the flow of information? Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Joint TEL SummerSchool- June09-8
9. 9. Networ Measures Closeness and Betweenness Degree Ego-centric measure defining a node community Communication activity Betweenness Zina Petrushyna Measure of the extent to which a node lies on the Community control Ralf Klamma paths between others Closeness Measure of how long it will take information to spread Depedence, consideretely from a given node to others in the network efficiency Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Joint TEL SummerSchool- June09-9
10. 10. Examples Zina Petrushyna Ralf Klamma Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Joint TEL SummerSchool- June09-10