How to Analyse Social Network? Social networks can be represented by complex networks.

Reviews Social network is a social structure made up of individuals (or organizations) called “nodes”, which are connected by one or more types of relationships, represented by “links”.  Friendship  Kinship  Common Interest  …. Graph-based structures are very complex. 2 Source:

Introduction Various nature and society systems can be described as complex networks  social systems, biological systems, and communication systems. 3 By presented as a graph, vertices (nodes) represent individuals or organizations and edges (links) represent interaction among them Source:

Types of Network Models The network of co-authorship relationships in SEG's journal Geophysics is scale- free SEG's journal Geophysics 4 Source:

Degree:  The degree of a vertex counts the number of edges that Oriented Degree when Edges Directed:  The in-degree of a vertex (deg - ) counts the number of edges that stick in to the vertex.  The out-degree (deg + ) counts the number sticking out. 5 Network Analysis

There are various measures of the centrality of a vertex within a graph that determine the relative importance of a vertex within the graph  how important a person is within a social network who is the most well-known author in the citation network 6 Centrality Measures

Degree centrality  Degree centrality is defined as the number of links incident upon a node (i.e., the number of ties that a node has).  Degree is often interpreted in terms of the immediate risk of node for catching whatever is flowing through the network such as a virus, or some information.  If the network is directed (meaning that ties have direction), then we usually define two separate measures of degree centrality, namely indegree and outdegree. 7 Centrality Measures

Degree centrality  Indegree is a count of the number of ties directed to the node.  Outdegree is the number of ties that the node directs to others. For positive relations such as friendship or advice, we normally interpret indegree as a form of popularity, and outdegree as gregariousness. 8 Centrality Measures

Degree centrality  An entity with high degree centrality: Is generally an active player in the network. Is often a connector or hub in the network. Is not necessarily the most connected entity in the network (an entity may have a large number of relationships, the majority of which point to low-level entities). May be in an advantaged position in the network. May have alternative avenues to satisfy organizational needs, and consequently may be less dependent on other individuals. Can often be identified as third parties or deal makers. 9 Centrality Measures

Degree centrality  An entity with high degree centrality:  Alice has the highest degree centrality, which means that she is quite active in the network. However, she is not necessarily the most powerful person because she is only directly connected within one degree to people in her clique—she has to go through Rafael to get to other cliques. 10 Centrality Measures Source:

Degree centrality 11 Centrality Measures

Betweenness Centrality  Betweenness is a centrality measure of a vertex within a graph.  Vertices that occur on many shortest paths between other vertices have higher betweenness than those that do not. 12 Centrality Measures

Betweenness Centrality  An entity with a high betweenness centrality generally: Holds a favored or powerful position in the network. Represents a single point of failure—take the single betweenness spanner out of a network and you sever ties between cliques. Has a greater amount of influence over what happens in a network. 13 Centrality Measures

Betweenness Centrality  An entity with a high betweenness centrality generally:  Rafael has the highest betweenness because he is between Alice and Aldo, who are between other entities. Alice and Aldo have a slightly lower betweenness because they are essentially only between their own cliques. Therefore, although Alice has a higher degree centrality, Rafael has more importance in the network in certain respects. 14 Centrality Measures Source:

Betweenness centrality 15 Centrality Measures

Closeness Centrality Closeness is one of the basic concepts in a topological space.  We say two sets are close if they are arbitrarily near to each other.  The concept can be defined naturally in a metric space where a notion of distance between elements of the space is defined, but it can be generalized to topological spaces where we have no concrete way to measure distances. 16 Centrality Measures

Closeness Centrality  Closeness is a centrality measure of a vertex within a graph. Vertices that are 'shallow' to other vertices (that is, those that tend to have short geodesic distances to other vertices with in the graph) have higher closeness.  Closeness is preferred in network analysis to mean shortest-path length, as it gives higher values to more central vertices, and so is usually positively associated with other measures such as degree.  Closeness centrality measures how quickly an entity can access more entities in a network 17 Centrality Measures

Closeness Centrality  An entity with a high closeness centrality generally: Has quick access to other entities in a network. Has a short path to other entities. Is close to other entities. Has high visibility as to what is happening in the network. 18 Centrality Measures

Closeness Centrality Rafael has the highest closeness centrality because he can reach more entities through shorter paths. As such, Rafael's placement allows him to connect to entities in his own clique, and to entities that span cliques. 19 Centrality Measures Source:

Hub and Authority (for directed graph) If an entity has a high number of relationships pointing to it, it has a high authority value, and generally:  Is a knowledge or organizational authority within a domain.  Acts as definitive source of information. Hubs are entities that point to a relatively large number of authorities. They are essentially the mutually reinforcing analogues to authorities. Authorities point to high hubs. Hubs point to high authorities. You cannot have one without the other. 20 Centrality Measures Source:

Eigenvector Centrality  Eigenvector centrality is a measure of the importance of a node in a network. It assigns relative scores to all nodes in the network based on the principle that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.  Google's PageRank is a variant of the Eigenvector centrality measure. 21 Centrality Measures

Eigenvector Centrality 22 Centrality Measures

Eigenvector Centrality 23 Centrality Measures

Social Network Analysis: Theory and Applications Graphs (ppt), Zeph Grunschlag, KONECT:  Pajek:  References