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. Source: http://followingfactory.com/

Introduction Complex Networks Various nature and society systems can be described as complex networks social systems, biological systems, and communication systems. By presented as a graph, vertices (nodes) represent individuals or organizations and edges (links) represent interaction among them Source: http://www.fmsasg.com/SocialNetworkAnalysis

Types of Network Models Complex Networks Types of Network Models The network of co-authorship relationships in SEG's journal Geophysics is scale-free  Source: http://www.agilegeoscience.com/journal/tag/networks

Social Network Analysis 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.

Social Network Analysis Centrality Measures 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

Social Network Analysis 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.

Social Network Analysis 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.

Social Network Analysis 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.

Social Network Analysis 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. Source: http://www.fmsasg.com/SocialNetworkAnalysis/

Social Network Analysis Centrality Measures Degree centrality

Social Network Analysis 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.

Social Network Analysis 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.

Social Network Analysis 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. Source: http://www.fmsasg.com/SocialNetworkAnalysis/

Social Network Analysis Centrality Measures Betweenness centrality

Social Network Analysis 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.

Social Network Analysis 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

Social Network Analysis 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.

Social Network Analysis 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. Source: http://www.fmsasg.com/SocialNetworkAnalysis/

Social Network Analysis Centrality Measures 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. Source: http://www.fmsasg.com/SocialNetworkAnalysis/

Social Network Analysis Centrality Measures 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.

Social Network Analysis Centrality Measures Eigenvector Centrality

Social Network Analysis Centrality Measures Eigenvector Centrality

Social Network Analysis Centrality Measures

Social Network Analysis RFID Datenvolumen Social Network Analysis Centrality Measures PageRank Only Structure Consideration Knowledge of Global Network Structure Broken Link Problems

Social Network Analysis Software KONECT: the Koblenz Network Collection contains 168 network datasets (for instance) Animal networks are networks of contacts between animals. Authorship networks are unweighted bipartite networks consisting of links between authors and their works. Citation networks consist of documents that reference each other. Coauthorship networks are unipartite network connecting authors who have written works together. Communication networks contain edges that represent individual messages between persons. consists of Matlab code to generate statistics and plots about them Source: konect.uni-koblenz.de/networks

“Pajek”: Large Network Analysis Software

Introduction to Slovenian Spider: Pajek http://vlado.fmf.uni-lj.si/pub/networks/pajek/ Free software Windows 32 bit Pajek 2.05 “Whom would you choose as a friend ?” 28

Introduction Its applications: Communication networks: links among pages or servers on Internet, usage of phone calls Transportation networks Flow graphs of programs Bibliographies, citation networks 29

Data Structures Six data structures: Network(*.net) – main object (vertices and lines - arcs, edges) Partition(*.clu) – nominal property of vertices (gender); Vector(*.vec) – numerical property of vertices; permutation (*.per) – reordering of vertices; cluster (*.cls) – subset of vertices (e.g. a cluster from partition); hierarchy (*.hie) – hierarchically ordered clusters and vertices.

Introduction Pajek 2.05

Network Definitions Graph Theory Graphs represent the structure of networks Directed and undirected graphs Lists of vertices arcs and edges, where each arch and edge has a value. To view the network data files: NotePad, EditPlus

Network Data File Open Network Data File (*.net) Number of Vertices 33

Transform Transform

Report Information

Visualization Energy – Idea: the network is represented like a physical system, and we are searching for the state with minimal energy. Two algorithms are included: Layout/Energy/Kamada-Kawai – slower Layout/Energy/Fruchterman-Reingold – faster, drawing in a plane or space (2D or 3D), and selecting the repulsion factor

Network Creation 37

Partitions File name: *.clu

Degree

Social Network Analysis References Social Network Analysis: Theory and Applications Graphs (ppt), Zeph Grunschlag, 2001-2002. KONECT: http://konect.uni-koblenz.de/networks Pajek: http://pajek.imfm.si/doku.php?id=download http://www.fmsasg.com/SocialNetworkAnalysis/