Graph theory helps us understand the concept of centrality, which is a measure of the importance of different phenomena occurring within a social network. By incorporating centrality, we should be able to measure how influential or significant our application is within an overall network (Freeman, Borgatti & White, 1991). There are four main measures of centrality:
Degree Centrality
Explores the number of edges a vertex in a graph has. When applying this logic to the Web, degree centrality can be used to identify the number of links coming in or out of an individual node. We can infer the importance of a node from its centrality within a network, and degree centrality informs us a node’s opportunity to directly influence other nodes. This would give us a measure of our popularity as an individual application within a social network.
Betweenness Centrality
Tries to capture each node’s role as a connector between other groups of nodes. It evaluates the number of shortest paths going through a node and tells us how vital a node is to communication within the network- essentially how many other web pages between which our application sits. Betweenness centrality gives us an indication of a node’s informal power though gatekeeping and brokering, and it provides an indication of the key influencers within a social network.
Closeness Centrality
Tries to capture how close a node is to any other node within a network, namely, the average of the shortest distance to all other nodes within the network. Closeness centrality tells us the time it takes for a node to receive information and provides a measure of its direct influence and how quickly a message can travel from one node to the whole graph.
Eigenvector Centrality
Provides a way of thinking about the most important nodes within a network, instead of looking at specific paths or the number of links for one node only. It considers the idea that there is a way of ranking the importance of all pages, and the notion that the most important pages are connected to other important pages. So, whatever the initial idea of importance, by ranking the importance of the rest of the graph, we can determine the importance of a specific node.
Freeman , L.C, Borgatti, S.P & White , D.R. 1991. Centrality in Valued Graphs: A Measure of Betweenness Based on Network Flow . Social Networks . [Online]. 13(1), 141-154. [27 March 2018]. Available from: https://cloudfront.escholarship.org/dist/prd/content/qt5rd2w4qf/qt5rd2w4qf.pdf.
Written by Ashton Kingdon
