Network Analysis and Modeling CSCI 5352

CSCI 5352 Lecture 3 3 September 2013 Prof. Aaron Clauset 1 Which vertices are important? A common question when analyzing the structure of a network is which vertices are more or less important? This is not yet a well-defined question, and thus how we answer it depends greatly on what we mean by important. There are several general classes of answers. One is to define importance in terms of structural features in the network, e.g., high-degree vertices or being in the “middle” of the network, while another is to define importance in terms of some kind of dynamical process, e.g., vertices where random walkers tend to accumulate. Measures of vertex importance are often called centrality measures, in which more central vertices are more important, and less central ones less important. Here, we will cover a few of the more commonly used forms of centrality measures. However, every centrality measure comes with a set of assumptions, and thus it is crucial to consider whether or not those assumptions fit with the system or question of interest. In most cases, a centrality measure can be calculated, but in some of those cases, its values may be meaningless or misleading. As a running example for these centrality measures, we will apply each to a single network: the popular Zachary’s karate club network,1 which represents the social network of friendships between 34 members of a karate club at a US university in the 1970s. During the course of Zachary’s study, the club split into two factions, centered around two leaders in the club.