Network Analysis: understanding nodes importance and community detection

Abstract

In this dissertation, the ideas of network analysis are applied to many network graphs. Many different measures for the importance of nodes in a network are presented. The identification of community structure within network graphs is an important part of this dissertation. Different definitions can present a community in a network. While these definitions vary somewhat, they often satisfy the condition that a node in a community is more likely to be connected to another node in the same community than a node in another community. Various methods that have been developed for discovering clusters in networks are discussed. The use of modularity to detect community structure provides a good outcome in general.