Quantifying and Comparing Centrality Measures for Network Individuals as Applied to the Enron Corpus

Abstract

The ever increasing body of social networks creates an opportunity for extensive network analysis and investigations of communications, cliques, and network contributions. In this study, we focus our attention on the Enron email corpus and the corresponding network of employees, attempting to gather information from the email communications. Methods of data reduction on the email corpus were used to create a weighted adjacency matrix in which each i, j-entry corresponds to a weighted count of correspondences from employee i to employee j. While there are many ways to measure importance within a corporate network, of which job title constitutes one such measure, our study focuses on five primary measures: eigenvector centrality, row-sums of a topological overlap matrix, closeness, betweenness, and Opsahl metric. These network analysis metrics were applied to the weighted adjacency matrix to calculate the centrality measures for each individual employee, which were subsequently compiled into ordinally ranked lists of employees for each centrality measure based on decreasing importance. Additionally, the centrality data was visualized using the DataDriven Documents (D3) javascript library, allowing for network visualization in terms of department job title and number of emails sent. In applying the centrality measures to network data, we explore the differences inherent in each measure and work to compare them as well as the corresponding employee importance rankings for each. The metrics in our analysis determined individual importance of employees by applying significant weight to various aspects of the employees’ network roles. By identifying employees that are connected to a large number of individuals and simultaneously have extensive correspondences with those individuals, the Opsahl score combines the other measures, proving to be the most useful metric in exploring Enron’s inner-corporate structure.