Using Moments and L-Moments to Characterize Graphical Networks

• Activity Number: 504
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Fairul Mohd-Zaid* and Christine Schubert Kabban
• Companies: Air Force Research Lab and Air Force Institute of Technology
• Keywords: L-moments ; Moments ; Random Graphs ; Erdos-Renyi ; Watts-Strogatz

Abstract

Networks that can be modeled graphically may also be summarized through nodal measures, e.g. degree. Nodal measures themselves may be summarized across the network; however, such summaries are often focused on single statistics. Although the mean is the most commonly used statistical summary of a nodal measure, the probability distribution of the nodal measure may be better described using sets of summary measures. The collection of these summary measures may then be used to more fully characterize the network. The purpose of this study was to examine the feasibility of characterizing a network using summary measures of the probability distribution for the nodal network measures. In a large simulation, nodal measures of the degree, betweenness, and closeness for Erdos-Renyi and Watts-Strogatz generated graphs of varying parameter and size were computed. Five summary measures based upon moments and four summary measures based upon L-moments were examined. Through clustering and predictive modeling, the results of the analysis demonstrate that uncorrelated moments and L-moments are dependent on the network type and that the mean alone is not sufficient to characterize the network.