Spectral Analysis of Social Networks to Identify Periodicity

Abstract

Two key problems in the study of longitudinal networks are determining when to chunk continuous time data into discrete time periods for network analysis and identifying periodicity in the data. In addition, statistical process control applied to longitudinal social network measures can be biased by the effects of relational dependence and periodicity in the data. Thus, the detection of change is often obscured by random noise. Fourier analysis is used to determine statistically significant periodic frequencies in longitudinal network data. Two approaches are then offered: using significant periods as a basis to chunk data for longitudinal network analysis or using the significant periods to filter the longitudinal data. E-mail communication collected at the United States Military Academy is examined.

Keywords:

• Fourier analysis
• longitudinal networks
• network dynamics
• social network analysis
• statistical process control

Acknowledgments

This research is part of the United States Military Academy Network Science Center and the Dynamics Networks project in the Center for Computational Analysis of Social and Organizational Systems (CASOS; http://www.casos.cs.cmu.edu) at Carnegie Mellon University. This work was supported in part by The Army Research Institute for the Behavioral and Social Sciences, Army Project No. 611102B74 F; The Army Research Organization, Project No. 9FDATXR048; and The Army Research Lab under the Collaborative Technology Alliances DAAD19-01-2-0009 and 20002504. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the National Science Foundation, the Army Research Institute, the Army Research Lab, or the U.S. government. The authors would like to thank Jon Storrick for building an operational version in *ORA.

Notes

¹These methods have been made available as part of the over-time analysis report in *ORA, http://www.casos.cs.cmu.edu/projects/ora.