Using Coherencies to Examine Network Evolution

This paper explores the use of spectral analysis to examine network evolution and co-evolution. Given a sufficient number of measurements of a valued network over time, a matrix (Κ Κ Κ Κ) may be created, where κ ij is the squared coherency between nodes i and j. Since Κ Κ Κ Κ is a matrix of relations, it may be analyzed like any other network to determine which nodes co-evolve, and which change independently. To illustrate this approach, cross-spectral analyses were conducted among 250 pairs of nation-states based on terrorism news coverage (2000 to 2012) to create matrix Κ Κ Κ Κ. Then, a network analysis was conducted. The results indicate that the United States was the most central country, and that the nations co-evolved in two large groups (the Middle East and East Asia), and numerous smaller ones. The proposed method is extended to include exogenous variables (terrorist events and oil prices) and to two or more networks to examine network co-evolution. Co-evolution is demonstrated with additional data on networks of co-association in terrorism news coverage (2011-2013) and a comparable data set on the coverage of the Arab Spring (2011-2013).