Time-dependent complex networks: Dynamic centrality, dynamic motifs, and cycles of social interactions

We develop a new approach to the study of the dynamics of link utilization in complex networks using data of empirical social networks. Counter to the perspective that nodes have particular roles, we find roles change dramatically from day to day. "Local hubs" have a power law degree distribution over time, with no characteristic degree value. We further study the dynamics of local motif structure in time-dependent networks, and find recurrent patterns that might provide empirical evidence for cycles of social interaction. Our results imply a significant reinterpretation of the concept of node centrality and network local structure in complex networks, and among other conclusions suggest that interventions targeting hubs will have significantly less effect than previously thought.