  The characterization of the "most connected" nodes in static or slowly
evolving complex networks has helped in understanding and predicting the
behavior of social, biological, and technological networked systems, including
their robustness against failures, vulnerability to deliberate attacks, and
diffusion properties. However, recent empirical research of large dynamic
networks (characterized by connections that are irregular and evolve rapidly)
has demonstrated that there is little continuity in degree centrality of nodes
over time, even when their degree distributions follow a power law. This
unexpected dynamic centrality suggests that the connections in these systems
are not driven by preferential attachment or other known mechanisms. We present
a novel approach to explain real-world dynamic networks and qualitatively
reproduce these dynamic centrality phenomena. This approach is based on a
dynamic preferential attachment mechanism, which exhibits a sharp transition
from a base pure random walk scheme.
