  In this paper, we explore how network centrality and network entropy can be
used to identify a bifurcation network event. A bifurcation often occurs when a
network undergoes a qualitative change in its structure as a response to
internal changes or external signals. In this paper, we show that network
centrality allows us to capture important topological properties of dynamic
networks. By extracting multiple centrality features from a network for
dimensionality reduction, we are able to track the network dynamics underlying
an intrinsic low-dimensional manifold. Moreover, we employ von Neumann graph
entropy (VNGE) to measure the information divergence between networks over
time. In particular, we propose an asymptotically consistent estimator of VNGE
so that the cubic complexity of VNGE is reduced to quadratic complexity that
scales more gracefully with network size. Finally, the effectiveness of our
approaches is demonstrated through a real-life application of cyber intrusion
detection.
