The Role of Individual Edges in Edge Controllability of Complex Networks

Dynamical processes occurring on edges of complex networks are relevant to many real situations. Controlling the edge dynamics is a fundamental challenge in network science. Inspired by recent advances in the edge controllability theories, we explore the role of individual edges in the edge controllability by classifying each edge into one of three categories: critical, redundant, and intermittent. An analytical framework is developed to identify the category of each edge, leading to the discovery that the proportions of three types of edges are to a great extent encoded by the degree distribution, and are affected by the in- and out-degree correlation. In addition, we propose the probability distribution of intermittent edges, and find that the probability distribution has multimodality, which is common in model and real networks.