Abstract
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.
Highlights
The edge dynamics is relevant to various real-world systems with complex network topological features [1]–[3]
We develop an analytical framework to identify the category of each edge and find that, unlike nodal dynamics [18], [19], the category of an edge in the edge controllability is determined by its local structure
Applying our framework to a large number of model and real networks, we find that the proportions of three types of edges are to a great extent encoded by the degree distribution, and are affected by the inand out-degree correlation
Summary
The edge dynamics is relevant to various real-world systems with complex network topological features [1]–[3] It is suitable for modeling networks where nodes are active components with information processing capabilities. The information received and passed by a node can be represented by the state variables on its incoming and outgoing edges. Control of the edge dynamics in a network, is exclusively determined by the local structure of each node. We develop an analytical framework to identify the category of each edge and find that, unlike nodal dynamics [18], [19], the category of an edge in the edge controllability is determined by its local structure. The uncovered multimodality offers new insights into the role of individual edges in the edge controllability
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