Analysis of relative influence of nodes in directed networks

Abstract

Many complex networks are described by directed links; in such networks, a link represents, for example, the control of one node over the other node or unidirectional information flows. Some centrality measures are used to determine the relative importance of nodes specifically in directed networks. We analyze such a centrality measure called the influence. The influence represents the importance of nodes in various dynamics such as synchronization, evolutionary dynamics, random walk, and social dynamics. We analytically calculate the influence in various networks, including directed multipartite networks and a directed version of the Watts-Strogatz small-world network. The global properties of networks such as hierarchy and position of shortcuts, rather than local properties of the nodes, such as the degree, are shown to be the chief determinants of the influence of nodes in many cases. The developed method is also applicable to the calculation of the PageRank. We also numerically show that in a coupled oscillator system, the threshold for entrainment by a pacemaker is low when the pacemaker is placed on influential nodes. For a type of random network, the analytically derived threshold is approximately equal to the inverse of the influence. We numerically show that this relationship also holds true in a random scale-free network and a neural network.

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Cited by in corpus (8)

• Random walks and diffusion on networks
• Phase synchronization between collective rhythms of globally coupled oscillator groups: noiseless non-identical case
• Collective phase dynamics of globally coupled oscillators: Noise-induced anti-phase synchronization
• Dynamics-based centrality for general directed networks
• Measuring centrality by a generalization of degree
• Reconstructing directed networks for better synchronization
• Phase synchronization between collective rhythms of fully locked oscillator groups
• Noise stability of synchronization and optimal network structures