In this chapter, we investigate the influence of a node on a network. By virtue of the classical control theory, the influence of a node is represented by the controllable subspace, which is further transformed into a specified graph named general-cacti. An algorithm is developed to calculate the influence, which contains the searching of different kinds of circles and the longest path in the directed graph. Moreover, eight real networks are studied and simulations show that (1) a node in dense and homogeneous networks could have more influence comparing with nodes in sparse and heteroge- neous networks, (2) any single studied classical centrality measure including output degree, betweenness and PageRank could not rank the influence and (3) a node with high rank in all these three measures could have more influence.

The controllable subspace algorithm can accurately measure the influence of nodes in complex networks, revealing that dense and homogeneous networks have more influence than sparse and heterogeneous networks.

Controllable Subspace as a New Characterization of Influence of Nodes in Complex Networks

Key Takeaway: The controllable subspace algorithm can accurately measure the influence of nodes in complex networks, revealing that dense and homogeneous networks have more influence than sparse and heterogeneous networks.