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We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly determined by the networks degree distribution. We rigorously prove that in a directed network without loops the control centrality of a node is uniquely determined by its layer index or topological position in the underlying hierarchical structure of the network. Inspired by the deep relation between control centrality and hierarchical structure in a general directed network, we design an efficient attack strategy against the controllability of malicious networks.
Community structure is one of the most relevant features encountered in numerous real-world applications of networked systems. Despite the tremendous effort of scientists working on this subject over the past few decades to characterize, model, and a
Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other. Uncovering this c
In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks
A number of recent works have concentrated on a few statistical properties of complex networks, such as the clustering, the right-skewed degree distribution and the community, which are common to many real world networks. In this paper, we address th
We investigate the effect of a specific edge weighting scheme $sim (k_i k_j)^{beta}$ on distributed flow efficiency and robustness to cascading failures in scale-free networks. In particular, we analyze a simple, yet fundamental distributed flow mode