Related papers: Total communicability as a centrality measure

Methods for efficiently controlling dynamics propagated on networks are usually based on identifying the most influential nodes. Knowledge of these nodes can be used for the targeted control of dynamics such as epidemics, or for modifying…

Measures of complex network analysis, such as vertex centrality, have the potential to unveil existing network patterns and behaviors. They contribute to the understanding of networks and their components by analyzing their structural…

As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particular, node centrality…

Measuring the importance of nodes in a network with a centrality measure is a core task in any network application. There are many measures available and it is speculated that many encode similar information. We give an explicit non-linear…

Quantification of symmetries in complex networks is typically done globally in terms of automorphisms. Extending previous methods to locally assess the symmetry of nodes is not straightforward. Here we present a new framework to quantify…

Nestedness is a property of interaction networks widely observed in natural mutualistic communities. Despite a widespread interest on this pattern, no general consensus exists on how to measure it. Instead, several metrics aiming at…

Many systems, ranging from biological and engineering systems to social systems, can be modeled as directed networks, with links representing directed interaction between two nodes. To assess the importance of a node in a directed network,…

Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. As there are many ways in which a node can be important, many different centrality measures are in use. Here,…

Understanding the network structure, and finding out the influential nodes is a challenging issue in the large networks. Identifying the most influential nodes in the network can be useful in many applications like immunization of nodes in…

We consider a broad class of walk-based, parameterized node centrality measures for network analysis. These measures are expressed in terms of functions of the adjacency matrix and generalize various well-known centrality indices, including…

In this article we introduce an entropy-based, scale-dependent centrality that is evaluated as the Shannon entropy of the distribution at time t of a continuous-time random walk. It ranks nodes as a function of the time t, which acts as a…

Many topological and dynamical properties of complex networks are defined by assuming that most of the transport on the network flows along the shortest paths. However, there are different scenarios in which non-shortest paths are used to…

We introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than larger ones, which makes this measure appropriate for characterizing network…

Hierarchy and centrality are two popular notions used to characterize the importance of entities in complex systems. Indeed, many complex systems exhibit a natural hierarchical structure, and centrality is a fundamental characteristic…

Recent development of network structure analysis shows that it plays an important role in characterizing complex system of many branches of sciences. Different from previous network centrality measures, this paper proposes the notion of…

We introduce a quantitative method to compare arbitrary pairs of graph centrality measures, based on the ordering of vertices induced by them. The proposed method is conceptually simple, mathematically elegant, and allows for a quantitative…

We introduce the concept of communicability angle between a pair of nodes in a graph. We provide strong analytical and empirical evidence that the average communicability angle for a given network accounts for its spatial efficiency on the…

Bonacich centrality measures the number of attenuated paths between nodes in a network. We use this metric to study network structure, specifically, to rank nodes and find community structure of the network. To this end we extend the…

We investigate the problem of enforcing a desired centrality measure in complex networks, while still keeping the original pattern of the network. Specifically, by representing the network as a graph with suitable nodes and weighted edges,…

We study the popular centrality measure known as effective conductance or in some circles as information centrality. This is an important notion of centrality for undirected networks, with many applications, e.g., for random walks,…