Related papers: Bringing order to network centrality measures
Centrality metrics are a popular tool in Network Science to identify important nodes within a graph. We introduce the Potential Gain as a centrality measure that unifies many walk-based centrality metrics in graphs and captures the notion…
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,…
High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order…
Today, there exist many centrality measures for assessing the importance of nodes in a network as a function of their position and the underlying topology. One class of such measures builds on eigenvector centrality, where the importance of…
Consider two networks on overlapping, non-identical vertex sets. Given vertices of interest in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph…
The non-trivial structure of such complex systems makes the analysis of their collective behavior a challenge. The problem is even more difficult when the information is distributed across networks (e.g., communication networks in different…
Identifying networks with similar characteristics in a given ensemble, or detecting pattern discontinuities in a temporal sequence of networks, are two examples of tasks that require an effective metric capable of quantifying network…
We propose a new method for assessing agents influence in network structures, which takes into consideration nodes attributes, individual and group influences of nodes, and the intensity of interactions. This approach helps us to identify…
Centrality measures aim to indicate who is important in a network. Various notions of `being important' give rise to different centrality measures. In this paper, we study how important the central vertices are for the connectivity…
Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand the information interchange in networks of dynamical systems, and uncover the interplay between…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
In real world complex networks, the importance of a node depends on two important parameters: 1. characteristics of the node, and 2. the context of the given application. The current literature contains several centrality measures that have…
Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to…
Network-valued data are encountered in a wide range of applications and pose challenges in learning due to their complex structure and absence of vertex correspondence. Typical examples of such problems include classification or grouping of…
With the impressive growth of network models in practically every scientific and technological area, we are often faced with the need to compare graphs, i.e., to quantify their (dis)similarity using appropriate metrics. This is necessary,…
We introduce Loop Ranking, a new ranking measure based on the detection of closed paths, which can be computed in an efficient way. We analyze it with respect to several ranking measures which have been proposed in the past, and are widely…
Ranking or assessing centrality in multivariate and non-Euclidean data is difficult because there is no canonical order and many depth notions become computationally fragile in high-dimensional or structured settings. We introduce a…
Recent research on temporal networks has highlighted the limitations of a static network perspective for our understanding of complex systems with dynamic topologies. In particular, recent works have shown that i) the specific order in…
Betweenness centrality is a classic measure that quantifies the importance of a graph element (vertex or edge) according to the fraction of shortest paths passing through it. This measure is notoriously expensive to compute, and the best…
We consider the problem of estimating a network's eigenvector centrality only from data on the nodes, with no information about network topology. Leveraging the versatility of graph filters to model network processes, data supported on the…