Related papers: Fast computation of matrix function-based centrali…
Given a social network, which of its nodes are more central? This question has been asked many times in sociology, psychology and computer science, and a whole plethora of centrality measures (a.k.a. centrality indices, or rankings) were…
Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency…
Multiplex networks are complex graph structures in which a set of entities are connected to each other via multiple types of relations, each relation representing a distinct layer. Such graphs are used to investigate many complex…
Network centralization, driven by hub nodes, impacts communication efficiency, structural integration, and dynamic processes such as diffusion and synchronization. Although numerous centralization measures exist, a major challenge lies in…
A fundamental problem in the study of networks is the identification of important nodes. This is typically achieved using centrality metrics, which rank nodes in terms of their position in the network. This approach works well for static…
Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. Most prominent centrality measures can be expressed as an aggregation of influence flows between pairs of…
We examine a node centrality measure based on the notion of total communicability, defined in terms of the row sums of the exponential of the adjacency matrix of the network. We argue that this is a natural metric for ranking nodes in a…
We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods…
Multilayer networks have become increasingly ubiquitous across diverse scientific fields, ranging from social sciences and biology to economics and international relations. Despite their broad applications, the inferential theory for…
The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…
Centrality describes the importance of nodes in a graph and is modeled by various measures. Its global analogue, called centralization, is a general formula for calculating a graph-level centrality score based on the node-level centrality…
Multiple-subject network data are fast emerging in recent years, where a separate connectivity matrix is measured over a common set of nodes for each individual subject, along with subject covariates information. In this article, we propose…
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…
Complex networks or graphs provide a powerful framework to understand importance of individuals and their interactions in real-world complex systems. Several graph theoretical measures have been introduced to access importance of the…
In graph-based applications, a common task is to pinpoint the most important or ``central'' vertex in a (directed or undirected) graph, or rank the vertices of a graph according to their importance. To this end, a plethora of so-called…
The centrality of a node within a network, however it is measured, is a vital proxy for the importance or influence of that node, and the differences in node centrality generate hierarchies and inequalities. If the network is evolving in…
To understand a node's centrality in a multiplex network, its centrality values in all the layers of the network can be aggregated. This requires a normalization of the values, to allow their meaningful comparison and aggregation over…
Complex networks are made up of vertices and edges. The edges, which may be directed or undirected, are equipped with positive weights. Modeling complex systems that consist of different types of objects leads to multilayer networks, in…
We introduce a new matrix function for studying graphs and real-world networks based on a double-factorial penalization of walks between nodes in a graph. This new matrix function is based on the matrix error function. We find a very good…
We report results from an experiment on ranking visual markers and node positioning techniques for network visualizations. Inspired by prior ranking studies, we rethink the ranking when the dataset size increases and when the markers are…