Related papers: Node and Edge Nonlinear Eigenvector Centrality for…

We describe centralities in temporal networks using a supracentrality framework to study centrality trajectories, which characterize how the importances of nodes change in time. We study supracentrality generalizations of eigenvector-based…

The purpose of the research is to find a centrality measure that can be used in place of PageRank and to find out the conditions where we can use it in place of PageRank. After analysis and comparison of graphs with a large number of nodes…

This paper introduces a novel framework that combines traditional centrality measures with eigenvalue spectra and diffusion processes for a more comprehensive analysis of complex networks. While centrality measures such as degree,…

Modern sociology has profoundly uncovered many convincing social criteria for behavioural analysis. Unfortunately, many of them are too subjective to be measured and presented in online social networks. On the other hand, data mining…

Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…

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…

Eigenvector centrality is an established measure of global connectivity, from which the importance and influence of nodes can be inferred. We introduce a local eigenvector centrality that incorporates both local and global connectivity.…

Graph neural network, as a powerful graph representation technique based on deep learning, has shown superior performance and attracted considerable research interest. However, it has not been fully considered in graph neural network for…

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…

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 representation learning has traditionally been used to find lower dimensional vector representations of the nodes in a network. However, there are very important edge driven mining tasks of interest to the classical network analysis…

Complex networks possess a rich, multi-scale structure reflecting the dynamical and functional organization of the systems they model. Often there is a need to analyze multiple networks simultaneously, to model a system by more than one…

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…

Complex systems, such as economic, social, biological, and ecological systems, usually feature interactions not only between pairwise entities but also among three or more entities. These multi-entity interactions are known as higher-order…

The discriminant power of centrality indices for the degree, eigenvector, closeness, betweenness and subgraph centrality is analyzed. It is defined by the number of graphs for which the standard deviation of the centrality of its nodes is…

Many networks can be characterised by the presence of communities, which are groups of units that are closely linked. Identifying these communities can be crucial for understanding the system's overall function. Recently, hypergraphs have…

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…

In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…

In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant…

This paper introduces a nonparametric framework for the setting where multiple networks are observed on the same set of nodes, also known as multiplex networks. Our objective is to provide a simple parameterization which explicitly captures…