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The goal of this paper is to present a centrality measurement for the nodes of a hypergraph, by using existing literature which extends eigenvector centrality from a graph to a hypergraph, and literature which give a general centrality…

This paper is concerned with distributed computation of several commonly used centrality measures in complex networks. In particular, we propose deterministic algorithms, which converge in finite time, for the distributed computation of the…

The non-backtracking matrix and its eigenvalues have many applications in network science and graph mining, such as node and edge centrality, community detection, length spectrum theory, graph distance, and epidemic and percolation…

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…

Semantic networks qualify the meaning of an edge relating any two vertices. Determining which vertices are most "central" in a semantic network is difficult because one relationship type may be deemed subjectively more important than…

In this paper we introduce the functional centrality as a generalization of the subgraph centrality. We propose a general method for characterizing nodes in the graph according to the number of closed walks starting and ending at the node.…

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 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…

Unlike classical centrality measures, recently developed community-aware centrality measures use a network's community structure to identify influential nodes in complex networks. This paper investigates their relationship on a set of fifty…

This paper examines the fundamental problem of identifying the most important nodes in a network. We use an axiomatic approach to this problem. Specifically, we propose six simple properties and prove that PageRank is the only centrality…

Group centrality measures are a generalization of standard centrality, designed to quantify the importance of not just a single node (as is the case with standard measures) but rather that of a group of nodes. Some nodes may have an…

Link prediction is a key aspect of graph machine learning, with applications as diverse as disease prediction, social network recommendations, and drug discovery. It involves predicting new links that may form between network nodes. Despite…

We introduce the avoidance Markov metrics and theories which provide more flexibility in the design of random walk and impose new conditions on the walk to avoid (or transit) a specific node (or a set of nodes) before the stopping criteria.…

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…

Centrality metrics have become a popular concept in network science and optimization. Over the years, centrality has been used to assign importance and identify influential elements in various settings, including transportation,…

We perform an extensive analysis of how sampling impacts the estimate of several relevant network measures. In particular, we focus on how a sampling strategy optimized to recover a particular spectral centrality measure impacts other…

Most people simultaneously belong to several distinct social networks, in which their relations can be different. They have opinions about certain topics, which they share and spread on these networks, and are influenced by the opinions of…

In areas such as computer software and hardware, manufacturing systems, and transportation, engineers encounter networks with arbitrarily large numbers of isomorphic subprocesses. Parameterized systems provide a framework for modeling such…

Existing centrality measures for social network analysis suggest the im-portance of an actor and give consideration to actor's given structural position in a network. These existing measures suggest specific attribute of an actor (i.e.,…

Measures of node centrality that describe the importance of a node within a network are crucial for understanding the behavior of social networks and graphs. In this paper, we address the problems of distributed estimation and control of…