Related papers: Eigenvector Centrality and Uniform Dominant Eigenv…

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.…

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…

The principal ratio of a graph is the ratio of the greatest and least entry of its principal eigenvector. Since the principal ratio compares the extreme values of the principal eigenvector it is sensitive to outliers. This can be…

This paper characterizes the difficulty of estimating a network's eigenvector centrality only from data on the nodes, i.e., with no information about the topology of the network. We model this nodal data as graph signals generated by…

Graphs (i.e., networks) have become an integral tool for the representation and analysis of relational data. Advances in data gathering have lead to multi-relational data sets which exhibit greater depth and scope. In certain cases, this…

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…

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…

Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network…

We study the blind centrality ranking problem, where our goal is to infer the eigenvector centrality ranking of nodes solely from nodal observations, i.e., without information about the topology of the network. We formalize these nodal…

We extend the concept of eigenvector centrality to multiplex networks, and introduce several alternative parameters that quantify the importance of nodes in a multi-layered networked system, including the definition of vectorial-type…

The theory of eigenvalues and eigenvectors is one of the fundamental and essential components in tensor analysis. Computing the dominant eigenpair of an essentially nonnegative tensor is an important topic in tensor computation because of…

In this paper we study the inverse eigenvector centrality problem on directed graphs: given a prescribed node centrality profile, we seek edge weights that realize it. Since this inverse problem generally admits infinitely many solutions,…

Identifying the most influential nodes in networked systems is of vital importance to optimize their function and control. Several scalar metrics have been proposed to that effect, but the recent shift in focus towards network structures…

Networks are often studied using the eigenvalues of their adjacency matrix, a powerful mathematical tool with a wide range of applications. Since in real systems the exact graph structure is not known, researchers resort to random graphs to…

We characterize all graphs for which there are eigenvectors of the graph Laplacian having all their components in {-1,+1} or {-1,0,+ 1}. Graphs having eigenvectors with components in {-1,+1} are called bivalent and are shown to be the…

Hypergraphs have been a powerful tool to represent higher-order interactions, where hyperedges can connect an arbitrary number of nodes. Quantifying the relative importance of nodes and hyperedges in hypergraphs is a fundamental problem in…

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…

An eigenvalue of a graph $G$ is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. It is well known that a graph $G$ has exactly two main eigenvalues if and only if there exists a unique pair of…

Graph signal processing uses the graph eigenvector basis to analyze signals. However, these graph eigenvectors are typically linearly ordered (by total variation), which may not be reasonable for many graph structures. There have been…

We review the properties of eigenvectors for the graph Laplacian matrix, aiming at predicting a specific eigenvalue/vector from the geometry of the graph. After considering classical graphs for which the spectrum is known, we focus on…