Related papers: Three hypergraph eigenvector centralities
The study of hypergraphs has received a lot of attention over the past few years, however up until recently there has been no interest in systems where higher order interactions are not undirected. In this article we introduce the notion of…
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…
We introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than larger ones, which makes this measure appropriate for characterizing network…
Uniform hypergraphs have a natural one-to-one correspondence to tensors. In this paper, we investigate the Estrada index and subgraph centrality of an $m$-uniform hypergraph $\mathcal{H}$ via the adjacency tensor. We establish some bounds…
Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to…
Centrality is widely recognized as one of the most critical measures to provide insight in the structure and function of complex networks. While various centrality measures have been proposed for single-layer networks, a general framework…
We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios…
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,…
The hierarchical product of two graphs represents a natural way to build a larger graph out of two smaller graphs with less regular and therefore more heterogeneous structure than the Cartesian product. Here we study the eigenvalue spectrum…
We present a simple proof for the universality of invariant and equivariant tensorized graph neural networks. Our approach considers a restricted intermediate hypothetical model named Graph Homomorphism Model to reach the universality…
Traditional graph centrality measures effectively quantify node importance but fail to capture the structural uniqueness of multi-scale connectivity patterns -- critical for understanding network resilience and function. This paper…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
In this work we investigate the problem of estimating the percolation centrality of every vertex in a graph. This centrality measure quantifies the importance of each vertex in a graph going through a contagious process. It is an open…
In graphs, the concept of adjacency is clearly defined: it is a pairwise relationship between vertices. Adjacency in hypergraphs has to integrate hyperedge multi-adicity: the concept of adjacency needs to be defined properly by introducing…
One way to study an hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this paper we study how properties of weighted hypergraphs are…
The spectral properties of the adjacency matrix provide a trove of information about the structure and function of complex networks. In particular, the largest eigenvalue and its associated principal eigenvector are crucial in the…
Triangle centrality is introduced for finding important vertices in a graph based on the concentration of triangles surrounding each vertex. It has the distinct feature of allowing a vertex to be central if it is in many triangles or none…
Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…
Eigenvalue interlacing is a versatile technique for deriving results in algebraic combinatorics. In particular, it has been successfully used for proving a number of results about the relation between the (adjacency matrix or Laplacian)…
The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…