Related papers: On a Notion of Graph Centrality Based on L1 Data D…
In this work we introduce a concept of complexity for undirected graphs in terms of the spectral analysis of the Laplacian operator defined by the incidence matrix of the graph. Precisely, we compute the norm of the vector of eigenvalues of…
A new metric for quantifying pairwise vertex connectivity in graphs is defined and an implementation presented. While general in nature, it features a combination of input features well-suited for social networks, including applicability to…
Graph Isomorphism is one of the classical problems of graph theory for which no deterministic polynomial-time algorithm is currently known, but has been neither proven to be NP-complete. Several heuristic algorithms have been proposed to…
Centrality metrics aim to identify the most relevant nodes in a network. In literature, a broad set of metrics exists, either measuring local or global centrality characteristics. Nevertheless, when networks exhibit a high spectral gap, the…
The centrality of a vertex v in a network intuitively captures how important v is for communication in the network. The task of improving the centrality of a vertex has many applications, as a higher centrality often implies a larger impact…
Centrality measures, quantifying the importance of vertices or edges, play a fundamental role in network analysis. To date, triggered by some positive approximability results, a large body of work has been devoted to studying centrality…
Given a connected graph $G=(V,E)$, the closeness centrality of a vertex $v$ is defined as $\frac{n-1}{\sum_{w \in V} d(v,w)}$. This measure is widely used in the analysis of real-world complex networks, and the problem of selecting the $k$…
In this paper, we propose a new method to compute the barycenter of large weighted graphs endowed with probability measures on their nodes. We suppose that the edge weights are distances between the nodes and that the probability measure on…
We present new values and bounds on the (normalised) closeness centrality $\bar{\mathsf{C}}_C$ of connected graphs and on its product $\bar{l}\bar{\mathsf{C}}_C$ with the mean distance $\bar{l}$ of these graphs. Our main result presents the…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
There is great significance in evaluating a node's Influence ranking in complex networks. Over the years, many researchers have presented different measures for quantifying node interconnectedness within networks. Therefore, this paper…
Betweenness centrality is a centrality measure based on the overall amount of shortest paths passing through a given vertex. A graph is betweenness-uniform if all its vertices have the same betweenness centrality. We study the properties of…
Subgraph centrality, introduced by Estrada and Rodr\'iguez-Vel\'azquez in [12], has become a widely used centrality measure in the analysis of networks, with applications in biology, neuroscience, economics and many other fields. It is also…
We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the…
We study the properties of several proximity measures for the vertices of weighted multigraphs and multidigraphs. Unlike the classical distance for the vertices of connected graphs, these proximity measures are applicable to weighted…
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…
New Matlab functions for network centrality are introduced. Instead of the mean distance, the generalized mean distance is used. If closer relationships are prioritized, this closeness measure is also defined for unconnected graphs. Instead…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
The application of deep learning to symbolic domains remains an active research endeavour. Graph neural networks (GNN), consisting of trained neural modules which can be arranged in different topologies at run time, are sound alternatives…
Measuring the importance of nodes in a network with a centrality measure is a core task in any network application. There are many measures available and it is speculated that many encode similar information. We give an explicit non-linear…