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Many networks, such as transportation, power, and water distribution, can be represented as graphs. Crucial challenge in graph representations is identifying the importance of graph edges and their influence on overall network efficiency…
Recent theoretical and empirical studies have focused on the structural properties of complex relational networks in social, biological and technological systems. Here we study the basic properties of twenty 1-square-mile samples of street…
This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. In particular, we are interested in…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…
Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…
Graph neural networks (GNN) have shown outstanding applications in many fields where data is fundamentally represented as graphs (e.g., chemistry, biology, recommendation systems). In this vein, communication networks comprise many…
Graph neural networks (GNNs) based on message passing between neighboring nodes are known to be insufficient for capturing long-range interactions in graphs. In this project we study hierarchical message passing models that leverage a…
In this article, we revisit and expand our prior work on graph similarity. As with our earlier work, we focus on a view of similarity which does not require node correspondence between graphs under comparison. Our work is suited to the…
The spread of a real symmetric matrix is defined as the difference between its largest and smallest eigenvalue. The study of graph-related matrices has attracted considerable attention, leading to a substantial body of findings. In this…
Let $G$ be a graph with $n$ vertices, and let $A(G)$ and $D(G)$ denote respectively the adjacency matrix and the degree matrix of $G$. Define $$ A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G) $$ for any real $\alpha\in [0,1]$. The collection of…
For a graph $G$, we associate a family of real symmetric matrices, $S(G)$, where for any $A\in S(G)$, the location of the nonzero off-diagonal entries of $A$ are governed by the adjacency structure of $G$. Let $q(G)$ be the minimum number…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
Graph neural networks (GNNs) are widely used for modeling complex interactions between entities represented as vertices of a graph. Despite recent efforts to theoretically analyze the expressive power of GNNs, a formal characterization of…
This paper explores the Harmonic matrix $MH(G)$ associated with a simple graph $ G $, where each entry corresponds to $ \frac{2}{d_i + d_j} $ for adjacent vertices $ v_i $ and $ v_j $. We investigate the spectral properties of this matrix,…
We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads…
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…
A vertex $v$ of a connected graph $G$ is said to be a boundary vertex of $G$ if for some other vertex $u$ of $G$, no neighbor of $v$ is further away from $u$ than $v$. The boundary $\partial(G)$ of $G$ is the set of all of its boundary…
As network research becomes more sophisticated, it is more common than ever for researchers to find themselves not studying a single network but needing to analyze sets of networks. An important task when working with sets of networks is…
Joint diagonalisation (JD) is a technique used to estimate an average eigenspace of a set of matrices. Whilst it has been used successfully in many areas to track the evolution of systems via their eigenvectors; its application in network…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…