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Recent studies reveal the connection between GNNs and the diffusion process, which motivates many diffusion-based GNNs to be proposed. However, since these two mechanisms are closely related, one fundamental question naturally arises: Is…
Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted in order to admit global synchronization, a condition called Laplacian coupling.…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…
The emergence of geometric deep learning as a novel framework to deal with graph-based representations has faded away traditional approaches in favor of completely new methodologies. In this paper, we propose a new framework able to combine…
The occurrence of diffusion on a graph is a prevalent and significant phenomenon, as evidenced by the spread of rumors, influenza-like viruses, smart grid failures, and similar events. Comprehending the behaviors of flow is a formidable…
Multiplex networks describe systems whose interactions can be of different nature, and are fundamental to understand complexity of networks beyond the framework of simple graphs. Recently it has been pointed out that restricting the…
We present a graph-based variational algorithm for multiclass classification of high-dimensional data, motivated by total variation techniques. The energy functional is based on a diffuse interface model with a periodic potential. We…
Despite significant advancements, Large Language Models (LLMs) exhibit blind spots that impair their ability to retrieve and process relevant contextual data effectively. We demonstrate that LLM performance in graph tasks with complexities…
Networks represent how the entities of a system are connected and can be partitioned differently, prompting ways to compare partitions. Common approaches for comparing network partitions include information-theoretic measures based on…
The similarity between objects is significant in a broad range of areas. While similarity can be measured using off-the-shelf distance functions, they may fail to capture the inherent meaning of similarity, which tends to depend on the…
Network robustness research aims at finding a measure to quantify network robustness. Once such a measure has been established, we will be able to compare networks, to improve existing networks and to design new networks that are able to…
Graph similarity metrics serve far-ranging purposes across many domains in data science. As graph datasets grow in size, scientists need comparative tools that capture meaningful differences, yet are lightweight and scalable. Graph Relative…
Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function.…
A unifying graph theoretic framework for the modelling of metro transportation networks is proposed. This is achieved by first introducing a basic graph framework for the modelling of the London underground system from a diffusion law point…
The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to…
We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the…
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…
Graph theory has drawn a lot of attention in the field of Neuroscience during the last decade, mainly due to the abundance of tools that it provides to explore the interactions of elements in a complex network like the brain. The local and…
The distance matrix $\mathcal{D}(G)$ of a graph $G$ is the matrix containing the pairwise distances between vertices. The transmission of a vertex $v_i$ in $G$ is the sum of the distances from $v_i$ to all other vertices and $T(G)$ is the…