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Graph classification is a challenging problem owing to the difficulty in quantifying the similarity between graphs or representing graphs as vectors, though there have been a few methods using graph kernels or graph neural networks (GNNs).…

Computing the size of maximum independent sets is a NP-hard problem for fixed graphs. Characterizing and designing efficient algorithms to estimate this independence number for random graphs are notoriously difficult and still largely open…

This paper proposes a simple but effective graph-based agglomerative algorithm, for clustering high-dimensional data. We explore the different roles of two fundamental concepts in graph theory, indegree and outdegree, in the context of…

Inspired by applications to theories of coding and communication in networks of nervous tissue, we study maximum entropy distributions on weighted graphs with a given expected degree sequence. These distributions are characterized by…

The article deals with two classes of growing random graphs following the preferential attachment rule with a linear weight function, L-graphs, and hybrid Pennock graphs. We determine the exact final vertex degree distribution and the exact…

Subgraphs such as cliques, loops and stars form crucial connections in the topologies of real-world networks. Random graph models provide estimates for how often certain subgraphs appear, which in turn can be tested against real-world…

Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical data analysis and signal processing and (ii) characterising classes of dynamical…

Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…

We consider network topology identification subject to a signal smoothness prior on the nodal observations. A fast dual-based proximal gradient algorithm is developed to efficiently tackle a strongly convex, smoothness-regularized network…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

Robustness is a critical measure of the resilience of large networked systems, such as transportation and communication networks. Most prior works focus on the global robustness of a given graph at large, e.g., by measuring its overall…

Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been…

For a set $S$ of vertices of a graph $G$, we define its density $0 \leq \sigma(S) \leq 1$ as the ratio of the number of edges of $G$ spanned by the vertices of $S$ to ${|S| \choose 2}$. We show that, given a graph $G$ with $n$ vertices and…

This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…

Consider the random graph sampled uniformly from the set of all simple graphs with a given degree sequence. Under mild conditions on the degrees, we establish a Large Deviation Principle (LDP) for these random graphs, viewed as elements of…

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…

We present a structural clustering algorithm for large-scale datasets of small labeled graphs, utilizing a frequent subgraph sampling strategy. A set of representatives provides an intuitive description of each cluster, supports the…

Graph learning plays a pivotal role and has gained significant attention in various application scenarios, from social network analysis to recommendation systems, for its effectiveness in modeling complex data relations represented by graph…

Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs…

We define a proportionally dense subgraph (PDS) as an induced subgraph of a graph with the property that each vertex in the PDS is adjacent to proportionally as many vertices in the subgraph as in the graph. We prove that the problem of…