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Truss decomposition is a method used to analyze large sparse graphs in order to identify successively better connected subgraphs. Since in many domains the underlying graph changes over time, its associated truss decomposition needs to be…
Drawings of highly connected (dense) graphs can be very difficult to read. Power Graph Analysis offers an alternate way to draw a graph in which sets of nodes with common neighbours are shown grouped into modules. An edge connected to the…
Graph Neural Networks (GNNs) have emerged as a notorious alternative to address learning problems dealing with non-Euclidean datasets. However, although most works assume that the graph is perfectly known, the observed topology is prone to…
Graph Neural Networks (GNNs) have demonstrated remarkable performance in a wide range of tasks, such as node classification, link prediction, and graph classification, by exploiting the structural information in graph-structured data.…
We consider the worst-case load-shedding problem in electric power networks where a number of transmission lines are to be taken out of service. The objective is to identify a pre-specified number of line outage that leads to the maximum…
In 2010, Butler introduced the unfolding operation on a bipartite graph to produce two bipartite graphs, which are cospectral for the adjacency and the normalized Laplacian matrices. In this article, we describe how the idea of unfolding a…
Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly-planar. Here, planarity is relaxed by allowing edge crossings, but only with respect to some local forbidden crossing configurations.…
A visualized graph is a powerful tool for data analysis and synthesis tasks. In this case, the task of visualization constitutes not only in displaying vertices and edges according to the graph representation, but also in ensuring that the…
Network Models with couplings between link pairs are the simplest models for a class of networks with Higher Order interactions. In this paper we give an analytic, general solution to this family of Random Graph Models extending previous…
The Dulmage--Mendelsohn decomposition (or the DM-decomposition) gives a unique partition of the vertex set of a bipartite graph reflecting the structure of all the maximum matchings therein. A bipartite graph is said to be DM-irreducible if…
Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…
We introduce a general framework for flow problems over hypergraphs. In our problem formulation, which we call the convex flow problem, we have a concave utility function for the net flow at every node and a concave utility function for…
Edges in real-world graphs are typically formed by a variety of factors and carry diverse relation semantics. For example, connections in a social network could indicate friendship, being colleagues, or living in the same neighborhood.…
Decision diagrams are an increasingly important tool in cutting-edge solvers for discrete optimization. However, the field of decision diagrams is relatively new, and is still incorporating the library of techniques that conventional…
Previous work has suggested that the structural restrictions of graphs from classes of bounded expansion--locally dense pockets in a globally sparse graph--naturally coincide with common properties of real-world networks such as clustering…
In this paper, we use the concept of colored edge graphs to model homogeneous faults in networks. We then use this model to study the minimum connectivity (and design) requirements of networks for being robust against homogeneous faults…
Learning-based methods for routing have gained significant attention in recent years, both in single-objective and multi-objective contexts. Yet, existing methods are unsuitable for routing on multigraphs, which feature multiple edges with…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
Testing a graph on 2-vertex- and 2-edge-connectivity are two fundamental algorithmic graph problems. For both problems, different linear-time algorithms with simple implementations are known. Here, an even simpler linear-time algorithm is…
We propose an efficient linear-time graph-based divisive cluster analysis approach called Reductive Clustering. The approach tries to reveal the hierarchical structural information through reducing the graph into a more concise one…