Related papers: K-Core Minimization: A Game Theoretic Approach
Multi-layer networks or multiplex networks are generally considered as the networks that have the same set of vertices but different types of edges. Multi-layer networks are especially useful when describing the systems with several kinds…
k-connectivity is an important measure of network robustness and resilience to random faults and disruptions. We undertake both local and global approaches to k-connectivity and calculate closed form analytic formulas for the probability…
We consider the following two variants of the Capacitated $k$-Edge Connected Subgraph} (Cap-k-ECS) problem. Near Min-Cuts Cover: Given a graph $G=(V,E)$ with edge costs and $E_0 \subseteq E$, find a min-cost edge set $J \subseteq E…
Random intersection graphs have received much attention recently and been used in a wide range of applications ranging from key predistribution in wireless sensor networks to modeling social networks. For these graphs, each node is equipped…
We investigate how the graph topology influences the robustness to noise in undirected linear consensus networks. We measure the structural robustness by using the smallest possible value of steady state population variance of states under…
Identifying critical nodes in complex networks is a fundamental task in graph mining. Yet, methods addressing an all-or-nothing coverage mechanics in a bipartite dependency network, a graph with two types of nodes where edges represent…
Network reliability measures the probability that a target node is reachable from a source node in an uncertain graph, i.e., a graph where every edge is associated with a probability of existence. In this paper, we investigate the novel and…
The \emph{maximal $k$-edge-connected subgraphs} problem is a classical graph clustering problem studied since the 70's. Surprisingly, no non-trivial technique for this problem in weighted graphs is known: a very straightforward…
Community detection is expensive, and the cost generally depends at least linearly on the number of vertices in the graph. We propose working with a reduced graph that has many fewer nodes but nonetheless captures key community structure.…
Random K-out graphs are used in several applications including modeling by sensor networks secured by the random pairwise key predistribution scheme, and payment channel networks. The random K-out graph with $n$ nodes is constructed as…
The k-core of a graph G is the maximal subgraph of G having minimum degree at least k. In 1996, Pittel, Spencer and Wormald found the threshold $\lambda_c$ for the emergence of a non-trivial k-core in the random graph $G(n,\lambda/n)$, and…
To enhance robustness of complex networked systems, a simple method is introducing reinforced nodes which always function during failure propagation. A random scheme of node reinforcement can be considered as a benchmark for finding an…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…
Extracting cohesive subgraphs from complex networks is a fundamental task in graph analytics and is essential for understanding biological, social, and web graphs. The edge-based $\gamma$-quasi-clique model offers a flexible alternative by…
In this paper, we study the crucial elements of complex networks, namely nodes, and edges and their properties such as their community structure, which play an important role in dictating the robustness of the network towards structural…
A fundamental characteristic of computer networks is their topological structure. The question of the description of the structural characteristics of computer networks represents a problem that is not completely solved. Search methods for…
We study the k-route cut problem: given an undirected edge-weighted graph G=(V,E), a collection {(s_1,t_1),(s_2,t_2),...,(s_r,t_r)} of source-sink pairs, and an integer connectivity requirement k, the goal is to find a minimum-weight subset…
Graph Neural Networks (GNNs) as deep learning models working on graph-structure data have achieved advanced performance in many works. However, it has been proved repeatedly that, not all edges in a graph are necessary for the training of…
We pursue the study of edge-irregulators of graphs, which were recently introduced in [Fioravantes et al. Parametrised Distance to Local Irregularity. IPEC, 2024]. That is, we are interested in the parameter Ie(G), which, for a given graph…
We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: - We give a greedy algorithm…