Related papers: The Parameterized Complexity of Centrality Improve…
Hierarchy and centrality are two popular notions used to characterize the importance of entities in complex systems. Indeed, many complex systems exhibit a natural hierarchical structure, and centrality is a fundamental characteristic…
Largest theoretical contribution to Neural Networks comes from VC Dimension which characterizes the sample complexity of classification model in a probabilistic view and are widely used to study the generalization error. So far in the…
Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the…
We study the parameterized complexity of a broad class of problems called "local graph partitioning problems" that includes the classical fixed cardinality problems as max k-vertex cover, k-densest subgraph, etc. By developing a technique…
Given a graph $G$ and an integer $b$, Bandwidth asks whether there exists a bijection $\pi$ from $V(G)$ to $\{1, \ldots, |V(G)|\}$ such that $\max_{\{u, v \} \in E(G)} | \pi(u) - \pi(v) | \leq b$. This is a classical NP-complete problem,…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
We investigate the parameterised complexity of the classic coverability problem for vector addition systems (VAS): given a finite set of vectors $V \subseteq\mathbb{Z}^d$, an initial configuration $s\in\mathbb{N}^d$, and a target…
This paper introduces a novel framework that combines traditional centrality measures with eigenvalue spectra and diffusion processes for a more comprehensive analysis of complex networks. While centrality measures such as degree,…
Centrality metrics aim to identify the most relevant nodes in a network. In literature, a broad set of metrics exists, either measuring local or global centrality characteristics. Nevertheless, when networks exhibit a high spectral gap, the…
We study the kernelization complexity of structural parameterizations of the Vertex Cover problem. Here, the goal is to find a polynomial-time preprocessing algorithm that can reduce any instance $(G,k)$ of the Vertex Cover problem to an…
In many networks, including networks of protein-protein interactions, interdisciplinary collaboration networks, and semantic networks, connections are established between nodes with complementary rather than similar properties. While…
In this paper, we study the complexity of the edge monitoring problem. A vertex $v$ monitors an edge $e$ if both extremities together with $v$ form a triangle in the graph. Given a graph $G=(V,E)$ and a weight function on edges $c$ where…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
Much of the past work in network analysis has focused on analyzing discrete graphs, where binary edges represent the "presence" or "absence" of a relationship. Since traditional network measures (e.g., betweenness centrality) utilize a…
Closeness is one of the most studied characteristics of networks. Residual closeness is a very sensitive measure of graphs robustness. Additional closeness is a measure of growth potentials of networks. In this article we calculate the…
In complex networks a common task is to identify the most important or "central" nodes. There are several definitions, often called centrality measures, which often lead to different results. Here we study extensively correlations between…
In the Maximum Connectivity Improvement (MCI) problem, we are given a directed graph $G=(V,E)$ and an integer $B$ and we are asked to find $B$ new edges to be added to $G$ in order to maximize the number of connected pairs of vertices in…
An added edge to a graph is called an inset edge. Predicting k inset edges which minimize the average distance of a graph is known to be NP-Hard. However, when k = 1 the complexity of the problem is polynomial. In this paper, some tools for…
Random geometric networks consist of 1) a set of nodes embedded randomly in a bounded domain $\mathcal{V} \subseteq \mathbb{R}^d$ and 2) links formed probabilistically according to a function of mutual Euclidean separation. We quantify how…