Related papers: Computing The Analytic Connectivity of A Uniform H…
Connectivity is a fundamental structural feature of a network that determines the outcome of any dynamics that happens on top of it. However, an analytical approach to obtain connection probabilities between nodes associated to paths of…
Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…
In many areas such as computational biology, finance or social sciences, knowledge of an underlying graph explaining the interactions between agents is of paramount importance but still challenging. Considering that these interactions may…
Trust plays an essential role in an individual's decision-making. Traditional trust prediction models rely on pairwise correlations to infer potential relationships between users. However, in the real world, interactions between users are…
Connectivity is a fundamental property of quantum graphs, previously studied in the operator system model for matrix quantum graphs and via graph homomorphisms in the quantum adjacency matrix model. In this paper, we develop an algebraic…
There is a wealth of applied problems that can be posed as a dynamical system defined on a network with both attractive and repulsive interactions. Some examples include: understanding synchronization properties of nonlinear oscillator;,…
The \emph{$k$-restricted edge-connectivity} of a graph $G$, denoted by $\lambda_k(G)$, is defined as the minimum size of an edge set whose removal leaves exactly two connected components each containing at least $k$ vertices. This graph…
For a set $Q$ of points in the plane and a real number $\delta \ge 0$, let $\mathbb{G}_\delta(Q)$ be the graph defined on $Q$ by connecting each pair of points at distance at most $\delta$. We consider the connectivity of…
Graphs are a powerful mathematical model, and they are used to represent real-world structures in various fields. In many applications, real-world structures with high connectivity and robustness are preferable. For enhancing the…
In this article, we give conditions on a graph under which the Lov\'{a}sz' original bound of the graph can be improved by increasing the topological connectivity of its neighbourhood complex. We also work out conditions under which…
Network topology inference is a cornerstone problem in statistical analyses of complex systems. In this context, the fresh look advocated here permeates benefits from convex optimization and graph signal processing, to identify the…
We define a graph-based rate optimization problem and consider its computation, which provides a unified approach to the computation of various theoretical limits, including the (conditional) graph entropy, rate-distortion functions and…
The problem of connectivity assessment in an asymmetric network represented by a weighted directed graph is investigated in this article. A power iteration algorithm in a centralized implementation is developed first to compute the…
In some physical implementations of quantum computers, 2-qubit operations can be applied only on certain pairs of qubits. Compilation of a quantum circuit into one compliant to such qubit connectivity constraint results in an increase of…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
A famous conjecture of Tuza states that the minimum number of edges needed to cover all the triangles in a graph is at most twice the maximum number of edge-disjoint triangles. This conjecture was couched in a broader setting by Aharoni and…
Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful…
Core-periphery structure is an emerging property of a wide range of complex systems and indicate the presence of group of actors in the system with an higher number of connections among them and a lower number of connections with a sparsely…
Long-term state estimation over graphs remains challenging as current graph estimation methods scale poorly on large, long-term graphs. To address this, our work advances a current state-of-the-art graph sparsification algorithm, maximizing…
In this paper we define a regularized version of the analytic torsion for quotients of a symmetric space of non-positive curvature by arithmetic lattices. The definition is based on the study of the renormalized trace of the corresponding…