Related papers: On the epidemic threshold of a network
The calculation of centrality measures is common practice in the study of networks, as they attempt to quantify the importance of individual vertices, edges, or other components. Different centralities attempt to measure importance in…
We study the following model of disease spread in a social network. At first, all individuals are either infected or healthy. Next, in discrete rounds, the disease spreads in the network from infected to healthy individuals such that a…
Human to human transmissible infectious diseases spread in a population using human interactions as its transmission vector. The early stages of such an outbreak can be modeled by a graph whose edges encode these interactions between…
We study the inverse eigenvector centrality problem on connected undirected graphs, namely, whether a given positive vector can be realized by assigning suitable edge weights. We provide a complete characterization in terms of stable sets…
A new measure to assess the centrality of vertices in an undirected and connected graph is proposed. The proposed measure, L1 centrality, can adequately handle graphs with weights assigned to vertices and edges. The study provides tools for…
Given a graph $G$, the adjacency matrix and degree diagonal matrix of $G$ are denoted by $A(G)$ and $D(G)$, respectively. In 2017, Nikiforov \cite{0007} proposed the $A_{\alpha}$-matrix: $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G),$ where…
Understanding how age-specific social contact patterns and susceptibility influence infectious disease transmission is crucial for accurate epidemic modeling. This study presents an eigenvector-based sensitivity analysis framework to…
A Chung-Lu random graph is an inhomogeneous Erd\H{o}s-R\'enyi random graph in which vertices are assigned average degrees, and pairs of vertices are connected by an edge with a probability that is proportional to the product of their…
Hypergraphs that can depict interactions beyond pairwise edges have emerged as an appropriate representation for modeling polyadic relations in complex systems. With the recent surge of interest in researching hypergraphs, the centrality…
Centrality describes the importance of nodes in a graph and is modeled by various measures. Its global analogue, called centralization, is a general formula for calculating a graph-level centrality score based on the node-level centrality…
The $k^{\text{th}}$ power of a graph $G=(V,E)$, $G^k$, is the graph whose vertex set is $V$ and in which two distinct vertices are adjacent if and only if their distance in $G$ is at most $k$. This article proves various eigenvalue bounds…
In this paper, a branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large…
In a network consisting of n nodes, our goal is to identify the most central k nodes with respect to the proposed definitions of centrality. Depending on the specific application, there exist several metrics for quantifying k-centrality,…
We study the spectra and eigenvectors of the adjacency matrices of scale-free networks when bi-directional interaction is allowed, so that the adjacency matrix is real and symmetric. The spectral density shows an exponential decay around…
The leading eigenvalue $\lambda$ of the adjacency matrix of a graph exerts much influence on the behavior of dynamical processes on that graph. It is thus relevant to relate notions of the importance (specifically, centrality measures) of…
Matrix-based centrality measures have enjoyed significant popularity in network analysis, in no small part due to our ability to rigorously analyze their behavior as parameters vary. Recent work has considered the relationship between…
Complex networks are characterized by heterogeneous distributions of the degree of nodes, which produce a large diversification of the roles of the nodes within the network. Several centrality measures have been introduced to rank nodes…
We investigate the containment of epidemic spreading in networks from a normative point of view. We consider a susceptible/infected model in which agents can invest in order to reduce the contagiousness of network links. In this setting, we…
The spreading of dangerous malware or faults in inter-dependent networks of electronics devices has raised deep concern, because from the ICT networks infections may propagate to other Critical Infrastructures producing the well-known…
Suppose that a cascade (e.g., an epidemic) spreads on an unknown graph, and only the infection times of vertices are observed. What can be learned about the graph from the infection times caused by multiple distinct cascades? Most of the…