Related papers: Graph reliability evaluation via random $K$-out-of…
The resilience of a complex interconnected system concerns the size of the macroscopic functioning node clusters after external perturbations based on a random or designed scheme. For a representation of the interconnected systems with…
In weighted graphs the shortest path between two nodes is often reached through an indirect path, out of all possible connections, leading to structural redundancies which play key roles in the dynamics and evolution of complex networks. We…
In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
Degree-based graph construction is an ubiquitous problem in network modeling, ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive…
In this paper, we introduce a new model to study network reliability with node failures. This model, strongly connected node reliability, is the directed variant of node reliability and measures the probability that the operational vertices…
Multi-agent networks are often modeled as interaction graphs, where the nodes represent the agents and the edges denote some direct interactions. The robustness of a multi-agent network to perturbations such as failures, noise, or malicious…
Graph-based tests are a class of non-parametric two-sample tests useful for analyzing high-dimensional data. The test statistics are constructed from similarity graphs (such as K-minimum spanning tree), and consequently, their performance…
The feed-forward relationship naturally observed in time-dependent processes and in a diverse number of real systems -such as some food-webs and electronic and neural wiring- can be described in terms of so-called directed acyclic graphs…
Let $G$ be a graph of order $n$ and let $u,v$ be vertices of $G$. Let $\kappa_G(u,v)$ denote the maximum number of internally disjoint $u$-$v$ paths in $G$. Then the average connectivity $\overline{\kappa}(G)$ of $G$, is defined as $…
Let the class A of graphs be bridge-addable; that is, whenever a graph G in A has vertices u and v in different components then the graph G+uv is in A. For a random graph sampled uniformly from the graphs in A on vertex set {1,..,n}, there…
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out degree of a vertex in the resulting directed graph. This…
Given two distributions F and G on the nonnegative integers we propose an algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from F and G, respectively, that with high probability will be graphical, that…
The operability of a network concerns its ability to remain operational, despite possible failures in its links or equipment. One may model the network through a graph to evaluate and increase this operability. Its vertices and edges…
Graph-theoretic tools and techniques have seen wide use in the multi-agent systems literature, and the unpredictable nature of some multi-agent communications has been successfully modeled using random communication graphs. Across both…
This work is divided into two main parts. The first part is devoted to exploring the connectivity of random subgraphs of cartesian products of $K_1$, $K_2$, and $P_3$. In the second part, the author presents a short review of the results…
A common model of robustness of a graph against random failures has all vertices operational, but the edges independently operational with probability $p$. One can ask for the probability that all vertices can communicate ({\em all-terminal…
The neighbor connectivity of a graph $G$ is the least number of vertices such that removing their closed neighborhoods from $G$ results in a graph that is disconnected, complete or empty. If a~graph is used to model the topology of an…
The analysis of complex networks has so far revolved mainly around the role of nodes and communities of nodes. However, the dynamics of interconnected systems is commonly focalised on edge processes, and a dual edge-centric perspective can…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…