Related papers: On Connectivity and Robustness in Random Intersect…
We consider the problem of diffusing information in networks that contain malicious nodes. We assume that each normal node in the network has no knowledge of the network topology other than an upper bound on the number of malicious nodes in…
In typical online social networks, users are linked by symmetric friend relations and can define circles of friends based on shared interests. In this paper, we look at social networks where users form links subject to both friendships and…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
This paper contains the proofs of Theorems 2 and 3 of the article entitled Random Electrical Networks on Complete Graphs, written by the same authors and published in the Journal of the London Mathematical Society, vol. 30 (1984), pp.…
In this note we establish a resilience version of the classical hitting time result of Bollob\'{a}s and Thomason regarding connectivity. A graph $G$ is said to be $\alpha$-resilient with respect to a monotone increasing graph property…
We employ the mathematical programming approach in conjunction with the graph theory to study the structure of correspondent banking networks. Optimizing the network requires decisions to be made to onboard, terminate or restrict the bank…
We find conditions for the connectivity of inhomogeneous random graphs with intermediate density. Our results generalize the classical result for G(n, p), when p = c log n/n. We draw n independent points X_i from a general distribution on a…
We establish the conditions under which several algorithmically exploitable structural features hold for random intersection graphs, a natural model for many real-world networks where edges correspond to shared attributes. Specifically, we…
Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many…
We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…
Let $\Lambda(T)$ denote the set of leaves in a tree $T$. One natural problem is to look for a spanning tree $T$ of a given graph $G$ such that $\Lambda(T)$ is as large as possible. This problem is called maximum leaf number, and it is a…
Network reliability is a well-studied problem that requires to measure the probability that a target node is reachable from a source node in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of…
Random $s$-intersection graphs have recently received considerable attention in a wide range of application areas. In such a graph, each vertex is equipped with a set of items in some random manner, and any two vertices establish an…
Link residual closeness is a newly proposed measure for network vulnerability. In this model, vertices are perfectly reliable and the links fail independently of each other. It measures the vulnerability even when the removal of links does…
In recent years, the notion of r-robustness for the communication graph of the network has been introduced to address the challenge of achieving consensus in the presence of misbehaving agents. Higher r-robustness typically implies higher…
In this paper, we investigate the exact asymptotic behavior of the connectivity probability in the Erdos-Renyi graph G(n,p), under different asymptotic assumptions on the edge probability p=p(n). We propose a novel approach based on the…
Two models are introduced to investigate graph matching in the presence of corrupt nodes. The weak model, inspired by biological networks, allows one or both networks to have a positive fraction of molecular entities interact randomly with…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…
We characterize some asymptotic properties of edge exchangeable random graphs in terms of the measure used to generate them. In particular, we give a necessary and sufficient condition for eventual forever connectedness, a sufficient…
We study the connectivity properties of random Bluetooth graphs that model certain "ad hoc" wireless networks. The graphs are obtained as "irrigation subgraphs" of the well-known random geometric graph model. There are two parameters that…