Related papers: Robustness of Regular Graphs Based on Natural Conn…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
Graphs are pervasive in our everyday lives, with relevance to biology, the internet, and infrastructure, as well as numerous other applications. It is thus necessary to have an understanding as to how quickly a graph disintegrates, whether…
Real networks are often dynamic. In response to it, analyses of algorithms on {\em dynamic networks} attract more and more attentions in network science and engineering. Random walks on dynamic graphs also have been investigated actively in…
In certain instances an electric network transforms in natural ways by the addition or removal of an edge. This can have interesting consequences for random walks, in light of the known relationships between electric resistance and random…
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…
Given an increasing graph property $\mathcal{P}$, a graph $G$ is $\alpha$-resilient with respect to $\mathcal{P}$ if, for every spanning subgraph $H\subseteq G$ where each vertex keeps more than a $(1-\alpha)$-proportion of its neighbours,…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
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…
Deep learning models have been shown to be vulnerable to adversarial attacks. This perception led to analyzing deep learning models not only from the perspective of their performance measures but also their robustness to certain types of…
We propose a consistent approach to the statistics of the shortest paths in random graphs with a given degree distribution. This approach goes further than a usual tree ansatz and rigorously accounts for loops in a network. We calculate the…
We investigate a special case of hereditary property in graphs, referred to as {\em robustness}. A property (or structure) is called robust in a graph $G$ if it is inherited by all the connected spanning subgraphs of $G$. We motivate this…
We study the algebraic connectivity for several classes of random semi-regular graphs. For large random semi-regular bipartite graphs, we explicitly compute both their algebraic connectivity and as well as the full spectrum distribution.…
Let G be a connected graph. The toughness of G is defined as t(G)=min{\frac{|S|}{c(G-S)}}, in which the minimum is taken over all proper subsets S\subset V(G) such that c(G-S)\geq 2 where c(G-S) denotes the number of components of G-S.…
We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…
Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
We present analytic and numeric results for percolation in a network formed of interdependent spatially embedded networks. We show results for a treelike and a random regular network of networks each with $(i)$ unconstrained interdependent…