Related papers: Temporal connectivity of Random Geometric Graphs
We propose a procedure to generate dynamical networks with bursty, possibly repetitive and correlated temporal behaviors. Regarding any weighted directed graph as being composed of the accumulation of paths between its nodes, our…
In this paper we study the synchronization properties of random geometric graphs. We show that the onset of synchronization takes place roughly at the same value of the order parameter that a random graph with the same size and average…
A graph G is c-closed if every two vertices with at least c common neighbors are adjacent to each other. Introduced by Fox, Roughgarden, Seshadhri, Wei and Wein [ICALP 2018, SICOMP 2020], this definition is an abstraction of the triadic…
Connectivity (or equivalently, unweighted maximum flow) is an important measure in graph theory and combinatorial optimization. Given a graph $G$ with vertices $s$ and $t$, the connectivity $\lambda(s,t)$ from $s$ to $t$ is defined to be…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
How do real graphs evolve over time? What are ``normal'' growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large…
Temporal graphs are graphs whose edges are labelled with times at which they are active. Their time-sensitivity provides a useful model of real networks, but renders many problems studied on temporal graphs more computationally complex than…
Connectivity of temporal graphs has been widely studied both as graph theory and as gossip theory. In particular, it is well known that in order to connect every vertex to every other, a temporal graph needs to have at least $2n-4$ edges…
This paper considers generalised network, intended as networks where (a) the edges connecting the nodes are nonlinear, and (b) stochastic processes are continuously indexed over both vertices and edges. Such topological structures are…
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…
Many real-world graphs or networks are temporal, e.g., in a social network persons only interact at specific points in time. This information directs dissemination processes on the network, such as the spread of rumors, fake news, or…
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…
A temporal graph has an edge set that may change over discrete time steps, and a temporal path (or walk) must traverse edges that appear at increasing time steps. Accordingly, two temporal paths (or walks) are temporally disjoint if they do…
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,…
A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…
We study the connectivity of random subgraphs of the $d$-dimensional Hamming graph $H(d, n)$, which is the Cartesian product of $d$ complete graphs on $n$ vertices. We sample the random subgraph with an i.i.d.\ Bernoulli bond percolation on…
The unit ball random geometric graph $G=G^d_p(\lambda,n)$ has as its vertices $n$ points distributed independently and uniformly in the $d$-dimensional unit ball, with two vertices adjacent if and only if their $l_p$-distance is at most…
Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in…
k-connectivity of random graphs is a fundamental property indicating reliability of multi-hop wireless sensor networks (WSN). WSNs comprising of sensor nodes with limited power resources are modeled by random graphs with unreliable nodes,…
Data of physical contacts and face-to-face communications suggest temporally varying networks as the media on which infections take place among humans and animals. Epidemic processes on temporal networks are complicated by complexity of…