Related papers: Isolation probabilities in dynamic soft random geo…
Random geometric graphs result from taking $n$ uniformly distributed points in the unit cube, $[0,1]^d$, and connecting two points if their Euclidean distance is at most $r$, for some prescribed $r$. We show that monotone properties for…
We consider random graphs with uniformly bounded edges on a Poisson point process conditioned to contain the origin. In particular we focus on the random connection model, the Boolean model and Miller-Abrahams random resistor network with…
The asynchronous rumor algorithm spreading propagates a piece of information, the so-called rumor, in a network. Starting with a single informed node, each node is associated with an exponential time clock with rate $1$ and calls a random…
When studying networks using random graph models, one is sometimes faced with situations where the notion of adjacency between nodes reflects multiple constraints. Traditional random graph models are insufficient to handle such situations.…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated…
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…
In~\cite{bgs2013}, exclusion sensitivity and exclusion stability for symmetric exclusion processes on graphs were defined as a natural analogue of noise sensitivity and noise stability in this setting. As these concepts were defined for any…
We present a modeling framework for dynamical and bursty contact networks made of agents in social interaction. We consider agents' behavior at short time scales, in which the contact network is formed by disconnected cliques of different…
We generalize the technique of smoothed analysis to distributed algorithms in dynamic network models. Whereas standard smoothed analysis studies the impact of small random perturbations of input values on algorithm performance metrics,…
Motivated by potential applications in power systems, we study a problem of optimizing a sum of $n$ convex functions on dynamic networks of $n$ nodes when each function is known to only a single node. The nodes' variables, while satisfy…
Graph models are widely used to analyse diffusion processes embedded in social contacts and to develop applications. A range of graph models are available to replicate the underlying social structures and dynamics realistically. However,…
In this work we make an attempt to understand social networks from a mathematical viewpoint. In the first instance we consider a network where each node representing an individual can connect with a neighbouring node with a certain…
Consider a graph where the sites are distributed in space according to a Poisson point process on $\mathbb R^n$. We study a population evolving on this network, with individuals jumping between sites with a rate which decreases…
We study a model for a statistical network formed by interactions between its nodes and links. Each node can be in one of two states (Ising spin up or down) and the node-link interaction facilitates linking between the like nodes. For high…
In this paper, we consider a vehicular network in which the wireless nodes are located on a system of roads. We model the roadways, which are predominantly straight and randomly oriented, by a Poisson line process (PLP) and the locations of…
Random walks are a common model for exploration and discovery of complex networks. While numerous algorithms have been proposed to map out an unknown network, a complementary question arises: in a known network, which nodes and edges are…
Broadcasting algorithms are important building blocks of distributed systems. In this work we investigate the typical performance of the classical and well-studied push model. Assume that initially one node in a given network holds some…
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…
We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple…