Related papers: Generalized threshold-based epidemics in random gr…
We propose a bond-percolation model intended to describe the consumption, and eventual exhaustion, of resources in transport networks. Edges forming minimum-length paths connecting demanded origin-destination nodes are removed if below a…
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…
This work shows potentials for rapid self-organisation of sensor networks where nodes collaborate to relay messages to a common data collecting unit (sink node). The study problem is, in the sense of graph theory, to find a shortest path…
We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is…
We study asymptotic percolation as $N\to \infty$ in an infinite random graph ${\cal G}_N$ embedded in the hierarchical group of order $N$, with connection probabilities depending on an ultrametric distance between vertices. ${\cal G}_N$ is…
Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible-infected-susceptible setting, spectral conditions characterise whether the disease vanishes. However, modelling human…
In this paper a random graph model $G_{\mathbb{Z}^2_N,p_d}$ is introduced, which is a combination of fixed torus grid edges in $(\mathbb{Z}/N \mathbb{Z})^2$ and some additional random ones. The random edges are called long, and the…
Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…
Multigraphs are graphs in which multiple links between pairs of nodes are allowed, whereas they are forbidden in simple graphs, the latter being widely used in network science. Simple graphs generated by the configuration model have served…
The threshold model has been widely adopted as a prototype for studying contagion processes on social networks. In this paper, we consider individual interactions in groups of three or more vertices and study the threshold model on…
Let $G=G(d)$ be a random graph with a given degree sequence $d$, such as a random $r$-regular graph where $r\ge 3$ is fixed and $n=|G|\to\infty$. We study the percolation phase transition on such graphs $G$, i.e., the emergence as $p$…
The spatial structure of populations is a key element in the understanding of the large scale spreading of epidemics. Motivated by the recent empirical evidence on the heterogeneous properties of transportation and commuting patterns among…
In this paper, we derive nonasymptotic theoretical bounds for the influence in random graphs that depend on the spectral radius of a particular matrix, called the Hazard matrix. We also show that these results are generic and valid for a…
Motivated by the analysis of social networks, we study a model of random networks that has both a given degree distribution and a tunable clustering coefficient. We consider two types of growth processes on these graphs: diffusion and…
The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system.…
We study intersection properties of two or more independent tree-like random graphs. Our setting encompasses critical, possibly long range, Bernoulli percolation clusters, incipient infinite clusters, as well as critical branching random…
We introduce the heterogeneous-$k$-core, which generalizes the $k$-core, and contrast it with bootstrap percolation. Vertices have a threshold $k_i$ which may be different at each vertex. If a vertex has less than $k_i$ neighbors it is…
One model of real-life spreading processes is First Passage Percolation (also called SI model) on random graphs. Social interactions often follow bursty patterns, which are usually modelled with i.i.d.~heavy-tailed passage times on edges.…
Edge-based percolation methods can be used to analyze disease transmission on complex social networks. This allows us to include complex social heterogeneity in our models while maintaining tractability. Here we review the seminal works on…
Percolation on complex networks is used both as a model for dynamics on networks, such as network robustness or epidemic spreading, and as a benchmark for our models of networks, where our ability to predict percolation measures our ability…