Related papers: The cone percolation on $\bbT_d$
Rumours have existed for a long time and have been known for serious consequences. The rapid growth of social media platforms has multiplied the negative impact of rumours; it thus becomes important to early detect them. Many methods have…
Bootstrap percolation is a process that is used to model the spread of an infection on a given graph. In the model considered here each vertex is equipped with an individual threshold. As soon as the number of infected neighbors exceeds…
We consider robustness and percolation properties of the networks of networks, in which random nodes in different individual networks (layers) can be interdependent. We explore the emergence of the giant mutually connected component,…
We investigate the long-time evolution of branching diffusion processes (starting with a finite number of particles) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. In the…
We consider the following interacting particle system: There is a ``gas'' of particles, each of which performs a continuous-time simple random walk on $\mathbb{Z}^d$, with jump rate $D_A$. These particles are called $A$-particles and move…
We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards…
A novel hierarchical model of complex network is proposed, and information propagation process taking place on top of the network is investigated. Our model is demonstrated to have small world property. We found that the frequency…
Rumour spreading is a protocol for modelling the spread of information through a network via user-to-user interaction. The Spatial Preferred Attachment (SPA) model is a random graph model for complex networks: vertices are placed in a…
We consider percolation on the discrete torus $\mathbb{Z}_n^d$ at $p_c(\mathbb{Z}^d)$, the critical value for percolation on the corresponding infinite lattice $\mathbb{Z}^d$, and within the scaling window around it. We assume that $d$ is a…
In this paper, we consider a random network such that there could be a link between any two nodes in the network with a certain probability (plink). Diffusion is the phenomenon of spreading information throughout the network, starting from…
In the last two decades, network science has blossomed and influenced various fields, such as statistical physics, computer science, biology and sociology, from the perspective of the heterogeneous interaction patterns of components…
Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…
It is well known that tree-based theories can describe the properties of undirected clustered networks with extremely accurate results [S. Melnik, \textit{et al}. Phys. Rev. E 83, 036112 (2011)]. It is reasonable to suggest that a motif…
We discuss how spreading processes on temporal networks are impacted by the shape of their inter-event time distributions. Through simple mathematical arguments and toy examples, we find that the key factor is the ordering in which events…
One major feature of social networks (e.g., massive online social networks) is the dissemination of information, such as news, rumors and opinions. Information can be propagated via natural connections in written, oral or electronic forms.…
Jigsaw percolation is a model for the process of solving puzzles within a social network, which was recently proposed by Brummitt, Chatterjee, Dey and Sivakoff. In the model there are two graphs on a single vertex set (the `people' graph…
Information diffusion is a fundamental process that takes place over networks. While it is rarely realistic to observe the individual transmissions of the information diffusion process, it is typically possible to observe when individuals…
Extended-range percolation is a robust percolation process that has relevance for quantum communication problems. In extended-range percolation nodes can be trusted or untrusted. Untrusted facilitator nodes are untrusted nodes that can…
We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate…
Statistical properties of coherent radiation propagating in a quasi - 1D random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission…