Related papers: Critical thresholds in stochastic rumors on trees
The frog model is a growing system of random walks where a particle is added whenever a new site is visited. A longstanding open question is how often the root is visited on the infinite $d$-ary tree. We prove the model undergoes a phase…
Spanning trees are fundamental for efficient communication in networks. For fault-tolerant communication, it is desirable to have multiple spanning trees to ensure resilience against failures of nodes and edges. To this end, various notions…
The threshold model is a simple but classic model of contagion spreading in complex social systems. To capture the complex nature of social influencing we investigate numerically and analytically the transition in the behavior of…
We study a simple model of information propagation in social networks, where two quantities are introduced: the spread factor, which measures the average maximal fraction of neighbors of a given node that interchange information among each…
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…
In this paper we consider a model of spreading information in heterogeneous systems wherein we have two kinds of objects. Some of them are active and others are passive. Active objects can, if they possess information, share it with an…
Community structure is an important factor in the behavior of real-world networks because it strongly affects the stability and thus the phase transition order of the spreading dynamics. We here propose a reversible social contagion model…
Biological systems can share and collectively process information to yield emergent effects, despite inherent noise in communication. While man-made systems often employ intricate structural solutions to overcome noise, the structure of…
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…
We consider the message complexity of verifying whether a given subgraph of the communication network forms a tree with specific properties both in the KT-$\rho$ (nodes know their $\rho$-hop neighborhood, including node IDs) and the KT-$0$…
We study the diffusion of a true and a false message (the rumor) in a social network. Upon hearing a message, individuals may believe it, disbelieve it, or debunk it through costly verification. Whenever the truth survives in steady state,…
The understanding and prediction of information diffusion processes on networks is a major challenge in network theory with many implications in social sciences. Many theoretical advances occurred due to stochastic spreading models.…
The Linear Threshold Model is a widely used model that describes how information diffuses through a social network. According to this model, an individual adopts an idea or product after the proportion of their neighbors who have adopted it…
Information and individual activities often spread globally through the network of social ties. While social contagion phenomena have been extensively studied within the framework of threshold models, it is common to make an assumption that…
We study a multi-call variant of the classic PUSH&PULL rumor spreading process where nodes can contact $k$ of their neighbors instead of a single one during both PUSH and PULL operations. We show that rumor spreading can be made faster at…
The contact process is a simple model for the spread of an infection in a structured population. We investigate the case when the underlying structure evolves dynamically as a degree-dependent dynamical percolation model. Starting with a…
Place an active particle at the root of the infinite $d$-ary tree and dormant particles at each non-root site. Active particles move towards the root with probability $p$ and otherwise move to a uniformly sampled child vertex. When an…
Critical thinking and skepticism are fundamental mechanisms that one may use to prevent the spreading of rumors, fake-news and misinformation. We consider a simple model in which agents without previous contact with the rumor, being…
We study a rumour model from a percolation theory and branching process point of view. The existence of a giant component is related to the event where the rumour, which started from the root of a tree, spreads out through an infinite…
We report numerical evidence that an epidemic-like model, which can be interpreted as the propagation of a rumor, exhibits critical behavior at a finite randomness of the underlying small-world network. The transition occurs between a…