Related papers: Temporal percolation in activity driven networks

In recent years, many variants of percolation have been used to study network structure and the behavior of processes spreading on networks. These include bond percolation, site percolation, $k$-core percolation, bootstrap percolation, the…

In this paper I introduce a framework for modeling temporal communication networks and dynamical processes unfolding on such networks. The framework originates from the realization that there is a meaningful division of temporal…

Temporal networks are such networks where nodes and interactions may appear and disappear at various time scales. With the evidence of ubiquity of temporal networks in our economy, nature and society, it's urgent and significant to focus on…

Most instruments - formalisms, concepts, and metrics - for social networks analysis fail to capture their dynamics. Typical systems exhibit different scales of dynamics, ranging from the fine-grain dynamics of interactions (which recently…

Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network…

We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which…

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…

Network properties govern the rate and extent of spreading processes on networks, from simple contagions to complex cascades. Recent advances have extended the study of spreading processes from static networks to temporal networks, where…

During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…

Although many tools have been developed and employed to characterize temporal networks, the issue of how to compare them remains largely open. It depends indeed on what features are considered as relevant, and on the way the differences in…

In evolving complex systems such as air traffic and social organizations, collective effects emerge from their many components' dynamic interactions. While the dynamic interactions can be represented by temporal networks with nodes and…

The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in…

Temporal networks model a variety of important phenomena involving timed interactions between entities. Existing methods for machine learning on temporal networks generally exhibit at least one of two limitations. First, time is assumed to…

We study numerically statistical properties and dynamical disease propagation using a percolation model on a one dimensional small world network. The parameters chosen correspond to a realistic network of school age children. We found that…

Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…

Spreading processes on networks are ubiquitous in both human-made and natural systems. Understanding their behavior is of broad interest; from the control of epidemics to understanding brain dynamics. While in some cases there exists a…

Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to…

Static wireless networks are by now quite well understood mathematically through the random geometric graph model. By contrast, there are relatively few rigorous results on the practically important case of mobile networks, in which the…

The collaboration network is an example of a social network which has both non-trivial temporal and spatial dependence. Based on the observations of collaborations in Physical Review Letters, a model of collaboration network is proposed…

Epidemiological contact network models have emerged as an important tool in understanding and predicting the spread of infectious disease, due to their capacity to engage individual heterogeneity that may underlie essential dynamics of a…