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The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…
Many pathogens spread primarily via direct contact between infected and susceptible hosts. Thus, the patterns of contacts or contact network of a population fundamentally shapes the course of epidemics. While there is a robust and growing…
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…
A growing set of applications consider the process of network formation by using subgraphs as a tool for generating the network topology. One of the pressing research challenges is thus to be able to use these subgraphs to understand the…
Statistical analysis on networks has received growing attention due to demand from various emerging applications. In dynamic networks, one of the key interests is to model the event history of time-stamped interactions amongst nodes. We…
Can evolving networks be inferred and modeled without directly observing their nodes and edges? In many applications, the edges of a dynamic network might not be observed, but one can observe the dynamics of stochastic cascading processes…
Since the development of writing 5000 years ago, human-generated data gets produced at an ever-increasing pace. Classical archival methods aimed at easing information retrieval. Nowadays, archiving is not enough anymore. The amount of data…
Dynamic processes in complex networks are crucial for better understanding collective behavior in human societies, biological systems, and the internet. In this paper, we first focus on the continuous Markov-based modeling of evolving…
We introduce a new approach to connectivity-dependent properties of diluted systems, which is based on the transfer-matrix formulation of the percolation problem. It simultaneously incorporates the connective properties reflected in…
Recent studies have investigated various dynamic processes characterizing collective behaviors in real-world systems. However, these dynamics have been studied individually in specific contexts. In this article, we present a holistic…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
By event-driven molecular dynamics simulations we investigate magneto-transport in a two-dimensional model with randomly distributed scatterers close to the field-induced localization transition. This transition is generated by percolating…
We introduce a new class of latent process models for dynamic relational network data with the goal of detecting time-dependent structure. Network data are often observed over time, and static network models for such data may fail to…
Simultaneous recordings from many neurons hide important information and the connections characterizing the network remain generally undiscovered despite the progresses of statistical and machine learning techniques. Discerning the presence…
Scientific fields differ in terms of their subject matter, research techniques, collaboration sizes, rates of growth, and so on. We investigate whether common dynamics might lurk beneath these differences, affecting how scientific fields…
As a fundamental structural transition in complex networks, core percolation is related to a wide range of important problems. Yet, previous theoretical studies of core percolation have been focusing on the classical Erd\H{o}s-R\'enyi…
The study of complex networks that account for different types of interactions has become a subject of interest in the last few years, specially because its representational power in the description of users interactions in diverse online…
Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem.…
We introduce the simplest model which relates the emergence of collective social/economic phenomena to the existence of a (possibly self-organized) percolation transition. We suggest a series of extensions to financial, economic, political…