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This paper introduces a probabilistic approach for tracking the dynamics of unweighted and directed graphs using state-space models (SSMs). Unlike conventional topology inference methods that assume static graphs and generate point-wise…
We examine some agreement-dynamics models that are placed on directed random graphs. In such systems a fraction of sites $\exp(-z)$, where $z$ is the average degree, becomes permanently fixed or flickering. In the Voter model, which has no…
Signed networks allow us to model conflicting relationships and interactions, such as friend/enemy and support/oppose. These signed interactions happen in real-time. Modeling such dynamics of signed networks is crucial to understanding the…
A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…
We study the asymptotic properties of distributed consensus algorithms over switching directed random networks. More specifically, we focus on consensus algorithms over independent and identically distributed, directed random graphs, where…
We investigate a model of evolving random network, introduced by us previously {[}{\it Phys. Rev. Lett.} {\bf 83}, 5587 (1999){]} . The model is a generalization of the Bak-Sneppen model of biological evolution, with the modification that…
Nonlinear networked systems are of interest in several areas of research, such as multi-agent systems and social networks. In this paper, we examine the controllability of several classes of nonlinear networked dynamics on which the…
In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in…
A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…
Diverse equilibrium systems with heterogeneous interactions lie at the edge of stability. Such marginally stable states are dynamically selected as the most abundant ones or as those with the largest basins of attraction. On the other hand,…
We analyze a class of stochastic processes, referred to as asynchronous and semi-anonymous dynamics (ASD), over directed labeled random networks. These processes are a natural tool to describe general best-response and noisy best-response…
We introduce a probabilistic pairwise \emph{attraction--repulsion} model for opinion dynamics on multilayer social networks, in which agents hold layer-specific states and interact through random matchings that couple multiple, time-varying…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
The aim of this paper is to analyze a class of consensus algorithms with finite-time or fixed-time convergence for dynamic networks formed by agents with first-order dynamics. In particular, in the analyzed class a single evaluation of a…
Random graphs offer a useful mathematical representation of a variety of real world complex networks. Exponential random graphs, for example, are particularly suited towards generating random graphs constrained to have specified statistical…
This paper studies the statistical properties of the web of import-export relationships among world countries using a weighted-network approach. We analyze how the distributions of the most important network statistics measuring…
Understanding spreading dynamics will benefit society as a whole in better preventing and controlling diseases, as well as facilitating the socially responsible information while depressing destructive rumors. In network-based spreading…
We study asynchronous dynamics in a network of interacting agents updating their binary states according to a time-varying threshold rule. Specifically, agents revise their state asynchronously by comparing the weighted average of the…
We study dynamic networks under an undirected consensus communication protocol and with one state-dependent weighted edge. We assume that the aforementioned dynamic edge can take values over the whole real numbers, and that its behaviour…
We study a mathematical model of social diffusion on a symmetric weighted network where individual nodes' states gradually assimilate to local social norms made by their neighbors' average states. Unlike physical diffusion, this process is…