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Networks are widely used to model the interaction between individual dynamical systems. In many instances, the total number of units as well as the interaction coupling are not fixed in time, but rather constantly evolve. In terms of…
How do real graphs evolve over time? What are ``normal'' growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large…
We consider weakly interacting jump processes on time-varying random graphs with dynamically changing multi-color edges. The system consists of a large number of nodes in which the node dynamics depends on the joint empirical distribution…
We study a recent model for edge exchangeable random graphs introduced by Crane and Dempsey; in particular we study asymptotic properties of the random simple graph obtained by merging multiple edges. We study a number of examples, and show…
We introduce a class of generative network models that insert edges by connecting the starting and terminal vertices of a random walk on the network graph. Within the taxonomy of statistical network models, this class is distinguished by…
We consider an SIR-type (Susceptible $\to$ Infected $\to$ Recovered) stochastic epidemic process with multiple modes of transmission on a contact network. The network is given by a random graph following a multilayer configuration model…
The Watts-Strogatz algorithm of transferring the square lattice to a small world network is modified by introducing preferential rewiring constrained by connectivity demand. The evolution of the network is two-step: sequential preferential…
This article proposes methods to model nonstationary temporal graph processes. This corresponds to modelling the observation of edge variables (relationships between objects) indicating interactions between pairs of nodes (or objects)…
Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of…
We propose an autoregressive framework for modelling dynamic networks with dependent edges. It encompasses models that accommodate, for example, transitivity, degree heterogenenity, and other stylized features often observed in real network…
Many important real-world networks manifest "small-world" properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is "preferential attachment", where nodes…
We introduce a new oriented evolving graph model inspired by biological networks. A node is added at each time step and is connected to the rest of the graph by random oriented edges emerging from older nodes. This leads to a statistical…
We study a random graph model with preferential edge attachment and detachment through the embedding into a generalized Yule model. We show that the in-degree distribution of a vertex chosen uniformly at random follows a power law in the…
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…
We consider Susceptible-Infected-Recovered (SIR) models on dense dynamic random graphs, in which the joint dynamics of vertices and edges are co-evolutionary, i.e., they influence each other bidirectionally. In particular, edges appear and…
The edge flipping is a non-reversible Markov chain on a given connected graph, which is defined by Chung and Graham in [CG12]. In the same paper, its eigenvalues and stationary distributions for some classes of graphs are identified. We…
A first-order percolation transition, called explosive percolation, was recently discovered in evolution networks with random edge selection under a certain restriction. However, the network percolation with more realistic evolution…
We investigate a growing network model that combines preferential and uniform attachment with two distinct mechanisms of edge deletion. In addition to the usual uniform probability edge deletion, we introduce a novel node-based rule in…
In this paper, we proposed an evolving model via the hypergraph to illustrate the evolution of the citation network. In the evolving model, we consider the mechanism combined with preferential attachment and the aging influence. Simulation…
Motivated by the problem of detecting a change in the evolution of a network, we consider the preferential attachment random graph model with a time-dependent attachment function. Our goal is to detect whether the attachment mechanism…