Related papers: Two models of sparse and clustered dynamic network…
The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following…
Exchangeability is a desired statistical property of network ensembles requiring their invariance upon relabelling of the nodes. However combining sparsity of network ensembles with exchangeability is challenging. Here we propose a…
We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…
We study positive recurrence and transience of a two-station network in which the behavior of the server in each station is governed by a Markov chain with a finite number of server states; this service process can represent various service…
We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…
One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…
A graph G is c-closed if every two vertices with at least c common neighbors are adjacent to each other. Introduced by Fox, Roughgarden, Seshadhri, Wei and Wein [ICALP 2018, SICOMP 2020], this definition is an abstraction of the triadic…
Conventional studies of network growth models mainly look at the steady state degree distribution of the graph. Often long time behavior is considered, hence the initial condition is ignored. In this contribution, the time evolution of the…
Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques,…
Stream graphs are a very useful mode of representation for temporal network data, whose richness offers a wide range of possible approaches. The various methods aimed at generalising the classical approaches applied to static networks are…
When modeling network data using a latent position model, it is typical to assume that the nodes' positions are independently and identically distributed. However, this assumption implies the average node degree grows linearly with the…
Exponential random graphs are important to model the structure of real-world complex networks. Here we solve the two-star model with degree-degree correlations in the sparse regime. The model constraints the average correlation between the…
Using probabilistic approach, the transient dynamics of sparsely connected Hopfield neural networks is studied for arbitrary degree distributions. A recursive scheme is developed to determine the time evolution of overlap parameters. As…
Based on the daily data of American and Chinese stock markets, the dynamic behavior of a financial network with static and dynamic thresholds is investigated. Compared with the static threshold, the dynamic threshold suppresses the large…
In this work, we study the topological transition on the associated networks in a model proposed by Saeedian et al. (Scientific Reports 2019 9:9726), which considers a coupled dynamics of node and link states. Our goal was to better…
Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes…