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We propose an Embedding Network Autoregressive Model for multivariate networked longitudinal data. We assume the network is generated from a latent variable model, and these unobserved variables are included in a structural peer effect…
Analyzing 9,000 urban areas' street networks, we identify properties, including extreme betweenness centrality heterogeneity, that typical spatial network models fail to explain. Accordingly we propose a universal, parsimonious, generative…
In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes…
In an affiliation network vertices are linked to attributes and two vertices are declared adjacent whenever they share a common attribute. For example, two customers of an internet shop are called adjacent if they have purchased the same or…
A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,\ldots$, with probability $\pi_1>0$ a new vertex with one…
A recent line of work has established intriguing connections between the generalization/compression properties of a deep neural network (DNN) model and the so-called layer weights' stable ranks. Intuitively, the latter are indicators of the…
We study the growth of a directed transportation network, such as a food web, in which links carry resources. We propose a growth process in which new nodes (or species) preferentially attach to existing nodes with high indegree (in…
We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie with a certain radius. From a modelling…
What are the key-features that enable an information diffusion model to explain the inherent dynamic, and often competitive, nature of real-world propagation phenomena? In this paper we aim to answer this question by proposing a novel class…
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…
Cooperation is observed widely in nature and is thought an essential component of many evolutionary processes, yet the mechanisms by which it arises and persists are still unclear. Among several theories, network reciprocity -- a model of…
Introduced recently, the concept of hierarchical degree allows a more complete characterization of the topological context of a node in a complex network than the traditional node degree. This article presents analytical characterization…
One of the most important features observed in real networks is that, as a network's topology evolves so does the network's ability to perform various complex tasks. To explain this, it has also been observed that as a network grows certain…
We study the emergence of coherence in complex networks of mutually coupled non-identical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, on the isolated dynamics of the elements and the…
Considerable attention has been paid, in recent years, to the use of networks in modeling complex real-world systems. Among the many dynamical processes involving networks, propagation processes -- in which final state can be obtained by…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
We introduce a new threshold model of social networks, in which the nodes influenced by their neighbours can adopt one out of several alternatives. We characterize the graphs for which adoption of a product by the whole network is possible…
How does social network structure amplify or stifle behavior diffusion? Existing theory suggests that when social reinforcement makes the adoption of behavior more likely, it should spread more -- both farther and faster -- on clustered…
In this paper, we advance the network theory of aging and mortality by developing a causal mathematical model for the mortality rate. First, we show that in large networks, where health deficits accumulate at nodes representing health…
A new simple model of diffusion of innovations in a social network with upgrading costs is introduced. Agents are characterized by a single real variable, their technological level. According to local information agents decide whether to…