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The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network…

We study the evolution of heterogeneous networks of oscillators subject to a state-dependent interconnection rule. We find that heterogeneity in the node dynamics is key in organizing the architecture of the functional emerging networks. We…

Many social, technological, biological, and economical systems are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes. However, most…

The identification of important nodes in complex networks is an area of exciting growth due to its applications across various disciplines like disease controlling, community finding, data mining, network system controlling, just to name a…

Dynamic network data analysis requires joint modelling individual snapshots and time dynamics. This paper proposes a new two-way heterogeneity model towards this goal. The new model equips each node of the network with two heterogeneity…

We propose a dynamical process for network evolution, aiming at explaining the emergence of the small world phenomenon, i.e., the statistical observation that any pair of individuals are linked by a short chain of acquaintances computable…

We propose a dynamical model of price formation on a spatial market where sellers and buyers are placed on the nodes of a graph, and the distribution of the buyers depends on the positions and prices of the sellers. We find that, depending…

Finding accurate reduced descriptions for large, complex, dynamically evolving networks is a crucial enabler to their simulation, analysis, and, ultimately, design. Here we propose and illustrate a systematic and powerful approach to…

In this paper, based on the gravity principle of classical physics, we propose a tunable gravity-based model, which considers tag usage pattern to weigh both the mass and distance of network nodes. We then apply this model in solving the…

The movement of atmospheric air masses can be seen as a continuous and complex flow of particles hovering over our planet. It can however be locally simplified by considering three-dimensional trajectories of air masses connecting distant…

Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…

Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…

Although static networks have been extensively studied in machine learning, data mining, and AI communities for many decades, the study of dynamic networks has recently taken center stage due to the prominence of social media and its…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…

The connectivity properties of a weight-bearing network are exploited to enhance it's capacity. We study a 2-d network of sites where the weight-bearing capacity of a given site depends on the capacities of the sites connected to it in the…

Gravity is one of the most prominent models used across various social areas, including economics, demography, mobility, politics, and other systems where spatial interactions are relevant. The model represents a flexible approach that…

Many classes of network growth models have been proposed in the literature for capturing real-world complex networks. Existing research primarily focuses on global characteristics of these models, e.g., degree distribution. We aim to shift…

The study of dynamical systems on networks, describing complex interactive processes, provides insight into how network structure affects global behaviour. Yet many methods for network dynamics fail to cope with large or partially-known…

We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all…

Spatial dependency and spatial embedding are basic physical properties of many phenomena modeled by networks. The most indicated computational environment to deal with spatial information is to use Georeferenced Information System (GIS) and…