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Graph Neural Networks (GNNs) are gaining extensive attention for their application in graph data. However, the black-box nature of GNNs prevents users from understanding and trusting the models, thus hampering their applicability. Whereas…
Formation and fragmentation of networks is typically studied using percolation theory, but most previous research has been restricted to studying a phase transition in cluster size, examining the emergence of a giant component. This…
We introduce a numerical method to solve epidemic models on the underlying topology of complex networks. The approach exploits the mean-field like rate equations describing the system and allows to work with very large system sizes, where…
Inspired by the importance of inhibitory and excitatory couplings in the brain, we analyze the largest eigenvalue statistics of random networks incorporating such features. We find that the largest real part of eigenvalues of a network,…
In network theory, Pearson's correlation coefficients are most commonly used to measure the degree assortativity of a network. We investigate the behavior of these coefficients in the setting of directed networks with heavy-tailed degree…
There is great interest in predicting rare and extreme events in complex systems, and in particular, understanding the role of network topology in facilitating such events. In this work, we show that degree dispersion -- the fact that the…
Network epidemiology has become a core framework for investigating the role of human contact patterns in the spreading of infectious diseases. In network epidemiology represents the contact structure as a network of nodes (individuals)…
Nowadays, the emergence of online services provides various multi-relation information to support the comprehensive understanding of the epidemic spreading process. In this Letter, we consider the edge weights to represent such multi-role…
We study a general epidemic model with arbitrary recovery rate distributions. This simple deviation from the standard setup is sufficient to prove that heterogeneity in the dynamical parameters can be as important as the more studied…
The contact structure between hosts has a critical influence on disease spread. However, most networkbased models used in epidemiology tend to ignore heterogeneity in the weighting of contacts. This assumption is known to be at odds with…
In many complex systems, the dynamic processes that take place on a network and the changes in the network topology are intertwined. Here, we propose a model of coevolutionary dynamics of information spreading which is accompanied with link…
Many complex systems involve direct interactions among more than two entities and can be represented by hypergraphs, in which hyperedges encode higher-order interactions among an arbitrary number of nodes. To analyze structures and dynamics…
Network science is a powerful tool for analyzing complex systems in fields ranging from sociology to engineering to biology. This paper is focused on generative models of large-scale bipartite graphs, also known as two-way graphs or…
We consider a finite structured population of mobile individuals that strategically explore a network using a Markov movement model and interact with each other via a public goods game. We extend the model of Erovenko et al. (2019) from…
Degree distributions of graph representations for compact urban patterns are scale-dependent. Therefore, the degree statistics alone does not give us the enough information to reach a qualified conclusion on the structure of urban spatial…
This paper leverages linear systems theory to propose a principled measure of complexity for network systems. We focus on a network of first-order scalar linear systems interconnected through a directed graph. By locally filtering out the…
We study neural connectivity in cultures of rat hippocampal neurons. We measure the neurons' response to an electric stimulation for gradual lower connectivity, and characterize the size of the giant cluster in the network. The connectivity…
A key problem in the study and design of complex systems is the apparent disconnection between the microscopic and the macroscopic. It is not straightforward to identify the local interactions that give rise to an observed global…
We propose a maximally disassortative (MD) network model which realizes a maximally negative degree-degree correlation, and study its percolation transition to discuss the effect of a strong degree-degree correlation on the percolation…
Many of the structural characteristics of a network depend on the connectivity with and within the hubs. These dependencies can be related to the degree of a node and the number of links that a node shares with nodes of higher degree. In…