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We study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arises under various centrality measures, and…
Elucidating the mechanisms that lead to cooperation is still one of the main scientific challenges of current times, as many common cooperative scenarios remain elusive and at odds with Darwin's natural selection theory. Here, we study…
Recently, we introduced a quantity, "node weight", to describe the collaboration sharing or competition gain of the elements in the collaboration-competition networks, which can be well described by bipartite graphs. We find that the node…
Evolution produces complex and structured networks of interacting components in chemical, biological, and social systems. We describe a simple mathematical model for the evolution of an idealized chemical system to study how a network of…
Over the last two decades, network science has greatly advanced our understanding of how the collective behaviors of a complex system emerge from the interactions among its basic units. Multiplex networks, i.e. networks with many layers,…
Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the…
While traditional game models often simplify interactions among agents as static, real-world social relationships are inherently dynamic, influenced by both immediate payoffs and alternative information. Motivated by this fact, we introduce…
We study complex networks formed by triangulations and higher-dimensional simplicial complexes representing closed evolving manifolds. In particular, for triangulations, the set of possible transformations of these networks is restricted by…
Contagion processes have been proven to fundamentally depend on the structural properties of the interaction networks conveying them. Many real networked systems are characterized by clustered substructures representing either collections…
Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…
Many social and biological networks consist of communities - groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable interest in designing algorithms for detecting…
Ever since the Barab\'{a}si-Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured…
We study how the volatility, node- or link-based, affects the evolution of social networks in simple models. The model describes the competition between order -- promoted by the efforts of agents to coordinate -- and disorder induced by…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…
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…
Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…
Complex systems, represented as dynamic networks, comprise of components that influence each other via direct and/or indirect interactions. Recent research has shown the importance of using Higher-Order Networks (HONs) for modeling and…
The regulation of the cell state is a complex process involving several components. These complex dynamics can be modeled using Boolean networks, allowing us to explain the existence of different cell states and the transition between them.…
Contagion processes on networks, including disease spreading, information diffusion, or social behaviors propagation, can be modeled as simple contagion, i.e. involving one connection at a time, or as complex contagion, in which multiple…