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We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
Many natural, complex systems are remarkably stable thanks to an absence of feedback acting on their elements. When described as networks, these exhibit few or no cycles, and associated matrices have small leading eigenvalues. It has been…
We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The transition…
We study network properties of networks evolving in time based on optimal transport principles. These evolve from a structure covering uniformly a continuous space towards an optimal design in terms of optimal transport theory. At…
It is now generally assumed that the heterogeneity of most networks in nature probably arises via preferential attachment of some sort. However, the origin of various other topological features, such as degree-degree correlations and…
We examine a model of network formation in single-layer and multiplex networks in which individuals have positive incentives for social ties, closed triangles, and spillover edges. In particular, we investigate the influence of shocks to…
Our current world is linked by a complex mesh of networks where information, people and goods flow. These networks are interdependent each other, and present structural and dynamical features different from those observed in isolated…
Complex networks characterized by global transport processes rely on the presence of directed paths from input to output nodes and edges, which organize in characteristic linked components. The analysis of such network-spanning structures…
Scale-free and non-computable characteristics of natural networks are found to result from the least-time dispersal of energy. To consider a network as a thermodynamic system is motivated since ultimately everything that exists can be…
Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of…
We develop a new framework for modeling innovation networks which evolve over time. The nodes in the network represent firms, whereas the directed links represent unilateral interactions between the firms. Both nodes and links evolve…
We extend the observability model to multiplex networks. We present mathematical frameworks, valid under the treelike ansatz, able to describe the emergence of the macroscopic cluster of mutually observable nodes in both synthetic and…
Understanding the structure and formation of networks is a central topic in complexity science. Economic networks are formed by decisions of individual agents and thus not properly described by established random graph models. In this…
We model the production of complex goods in a large supply network. Each firm sources several essential inputs through relationships with other firms. Individual supply relationships are at risk of idiosyncratic failure, which threatens to…
Evolving Neural Networks (NNs) has recently seen an increasing interest as an alternative path that might be more successful. It has many advantages compared to other approaches, such as learning the architecture of the NNs. However, the…
The observed architecture of ecological and socio-economic networks differs significantly from that of random networks. From a network science standpoint, non-random structural patterns observed in real networks call for an explanation of…
Many real-world complex networks arise as a result of a competition between growth and rewiring processes. Usually the initial part of the evolution is dominated by growth while the later one rather by rewiring. The initial growth allows…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
Global coastlines and their dense populations have an uncertain future due to increased flooding, storms, and human modification. The distributary channel networks of deltas and marshes that plumb these coastlines present diverse…
A fundamental question in neuroscience is how structure and function of neural systems are related. We study this interplay by combining a familiar auto-associative neural network with an evolving mechanism for the birth and death of…