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We propose that negative degree correlation among nodes in a network of nonlinear oscillators, often detected in real world networks, is motivated by its positive effects on synchronizability. In so doing, we use a novel methodology to…
We study the avalanche dynamics in the data packet transport on scale-free networks through a simple model. In the model, each vertex is assigned a capacity proportional to the load with a proportionality constant $1+a$. When the system is…
Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models. In this work, we present a systematic analysis of scaling laws for quadratic and…
In the past few years, the discoveries of small-world and scale-free properties of many natural and artificial complex networks have stimulated significant advances in better understanding the relationship between the topology and the…
The concept of network efficiency, recently proposed to characterize the properties of small-world networks, is here used to study the effects of errors and attacks on scale-free networks. Two different kinds of scale-free networks, i.e.…
Link weight is crucial in weighted complex networks. It provides additional dimension for describing and adjusting the properties of networks. The topological role of weight is studied by the effects of random redistribution of link weights…
Kauffman net is a dynamical system of logical variables receiving two random inputs and each randomly assigned a boolean function. We show that the attractor and transient lengths exhibit scaleless behavior with power-law distributions over…
In this paper we deal with the structural properties of weighted networks. Starting from an empirical analysis of a linguistic network, we analyse the differences between the statistical properties of a real and a shuffled network and we…
Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…
Many recent large-scale studies of interaction networks have focused on networks of accumulated contacts. In this paper we explore social networks of ongoing relationships with an emphasis on dynamical aspects. We find a distribution of…
Plasticity of two-dimensional discrete dislocation systems is studied. It is shown, that at some threshold stress level the response becomes stress-rate dependent. Below this stress level the stress-plastic strain relation exhibits…
In this letter, we investigate the detailed epidemic spreading process in scale-free networks with links' weights that denote familiarity between two individuals and find that spreading velocity reaches a peak quickly then decays in a…
A random network is grown by introducing at unit rate randomly selected nodes on the Euclidean space. A node is randomly connected to its $i$-th predecessor of degree $k_i$ with a directed link of length $\ell$ using a probability…
We study a model of wealth dynamics [Bouchaud and M\'ezard 2000, \emph{Physica A} \textbf{282}, 536] which mimics transactions among economic agents. The outcomes of the model are shown to depend strongly on the topological properties of…
Large scale simulations of the movements of people in a ``virtual'' city and their analyses are used to generate new insights into understanding the dynamic processes that depend on the interactions between people. Models, based on these…
We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Every node is assigned an a-priori i.i.d. fitness with…
The in-degree and out-degree distributions of a growing network model are determined. The in-degree is the number of incoming links to a given node (and vice versa for out-degree. The network is built by (i) creation of new nodes which each…
Many social, technological and biological interactions involve network relationships whose outcome intimately depends on the structure of the network and on the strengths of the connections. Yet, although much information is now available…
The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…