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The evolutionary origin of universal statistics in biochemical reaction network is studied, to explain the power-law distribution of reaction links and the power-law distributions of chemical abundances. Using cell models with catalytic…
Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as…
We study a recent model of random networks based on the presence of an intrinsic character of the vertices called fitness. The vertices fitnesses are drawn from a given probability distribution density. The edges between pair of vertices…
Most real-world networks display not only a heterogeneous distribution of degrees, but also a heterogeneous distribution of weights in the strengths of the connections. Each of these heterogeneities alone has been shown to suppress…
We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…
In this theoretical study, we analyze quantum walks on complex networks, which model network-based processes ranging from quantum computing to biology and even sociology. Specifically, we analytically relate the average long time…
Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where…
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…
In this paper we generalize the concept of random networks to describe networks with non trivial features by a statistical mechanics approach. This framework is able to describe ensembles of undirected, directed as well as weighted…
We introduce a community network model which exhibits scale-free property and study the evolutionary Prisoner's Dilemma game (PDG) on this network model. It is found that the frequency of cooperators decreases with the increment of the…
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…
A network is scale-free if its connectivity density function is proportional to a power-law distribution. Scale-free networks may provide an explanation for the robustness observed in certain physical and biological phenomena, since the…
Scale independence is a ubiquitous feature of complex systems which implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution and stock…
We report on parallel observations in two seemingly unrelated areas of dynamical network research. The one is the so-called small world phenomenon and/or the observation of scale freeness in certain types of large (empirical) networks and…
Modern biological tools have made it possible to unequivocally demonstrate the deep relationship among species in terms of genes and basic molecular mechanisms. In addition, results from genetic, physical and physiological approaches…
We present a general computational theory of stem cell networks and their developmental dynamics. Stem cell networks are special cases of developmental control networks. Our theory generates a natural classification of all possible stem…
Many complex networks in nature have directed links, a property that affects the network's navigability and large-scale topology. Here we study the percolation properties of such directed scale-free networks with correlated in- and…
In this paper we explore the features of a graph generated by random walkers with nodes that have evolutionary attractiveness and Boltzmann-like transition probabilities that depend both on the euclidean distance between the nodes and on…
Networks coming from protein-protein interactions, transcriptional regulation, signaling, or metabolism may appear to have "unusual" properties. To quantify this, it is appropriate to randomize the network and test the hypothesis that the…
Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as models of such systems, ranging from ensembles of random Boolean networks as models for generic properties of gene regulation to working dynamical…