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The Yule-Simon model has been used as a tool to describe the growth of diverse systems, acquiring a paradigmatic character in many fields of research. Here we study a modified Yule-Simon model that takes into account the full hist...
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The Yule-Simon model has been used as a tool to describe the growth of diverse systems, acquiring a paradigmatic character in many fields of research. Here we study a modified Yule-Simon model that takes into account the full history of the system by means of a hyperbolic memory kernel. We show how the memory kernel changes the properties of preferential attachment and provide an approximate analytical solution for the frequency distribution density as well as for the frequency-rank distribution.
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The widespread occurrence of an inverse square relation in the hierarchical distribution of subcommunities within communities (or subspecies within species) has been recently invoked as a signature of hierarchical self-organizatio...
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The widespread occurrence of an inverse square relation in the hierarchical distribution of subcommunities within communities (or subspecies within species) has been recently invoked as a signature of hierarchical self-organization within social and ecological systems. Here we show that, whether such systems are self-organized or not, this behavior is the consequence of the treelike classification method. Different treelike classifications (both of real and truly random systems) display a similar statistical behavior when considering the sizes of their sub-branches.
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Linux operating system (LOS) is a sophisticated man-made system and one of the most ubiquitous operating systems. However, there is little research on the structure and functionality evolution of LOS from the prospective of networ...
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Linux operating system (LOS) is a sophisticated man-made system and one of the most ubiquitous operating systems. However, there is little research on the structure and functionality evolution of LOS from the prospective of networks. In this paper, we investigate the evolution of the LOS network. 62 major releases of LOS ranging from versions 1.0 to 4.1 are modeled as directed networks in which functions are denoted by nodes and function calls are denoted by edges. It is found that the size of the LOS network grows almost linearly, while clustering coefficient monotonically decays. The degree distributions are almost the same: the out-degree follows an exponential distribution while both in-degree and undirected degree follow power-law distributions. We further explore the functionality evolution of the LOS network. It is observed that the evolution of functional modules is shown as a sequence of seven events (changes) succeeding each other, including continuing, growth, contraction, birth, splitting, death and merging events. By means of a statistical analysis of these events in the top 4 largest components (i.e., arch, drivers, fs and net), it is shown that continuing, growth and contraction events occupy more than 95% events. Our work exemplifies a better understanding and describing of the dynamics of LOS evolution. (C) 2016 Elsevier B.V. All rights reserved.
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It is intended to state clearly the strategy of introduc- ing optical networks into access networks. A tool for evalu- ating the initial cost and the maintenance operation cost of the networks is investigated. The evaluation proce...
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It is intended to state clearly the strategy of introduc- ing optical networks into access networks. A tool for evalu- ating the initial cost and the maintenance operation cost of the networks is investigated. The evaluation procedure and the software structure for that purpose are reported. This paper is the first, as far that purpose are reported. This paper is the first, as far as the authors know, to report on a tool that can evaluate costs up to the maintenance cost.
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Motivated by biological aging dynamics, we introduce a network evolution model for social interaction networks. In order to study the effect of social interactions originating from biological and sociological reasons on the topolo...
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Motivated by biological aging dynamics, we introduce a network evolution model for social interaction networks. In order to study the effect of social interactions originating from biological and sociological reasons on the topological properties of networks, we introduce the activitydependent rewiring process. From the numerical simulations, we show that the degree distribution of the obtained networks follows a power-law distribution with an exponentially decaying tail, P(k) ~ (k + c) ~(-γ) exp(-k/k _0). The obtained value of γ is in the range 2 < γ < 3, which is consistent with the values for real social networks. Moreover, we also show that the degree-degree correlation of the network is positive, which is a characteristic of social interaction networks. The possible applications of our model to real systems are also discussed.
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Complex systems have been successfully modeled as networks exhibiting the varying extent of randomness and nonrandomness. Network scientists contemplate randomness as one of the most desirable characteristics for real complex syst...
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Complex systems have been successfully modeled as networks exhibiting the varying extent of randomness and nonrandomness. Network scientists contemplate randomness as one of the most desirable characteristics for real complex systems' efficient performance. However, the current methodologies for randomness (or nonrandomness) quantification are nontrivial. In this article, we empirically showcase severe limitations associated with the state-of-the-art graph spectral-based quantification approaches. Addressing these limitations led to the proposal of a novel spectrum-based methodology that leverages configuration models as a reference network to quantify the nonrandomness in a given candidate network. Besides, we derive mathematical formulations for demonstrating the dependence of nonrandomness on three structural properties: modularity, clustering, and the highest degree node's growth rate. We also introduce a novel graph signature (termed "cumulative spectral difference") to visualize the nonrandomness in the network. Later, this article also discusses the relationship between the proposed nonrandomness measure and the diffusion affinity of networks. Toward the end, this article extensively discusses observations emerging from these signatures for both real-world and simulated networks.
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Many biological and artifact networks often represent modular structures in which the network can be decomposed into several subnetworks. Here, we propose a simple model for the modular network evolution based on the nonlinear den...
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Many biological and artifact networks often represent modular structures in which the network can be decomposed into several subnetworks. Here, we propose a simple model for the modular network evolution based on the nonlinear denoising in node activities. This model suggests that modular networks can evolve under certain conditions - if the stipulated goals for the networks or the input and target output pairs involve modular features, or if the signal transfer in a node is carried out in a nonlinear manner with respect to the saturation at the upper and lower bounds. Our model highlights the positive role played by noise in modular network evolution.
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Although gene duplications occur at a higher rate, only a small fraction of these are retained. The position of a gene’s encoded product in the protein–protein interaction network has recently emerged as a determining factor of ...
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Although gene duplications occur at a higher rate, only a small fraction of these are retained. The position of a gene’s encoded product in the protein–protein interaction network has recently emerged as a determining factor of gene duplicability. However, the direction of the relationship between network centrality and duplicability is not universal: In Escherichia coli, yeast, y, and worm, duplicated genes more often act at the periphery of the network, whereas in humans, such genes tend to occupy the most central positions. Herein, we have inferred duplication events that took place in the different branches of the primate phylogeny. In agreement with previous observations, we found that duplications generally affected the most central network genes, which is presumably the process that has most inuenced the trend in humans. However, the opposite trend—that is, duplication being more common in genes whose encoded products are peripheral in the network—is observed for three recent branches, including, quite counterintuitively, the external branch leading to humans. This indicates a shift in the relationship between centrality and duplicability during primate evolution. Furthermore, we found that genes encoding interacting proteins exhibit phylogenetic tree topologies that are more similar than expected for random pairs and that genes duplicated in a given branch of the phylogeny tend to interact with those that duplicated in the same lineage. These results indicate that duplication of a gene increases the likelihood of duplication of its interacting partners. Our observations indicate that the structure of the primate protein–protein interaction network affects gene duplicability in previously unrecognized ways.
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Network structure will evolve over time, which will lead to changes in the spread of the epidemic. In this work, a network evolution model based on the principle of preferential attachment is proposed. The network will evolve into...
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Network structure will evolve over time, which will lead to changes in the spread of the epidemic. In this work, a network evolution model based on the principle of preferential attachment is proposed. The network will evolve into a scale-free network with a power-law exponent between 2 and 3 by our model, where the exponent is determined by the evolution parameters. We analyze the epidemic spreading process as the network evolves from a small-world one to a scale-free one, including the changes in epidemic threshold over time. The condition of epidemic threshold to increase is given with the evolution processes. The simulated results of real-world networks and synthetic networks show that as the network evolves at a low evolution rate, it is more conducive to preventing epidemic spreading.
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Markov chains provide us with a powerful tool for studying the structure of graphs and databases in details. We review the method of generalized inverses for Markov chains and apply it for the analysis of urban structures, evoluti...
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Markov chains provide us with a powerful tool for studying the structure of graphs and databases in details. We review the method of generalized inverses for Markov chains and apply it for the analysis of urban structures, evolution of languages, and musical compositions. We also discuss a generalization of L′evy flights over large complex networks and study the interplay between the nonlinearity of diffusion process and the topological structure of the network.
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