Local affinity in heterogeneous growing networks

In this paper we present a study of the influence of local affinity in heterogeneous preferential attachment (PA) networks. Heterogeneous PA models are a generalization of the Barabási-Albert model to heterogeneous networks, where the affinity between nodes biases the attachment probability of links. Threshold models are a class of heterogeneous PA models where the affinity between nodes is inversely related to the distance between their states. We propose a generalization of threshold models where network nodes have individual affinity functions, which are then combined to yield the affinity of each potential interaction. We analyze the influence of the affinity functions in the topological properties averaged over a network ensemble. The network topology is evaluated through the distributions of connectivity degrees, clustering coefficients and geodesic distances. We show that the relaxation of the criterion of a single global affinity still leads to a reasonable power-law scaling in the connectivity and clustering distributions under a wide spectrum of assumptions. We also show that the richer behavior of the model often exhibits a better agreement with the empirical observations on real networks.     

Influence of Selective Edge Removal and Refractory Period in a Self-Organized Critical Neuron Model

A simple model for a set of integrate-and-fire neurons based on the weighted network is introduced. By considering the neurobiological phenomenon in brain development and the difference of the synaptic strength, we construct weighted networks develop with link additions and followed by selective edge removal. Thenetwork exhibits the small-world and scale-free properties with high network efficiency. The model displays an avalanche activity on a power-law distribution. We investigate the effect of selective edge removal and the neuron refractory period on the self-organized criticality of the system.     

Self-organized Criticality in an Integrate-and-Fire Neuron Model Based on Modified Aging Networks

Based on an integrate-and-fire mechanism, we investigate self-organized criticality of a simple neuron model on a modified BA scale-free network with aging nodes. In our model, we find that the distribution of avalanche size follows power-law behavior. The critical exponent τ depends on the aging exponent α. The structures of the network with aging of nodes change with an increase of α. The different topological structures lead to different behaviors in models of integrate-and-fire neurons.     

Avalanche transmission and critical behaviour in load-bearing hierarchical networks

The strength and stability properties of hierarchical load-bearing networks and their strengthened variants have been discussed in a recent work. Here, we study the avalanche time distributions on these load-bearing networks. The avalanche time distributions of the V-lattice, a unique realization of the networks, show power-law behaviour when tested with certain fractions of its trunk weights. All other avalanche distributions show Gaussian peaked behaviour. Thus the V-lattice is the critical case of the network. We discuss the implications of this result.     

A Kind of Neural Network Model Displaying Self-Organized Criticality

Based on the LISSOM model and the OFC earthquake model, we introduce a selforganized neural network model, in which the distribution of the avalanche sizes (unstable neurons) shows power-law behavior. In addition, we analyze the influence of various factors of the model on the power-law behavior of the avalanche size distribution.     

An evolutionary model of social networks

Social networks in communities, markets, and societies self-organise through the interactions of many individuals. In this paper we use a well-known mechanism of social interactions — the balance of sentiment in triadic relations — to describe the development of social networks. Our model contrasts with many existing network models, in that people not only establish but also break up relations whilst the network evolves. The procedure generates several interesting network features such as a variety of degree distributions and degree correlations. The resulting network converges under certain conditions to a steady critical state where temporal disruptions in triangles follow a power-law distribution.     

A Modified Earthquake Model Based on Generalized Barabási-Albert Scale-Free Networks

A modified Olami-Feder-Christensen model of self-organized criticality on generalized Barabási-Albert (GBA) scale-free networks is investigated. We find that our model displays power-law behavior and the avalanche dynamical behavior is sensitive to the topological structure of networks. Furthermore, the exponent τ of the model depends on b, which weights the distance in comparison with the degree in the GBA network evolution.     

Self-organized criticality model for brain plasticity

Networks of living neurons exhibit an avalanche mode of activity, experimentally found in organotypic cultures. Here we present a model that is based on self-organized criticality and takes into account brain plasticity, which is able to reproduce the spectrum of electroencephalograms (EEG). The model consists of an electrical network with threshold firing and activity-dependent synapse strengths. The system exhibits an avalanche activity in a power-law distribution. The analysis of the power spectra of the electrical signal reproduces very robustly the power-law behavior with the exponent 0.8, experimentally measured in EEG spectra. The same value of the exponent is found on small-world lattices and for leaky neurons, indicating that universality holds for a wide class of brain models.     

Return probability for random walks on scale-free complex trees

The time course of random processes usually differs depending on the topology of complex networks which are a substrate for the process. However, as this Letter demonstrates, the first-return as well as the survival probabilities for random walks on the scale-free (SF) trees decay in time according to the same invariant power-law behavior. This means that both quantities are independent of the node power-law degree distributions which are distinguished by different scaling exponents. It is also shown here that the crucial property of the networks, affecting the dynamics of random walks, is their tree-like topology and not SF architecture. All analytical results quantifying these predictions have been verified through extensive computer simulations.     

Transient dynamics of sparsely connected Hopfield neural networks with arbitrary degree distributions

Using probabilistic approach, the transient dynamics of sparsely connected Hopfield neural networks is studied for arbitrary degree distributions. A recursive scheme is developed to determine the time evolution of overlap parameters. As illustrative examples, the explicit calculations of dynamics for networks with binomial, power-law, and uniform degree distribution are performed. The results are good agreement with the extensive numerical simulations. It indicates that with the same average degree, there is a gradual improvement of network performance with increasing sharpness of its degree distribution, and the most efficient degree distribution for global storage of patterns is the delta function.     

Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.     

用户需求行为对互联网动力学整体特性的影响

由Internet构成的复杂网络的动力学特性主要受到用户需求行为的影响,具备时域的统计规律性. 通过对区域群体用户需求行为的时域实验统计分析,发现用户对Web网站的访问频度及其生成的二分网络的入度分布也呈现幂律分布和集聚现象,其幂指数介于1.7到1.8之间. 建立了虚拟资源网络VRN和物理拓扑网络PTN双层模型,分析了双层模型映射机理,并对网络用户需求行为进行建模. 虚拟资源网络VRN对物理拓扑网络PTN映射过程的不同机理,模拟了Internet资源网络到物理网络的不同影响模式. 幂律分布的用户需求特性会 关键词： 复杂网络 无标度拓扑 用户需求 相变     

Interpersonal interactions and human dynamics in a large social network

We study a large social network consisting of over 10⁶ individuals, who form an Internet community and organize themselves in groups of different sizes. On the basis of the users’ list of friends and other data registered in the database we investigate the structure and time development of the network. The structure of this friendship network is very similar to the structure of different social networks. However, here a degree distribution exhibiting two scaling regimes, power-law for low connectivity and exponential for large connectivity, was found. The groups size distribution and distribution of number of groups of an individual have power-law form. We found very interesting scaling laws concerning human dynamics. Our research has shown how long people are interested in a single task.     

Self-organized Critical Model Based on Complex Brain Networks with Hierarchical Organization

The dynamical behavior in the cortical brain network of macaque is studied by modelling each cortical area with a subnetwork of interacting excitable neurons. We find that the avalanche of our model on different levels exhibits power-law. Furthermore the power-law exponent of the distribution and the average avalanche size are affected by the topology of the network.     

The emergence of scale-free networks with a seceding mechanism

In order to explore further the underlying mechanism of scale-free networks, we study stochastic secession as a mechanism for the creation of complex networks. In this evolution the network growth incorporates the addition of new nodes, the addition of new links between existing nodes, the deleting and rewiring of some existing links, and the stochastic secession of nodes. To random growing networks with preferential attachment, the model yields scale-free behavior for the degree distribution. Furthermore, we obtain an analytical expression of the power-law degree distribution with scaling exponent γ ranging from 1.1 to 9. The analytical expressions are in good agreement with the numerical simulation results.     

Self-organized Criticality in a Model Based on Neural Network

Based on the LISSOM neural network model, we introduce a model to investigate self-organized criticality in the activity of neural populations. The influence of connection (synapse) between neurons has been adequately considered in this model. It is found to exhibit self-organized criticality (SOC) behavior under appropriate conditions. We also find that the learning process has promotive influence on emergence of SOC behavior. In addition, we analyze the influence of various factors of the model on the SOC behavior, which is characterized by the power-law behavior of the avalanche size distribution.     

Time distribution and loss of scaling in granular flow

Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling p) and deterministic critical slope processes with internal correlation time t_c equal to the avalanche lifetime, in model A, and ,in model B. In both cases nonuniversal scaling properties of avalanche distributions are found for , where is related to directed percolation threshold in d=3. Distributions of avalanche durations for are studied in detail, exhibiting multifractal scaling behavior in model A, and finite size scaling behavior in model B, and scaling exponents are determined as a function of p. At a phase transition to noncritical steady state occurs. Due to difference in the relaxation mechanisms, avalanche statistics at approaches the parity conserving universality class in model A, and the mean-field universality class in model B. We also estimate roughness exponent at the transition. Received: 29 May 1998 / Revised: 8 September 1998 / Accepted: 10 September 1998     

Self-organized Criticality in Hierarchical Brain Network

It is shown that the cortical brain network of the macaque displays a hierarchically clustered organization and the neuron network shows small-world properties. Now the two factors will be considered in our model and the dynamical behavior of the model will be studied. We study the characters of the model and find that the distribution of avalanche size of the model follows power-law behavior.     

Recursive weighted treelike networks

We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical results indicate that the resulting networks have power-law distributions of degree, strength, weight and betweenness, a scale-free behavior for degree correlations, logarithmic small average path length and diameter with network size. The obtained properties are in agreement with empirical data observed in many real-life networks, which shows that the presented model may provide valuable insight into the real systems.     

Detecting community structure from coherent oscillation of excitable systems

Many networks are proved to have community structures. On the basis of the fact that the dynamics on networks are intensively affected by the related topology, in this paper the dynamics of excitable systems on networks and a corresponding approach for detecting communities are discussed. Dynamical networks are formed by interacting neurons; each neuron is described using the FHN model. For noisy disturbance and appropriate coupling strength, neurons may oscillate coherently and their behavior is tightly related to the community structure. Synchronization between nodes is measured in terms of a correlation coefficient based on long time series. The correlation coefficient matrix can be used to project network topology onto a vector space. Then by the K-means cluster method, the communities can be detected. Experiments demonstrate that our algorithm is effective at discovering community structure in artificial networks and real networks, especially for directed networks. The results also provide us with a deep understanding of the relationship of function and structure for dynamical networks.