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Complex hypernetworks are ubiquitous in the real system. It is very important to investigate the evolution mechanisms. In this paper, we present a local-world evolving hypernetwork model by taking into account the hyperedge growth and local-world hyperedge preferential attachment mechanisms. At each time step, a newly added hyperedge encircles a new coming node and a number of nodes from a randomly selected local world. The number of the selected nodes from the local world obeys the uniform distribution and its mean value is m. The analytical and simulation results show that the hyperdegree approximately obeys the power-law form and the exponent of hyperdegree distribution is γ = 2 + 1/m. Furthermore, we numerically investigate the node degree, hyperedge degree, clustering coefficient, as well as the average distance, and find that the hypernetwork model shares the scale-free and small-world properties, which shed some light for deeply understanding the evolution mechanism of the real systems. 相似文献
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《Physica A》2007
Networks generated by local-world evolving network model display a transition from exponential network to power-law network with respect to connectivity distribution. We investigate statistical properties of the evolving networks and the responses of these networks under random errors and intentional attacks. It has been found that local world size M has great effect on the network's heterogeneity, thus leading to transitional behaviors in network's robustness against errors and attacks. Numerical results show that networks constructed with local preferential attachment mechanism can maintain the robustness of scale-free networks under random errors and concurrently improve reliance against targeted attacks on highly connected nodes. 相似文献
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The class of generative models has already attracted considerable interest from researchers in recent years and much expanded the original ideas described in BA model. Most of these models assume that only one node per time step joins the network. In this paper, we grow the network by adding n interconnected nodes as a local structure into the network at each time step with each new node emanating m new edges linking the node to the preexisting network by preferential attachment. This successfully generates key features observed in social networks. These include power-law degree distribution pk∼k−(3+μ), where μ=(n−1)/m is a tuning parameter defined as the modularity strength of the network, nontrivial clustering, assortative mixing, and modular structure. Moreover, all these features are dependent in a similar way on the parameter μ. We then study the susceptible-infected epidemics on this network with identical infectivity, and find that the initial epidemic behavior is governed by both of the infection scheme and the network structure, especially the modularity strength. The modularity of the network makes the spreading velocity much lower than that of the BA model. On the other hand, increasing the modularity strength will accelerate the propagation velocity. 相似文献
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In real-life networks, incomers may only connect to a few others in a local area for their limited information, and individuals in a local area are likely to have close relations. Accordingly, we propose a local preferential attachment model. Here, a local-area-network stands for a node and all its neighbors, and the new nodes perform nonlinear preferential attachment, , in local areas. The stable degree distribution and clustering-degree correlations are analytically obtained. With the increasing of α, the clustering coefficient increases, while assortativity decreases from positive to negative. In addition, by adjusting the parameter α, the model can generate different kinds of degree distribution, from exponential to power-law. The hierarchical organization, independent of α, is the most significant character of this model. 相似文献
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H. Bauke C. Moore J. B. Rouquier D. Sherrington 《The European Physical Journal B - Condensed Matter and Complex Systems》2011,83(4):519-524
Preferential attachment is a popular model of growing networks. We consider a generalized
model with random node removal, and a combination of preferential and random attachment.
Using a high-degree expansion of the master equation, we identify a topological phase
transition depending on the rate of node removal and the relative strength of preferential
vs. random attachment, where the degree distribution goes from a power law to one with an
exponential tail. 相似文献
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We present a weighted scale-free network model, in which the power-law exponents can be controlled by the model parameters. The network is generated through the weight-driven preferential attachment of new nodes to existing nodes and the growth of the weights of existing links. The simplicity of the model enables us to derive analytically the various statistical properties, such as the distributions of degree, strength, and weight, the degree-strength and degree-weight relationship, and the dependencies of these power-law exponents on the model parameters. Finally, we demonstrate that networks of words, coauthorship of researchers, and collaboration of actor/actresses are quantitatively well described by this model. 相似文献
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Community structure is an important characteristic in real complex network. It is a network consists of groups of nodes within which links are dense but among which links are sparse. In this paper, the evolving network include node, link and community growth and we apply the community size preferential attachment and strength preferential attachment to a growing weighted network model and utilize weight assigning mechanism from BBV model. The resulting network reflects the intrinsic community structure with generalized power-law distributions of nodes' degrees and strengths. 相似文献
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Y.-P. Jeon B. J. McCoy 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,60(4):521-528
Networks are commonly observed structures in complex
systems with interacting and interdependent parts that self-organize. For
nonlinearly growing networks, when the total number of connections increases
faster than the total number of nodes, the network is said to accelerate. We
propose a systematic model for the dynamics of growing networks represented
by distribution kinetics equations. We define the nodal-linkage
distribution, construct a population dynamics equation based on the
association-dissociation process, and perform the moment calculations to
describe the dynamics of such networks. For nondirectional networks with
finite numbers of nodes and connections, the moments are the total number of
nodes, the total number of connections, and the degree (the average number
of connections per node), represented by the average moment. Size
independent rate coefficients yield an exponential network describing the
network without preferential attachment, and size dependent rate
coefficients produce a power law network with preferential attachment. The
model quantitatively describes accelerating network growth data for a
supercomputer (Earth Simulator), for regulatory gene networks, and for the
Internet. 相似文献
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Many real systems possess accelerating statistics where the total number of edges grows faster than the network size. In this paper, we propose a simple weighted network model with accelerating growth. We derive analytical expressions for the evolutions and distributions for strength, degree, and weight, which are relevant to accelerating growth. We also find that accelerating growth determines the clustering coefficient of the networks. Interestingly, the distributions for strength, degree, and weight display a transition from scale-free to exponential form when the parameter with respect to accelerating growth increases from a small to large value. All the theoretical predictions are successfully contrasted with numerical simulations. 相似文献
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为了研究信息传播过程对复杂网络结构演化的影响,提出了一种信息传播促进网络增长的网络演化模型,模型包括信息传播促进网内增边、新节点通过局域世界建立第一条边和信息传播促进新节点连边三个阶段,通过多次自回避随机游走模拟信息传播过程,节点根据路径节点的节点度和距离与其选择性建立连接。理论分析和仿真实验表明,模型不仅具有小世界和无标度特性,而且不同参数下具有漂移幂律分布、广延指数分布等分布特性,呈现小变量饱和、指数截断等非幂律现象,同时,模型可在不改变度分布的情况下调节集聚系数,并能够产生从同配到异配具有不同匹配模式的网络. 相似文献
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We introduce an abstract evolutionary formalism that generates weighted networks whose growth under stochastic preferential attachment triggers unrestricted weight rearrangements in existing links. The class of resulting algorithms for different parameter values includes the Barabási-Albert and Barrat-Barthélemy-Vespignani models as special cases. We solve the recursions that describe the average growth to derive exact solutions for the expected degree and strength distribution, the individual strength and weight development and the joint distribution of neighboring degrees. We find that the network exhibits a particular form of self-similarity, namely every sufficiently interconnected node has on average the same constitution of small-degree neighbors as any other node of large degree. Finally we suggest potential applications in several fields of interest. 相似文献
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We investigate the emergence of scale-free behaviour in a traffic system by using the NaSch model to simulate the evolution of traffic flow. A kind of evolution networks has been proposed, which is based on the evolution of the traffic flow. The network growth does not take into account preferential attachment, and the attachment of new node is independent of degree. The simulation results demonstrate that the output distribution of links is well described by a scale-free distribution. 相似文献
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We propose a weighted evolving network model in which the underlying topological structure is still driven by the degree according to the preferential attachment rule while the weight assigned to the newly established edges is dependent on the degree in a nonlinear form. By varying the parameter a that controls the function determining the assignment of weight, a wide variety of power-law behaviours of the total weight distributions as well as the diversity of the weight distributions of edges are displayed. Variation of correlation and heterogeneity in the network is illustrated as well. 相似文献
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Yuying Gu 《Physics letters. A》2008,372(25):4564-4568
A new type network growth rule which comprises node addition with the concept of local-world connectivity and node deleting is studied. A series of theoretical analysis and numerical simulation to the LWD network are conducted in this Letter. Firstly, the degree distribution p(k) of this network changes no longer pure scale free but truncates by an exponential tail and the truncation in p(k) increases as pa decreases. Secondly, the connectivity is tighter, as the local-world size M increases. Thirdly, the average path length L increases and the clustering coefficient 〈C〉 decreases as generally node deleting increases. Finally, 〈C〉 trends up when the local-world size M increases, so as to kmax. Hence, the expanding local-world can compensate the infection of the node deleting. 相似文献
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Scale-Free Graph with Preferential Attachment and Evolving Internal Vertex Structure 总被引:1,自引:0,他引:1
Krzysztof Choromański Michał Matuszak Jacek Miȩkisz 《Journal of statistical physics》2013,151(6):1175-1183
We extend the classical Barabási-Albert preferential attachment procedure to graphs with internal vertex structure given by weights of vertices. In our model, weight dynamics depends on the current vertex degree distribution and the preferential attachment procedure takes into account both weights and degrees of vertices. We prove that such a coupled dynamics leads to scale-free graphs with exponents depending on parameters of the weight dynamics. 相似文献
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This article investigates the functional properties of complex
networks used as grid computing systems. Complex networks following
the Erdös-Rényi model and other models with a preferential
attachment rule (with and without growth) or priority to the
connection of isolated nodes are studied. Regular networks are also
considered for comparison. The processing load of the parallel
program executed on the grid is assigned to the nodes on demand, and
the efficiency of the overall computation is quantified in terms of
the parallel speedup. It is found that networks with preferential
attachment allow lower computing efficiency than networks with
uniform link attachment. At the same time, considering only node
clusters of the same size, preferential attachment networks display
better efficiencies. The regular networks, on the other hand,
display a poor efficiency, due to their implied larger internode
distances. A correlation is observed between the topological
properties of the network, specially average cluster size, and their
respective computing efficiency. 相似文献