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1.
In many real-life networks, both the scale-free distribution of degree and small-world behavior are important features. There are many random or deterministic models of networks to simulate these features separately. However, there are few models that combine the scale-free effect and small-world behavior, especially in terms of deterministic versions. What is more, all the existing deterministic algorithms running in the iterative mode generate networks with only several discrete numbers of nodes. This contradicts the purpose of creating a deterministic network model on which we can simulate some dynamical processes as widely as possible. According to these facts, this paper proposes a deterministic network generation algorithm, which can not only generate deterministic networks following a scale-free distribution of degree and small-world behavior, but also produce networks with arbitrary number of nodes. Our scheme is based on a complete binary tree, and each newly generated leaf node is further linked to its full brother and one of its direct ancestors. Analytical computation and simulation results show that the average degree of such a proposed network is less than 5, the average clustering coefficient is high (larger than 0.5, even for a network of size 2 million) and the average shortest path length increases much more slowly than logarithmic growth for the majority of small-world network models. 相似文献
2.
Chinese is spoken by the largest number of people in the world, and it is regarded as one of the most important languages. In this paper, we explore the statistical properties of Chinese language networks (CLNs) within the framework of complex network theory. Based on one of the largest Chinese corpora, i.e. People’s Daily Corpus, we construct two networks (CLN1 and CLN2) from two different respects, with Chinese words as nodes. In CLN1, a link between two nodes exists if they appear next to each other in at least one sentence; in CLN2, a link represents that two nodes appear simultaneously in a sentence. We show that both networks exhibit small-world effect, scale-free structure, hierarchical organization and disassortative mixing. These results indicate that in many topological aspects Chinese language shapes complex networks with organizing principles similar to other previously studied language systems, which shows that different languages may have some common characteristics in their evolution processes. We believe that our research may shed some new light into the Chinese language and find some potentially significant implications. 相似文献
3.
We propose a new tree-like network model. Our results indicate that the tree-like model has a small-world effect with a small average path length and large clustering coefficient. Strikingly, our tree-like model is scale-free. We also add weight to the links following the network structure. With this adding-weight method, the weight of the nodes shows exponential growth, which is ubiquitous in social networks. 相似文献
4.
S. M.G. Caldeira T. C. Petit Lobão R. F.S. Andrade A. Neme J. G.V. Miranda 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,49(4):523-529
Complex network theory is used to investigate the
structure of meaningful concepts in written texts of individual
authors. Networks have been constructed after a two phase
filtering, where words with less meaning contents are eliminated
and all remaining words are set to their canonical form, without
any number, gender or time flexion. Each sentence in the text is
added to the network as a clique. A large number of written texts
have been scrutinised, and it is found that texts have small-world
as well as scale-free structures. The growth process of these
networks has also been investigated, and a universal evolution of
network quantifiers have been found among the set of texts written
by distinct authors. Further analyses, based on shuffling
procedures taken either on the texts or on the constructed
networks, provide hints on the role played by the word frequency
and sentence length distributions to the network structure. 相似文献
5.
A Robustness Model of Complex Networks with Tunable Attack Information Parameter 总被引:1,自引:0,他引:1 下载免费PDF全文
We introduce a novel model for robustness of complex with a tunable attack information parameter. The random failure and intentional attack known are the two extreme cases of our model. Based on the model, we study the robustness of complex networks under random information and preferential information, respectively. Using the generating function method, we derive the exact value of the critical removal fraction of nodes for the disintegration of networks and the size of the giant component. We show that hiding just a small fraction of nodes randomly can prevent a scale-free network from collapsing and detecting just a small fraction of nodes preferentially can destroy a scale-free network. 相似文献
6.
We propose a new concept, two-step degree. Defining it as the capacity of a node of complex networks, we establish a novel capacity-load model of cascading failures of complex networks where the capacity of nodes decreases during the process of cascading failures. For scale-free networks, we find that the average two-step degree increases with the increase of the heterogeneity of the degree distribution, showing that the average two- step degree can be used for measuring the heterogeneity of the degree distribution of complex networks. In addition, under the condition that the average degree of a node is given, we can design a scale-free network with the optimal robustness to random failures by maximizing the average two-step degree. 相似文献
7.
Previous studies concerning pinning control of complex-network synchronization have very often demonstrated that in an unweighted symmetrical scale-free network, controlling the high-degree nodes is more efficient than controlling randomly chosen ones; due to the heterogeneity of the node-degree or edge-connection distribution of the scale-free network, small-degree nodes have relatively high probabilities of being chosen at random but their control has less influence on the other nodes through the network. This raises the question of whether or not controlling the high-degree nodes is always better than controlling the small ones in scale-free networks. Our answer to this is yes and no. In this study, we carry out extensive numerical simulations to show that in an unweighted symmetrical Barabasi-Albert scale-free network, when the portion of controlled nodes is relatively large, controlling the small nodes becomes better than controlling the big nodes and controlling randomly chosen nodes has approximately the same effect as controlling the big ones. However, we also show that for normalized weighted scale-free networks, controlling the big nodes is in fact always better than controlling the small ones. 相似文献
8.
Zhongzhi Zhang Shuigeng Zhou Lichao Chen 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,58(3):337-344
We present a family of scale-free network model consisting
of cliques, which is established by a simple recursive algorithm. We
investigate the networks both analytically and numerically. The
obtained analytical solutions show that the networks follow a
power-law degree distribution, with degree exponent continuously
tuned between 2 and 3. The exact expression of clustering
coefficient is also provided for the networks. Furthermore, the
investigation of the average path length reveals that the networks
possess small-world feature. Interestingly, we find that a special
case of our model can be mapped into the Yule process. 相似文献
9.
This paper studies the evolutionary ultimatum game on networks when agents have incomplete information about the strategies of their neighborhood agents. Our model assumes that agents may initially display low fairness behavior, and therefore, may have to learn and develop their own strategies in this unknown environment. The Genetic Algorithm Learning Classifier System (GALCS) is used in the model as the agent strategy learning rule. Aside from the Watts-Strogatz (WS) small-world network and its variations, the present paper also extends the spatial ultimatum game to the Barabási-Albert (BA) scale-free network. Simulation results show that the fairness level achieved is lower than in situations where agents have complete information about other agents’ strategies. The research results display that fairness behavior will always emerge regardless of the distribution of the initial strategies. If the strategies are randomly distributed on the network, then the long-term agent fairness levels achieved are very close given unchanged learning parameters. Neighborhood size also has little effect on the fairness level attained. The simulation results also imply that WS small-world and BA scale-free networks have different effects on the spatial ultimatum game. In ultimatum game on networks with incomplete information, the WS small-world network and its variations favor the emergence of fairness behavior slightly more than the BA network where agents are heterogeneously structured. 相似文献
10.
Zhongzhi Zhang Shuigeng Zhou Tao Zou Lichao Chen Jihong Guan 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,60(2):259-264
We make a mapping from Sierpinski fractals to a new class
of networks, the incompatibility networks, which are scale-free,
small-world, disassortative, and maximal planar graphs. Some
relevant characteristics of the networks such as degree
distribution, clustering coefficient, average path length, and
degree correlations are computed analytically and found to be
peculiarly rich. The method of network representation can be applied
to some real-life systems making it possible to study the complexity
of real networked systems within the framework of complex network
theory. 相似文献
11.
Zhongzhi Zhang Shuyang Gao 《The European Physical Journal B - Condensed Matter and Complex Systems》2011,80(2):209-216
Random walks on complex networks, especially scale-free
networks, have attracted considerable interest in the past few
years. A lot of previous work showed that the average receiving time
(ART), i.e., the average of mean first-passage time (MFPT) for
random walks to a given hub node (node with maximum degree) averaged
over all starting points in scale-free small-world networks exhibits
a sublinear or linear dependence on network order N (number of
nodes), which indicates that hub nodes are very efficient in
receiving information if one looks upon the random walker as an
information messenger. Thus far, the efficiency of a hub node
sending information on scale-free small-world networks has not been
addressed yet. In this paper, we study random walks on the class of
Koch networks with scale-free behavior and small-world effect. We
derive some basic properties for random walks on the Koch network
family, based on which we calculate analytically the average sending
time (AST) defined as the average of MFPTs from a hub node to all
other nodes, excluding the hub itself. The obtained closed-form
expression displays that in large networks the AST grows with
network order as N ln N, which is larger than the linear scaling
of ART to the hub from other nodes. On the other hand, we also
address the case with the information sender distributed uniformly
among the Koch networks, and derive analytically the global mean
first-passage time, namely, the average of MFPTs between all couples
of nodes, the leading scaling of which is identical to that of AST.
From the obtained results, we present that although hub nodes are
more efficient for receiving information than other nodes, they
display a qualitatively similar speed for sending information as
non-hub nodes. Moreover, we show that that AST from a starting point
(sender) to all possible targets is not sensitively affected by the
sender’s location. The present findings are helpful for better
understanding random walks performed on scale-free small-world
networks. 相似文献
12.
We study the robustness of complex networks under edge elimination. We propose three different edge elimination strategies and investigate their effects on the robustness of scale-free networks under intentional attack. We show that deleting a proper fraction of edges connecting hub nodes and hub nodes can enhance the robustness of scale-free networks under intentional attack. 相似文献
13.
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. 相似文献
14.
We propose a strategy updating mechanism based on pursuing the highest average payoff to investigate the prisoner's dilemma game and the snowdrift game. We apply the new rule to investigate cooperative behaviours on regular, small-world, scale-free networks, and find spatial structure can maintain cooperation for the prisoner's dilemma game. fn the snowdrift game, spatial structure can inhibit or promote cooperative behaviour which depends on payoff parameter. We further study cooperative behaviour on scale-free network in detail. Interestingly, non-monotonous behaviours observed on scale-free network with middle-degree individuals have the lowest cooperation level. We also find that large-degree individuals change their strategies more frequently for both games. 相似文献
15.
When we study the architecture of networks of spatially extended systems the nodes in the network are subject to local correlation structures. In this case, we show that for scale-free networks the traditional way to estimate the clustering coefficient may not be meaningful. Here we explain why and propose an approach that corrects this problem. 相似文献
16.
Co-occurrence networks of Chinese characters and words, and of English words, are constructed from collections of Chinese and English articles, respectively. Four types of collections are considered, namely, essays, novels, popular science articles, and news reports. Statistical parameters of the networks are studied, including diameter, average degree, degree distribution, clustering coefficient, average shortest path length, as well as the number of connected subnetworks. It is found that the character and word networks of each type of article in the Chinese language, and the word network of each type of article in the English language all exhibit scale-free and small-world features. The statistical parameters of these co-occurrence networks are compared within the same language and across the two languages. This study reveals some commonalities and differences between Chinese and English languages, and among the four types of articles in each language from a complex network perspective. In particular, it is shown that expressions in English are briefer than those in Chinese in a certain sense. 相似文献
17.
S. Carmi Z. Wu E. López S. Havlin H. Eugene Stanley 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(2):165-174
We study the transport properties of model networks such as
scale-free and Erd?s-Rényi networks as well as a real
network. We consider few possibilities for the trnasport problem.
We start by studying the conductance G between two arbitrarily
chosen nodes where each link has the same unit resistance. Our
theoretical analysis for scale-free networks predicts a broad
range of values of G, with a power-law tail distribution
$\Phi_{\rm SF}(G)\sim G^{-g_G}$
, where gG=2λ-1, and
λ is the decay exponent for the scale-free network degree
distribution. The power-law tail in ΦSF(G) leads to
large values of G, thereby significantly improving the transport
in scale-free networks, compared to Erd?s-Rényi networks
where the tail of the conductivity distribution decays
exponentially. We develop a simple physical picture of the
transport to account for the results. The other model for
transport is the max-flow model, where conductance is defined
as the number of link-independent paths between the two nodes, and
find that a similar picture holds. The effects of distance on the
value of conductance are considered for both models, and some
differences emerge. We then extend our study to the case of
multiple sources ans sinks, where the transport is defined between two
groups of nodes. We find a fundamental difference between
the two forms of flow when considering the quality of the
transport with respect to the number of sources, and find an
optimal number of sources, or users, for the max-flow case. A
qualitative (and partially quantitative) explanation is also
given. 相似文献
18.
Scale-free networks are prone to epidemic spreading. To provide cost-effective protection for such networks, targeted immunization was proposed to selectively immunize the hub nodes. In many real-life applications, however, the targeted immunization may not be perfect, either because some hub nodes are hidden and consequently not immunized, or because the vaccination simply cannot provide perfect protection. We investigate the effects of imperfect targeted immunization in scale-free networks. Analysis and simulation results show that there exists a linear relationship between the inverse of the epidemic threshold and the effectiveness of targeted immunization. Therefore, the probability of epidemic outbreak cannot be significantly lowered unless the protection is reasonably strong. On the other hand, even a relatively weak protection over the hub nodes significantly decreases the number of network nodes ever getting infected and therefore enhances network robustness against virus. We show that the above conclusions remain valid where there exists a negative correlation between nodal degree and infectiousness. 相似文献
19.
Xiao-Gai Tang 《Physica A》2009,388(22):4797-4802
We study the information traffic in scale-free networks where the information generation rate varies with time as a periodic function. We observe that when the fluctuation in packet generation rate increases, the average transit time increases and network performance degrades. In order to improve the transportation efficiency in this situation, we propose a new routing method called mixed routing. It operates in two modes: (1) when the packet generation rate is small, the shortest paths are used to deliver the packets to the destination; (2) when the packet generation rate is large, the traffic loads in central nodes are redistributed to other non-central nodes, using the so-called efficient routing method. We find that the time shifting between the two modes is very critical for the routing performance. Consequently, we provide an efficient method to determine the critical times to shift the routing modes for achieving good network performance. 相似文献
20.
Z.-Z. Zhang S.-G. Zhou T. Zou 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(3):259-271
In this paper, firstly, we study analytically the topological
features of a family of hierarchical lattices (HLs) from the view
point of complex networks. We derive some basic properties of HLs
controlled by a parameter q: scale-free degree distribution with
exponent γ=2+ln 2/(ln q), null clustering
coefficient, power-law behavior of grid coefficient, exponential
growth of average path length (non-small-world), fractal scaling
with dimension dB=ln (2q)/(ln 2), and disassortativity.
Our results show that scale-free networks are not always
small-world, and support the conjecture that self-similar scale-free
networks are not assortative. Secondly, we define a deterministic
family of graphs called small-world hierarchical lattices (SWHLs).
Our construction preserves the structure of hierarchical lattices,
including its degree distribution, fractal architecture, clustering
coefficient, while the small-world phenomenon arises. Finally, the
dynamical processes of intentional attacks and collective
synchronization are studied and the comparisons between HLs and
Barabási-Albert (BA) networks as well as SWHLs are shown. We
find that the self-similar property of HLs and SWHLs significantly
increases the robustness of such networks against targeted damage on
hubs, as compared to the very vulnerable non fractal BA networks,
and that HLs have poorer synchronizability than their counterparts
SWHLs and BA networks. We show that degree distribution of
scale-free networks does not suffice to characterize their
synchronizability, and that networks with smaller average path
length are not always easier to synchronize. 相似文献