arXiv subjects

Shuigeng Zhou

Publications and source records attributed to Shuigeng Zhou.

142 records · Page 8Linked to original sources

arXiv2008

Finite epidemic thresholds in fractal scale-free `large-world' networks

It is generally accepted that scale-free networks is prone to epidemic spreading allowing the onset of large epidemics whatever the spreading rate of the infection. In the paper, we show that disease propagation may be suppressed in particular fractal scale-free networks. We first study analytically the topological characteristics of a network model and show that it is simultaneously scale-free, highly clustered, "large-world", fractal and disassortative. Any previous model does not have all the properties as the one under consideration. Then, by using the renormalization group technique we analyze the dynamic susceptible-infected-removed (SIR) model for spreading of infections. Interestingly, we find the existence of an epidemic threshold, as compared to the usual epidemic behavior without a finite threshold in uncorrelated scale-free networks. This phenomenon indicates that degree distribution of scale-free networks does not suffice to characterize the epidemic dynamics on top of them. Our results may shed light in the understanding of the epidemics and other spreading phenomena on real-life networks with similar structural features as the considered model.

cond-mat.other↗

arXiv2008

Exact analytical solution of average path length for Apollonian networks

The exact formula for the average path length of Apollonian networks is found. With the help of recursion relations derived from the self-similar structure, we obtain the exact solution of average path length, $\bar{d}_t$, for Apollonian networks. In contrast to the well-known numerical result $\bar{d}_t \propto (\ln N_t)^{3/4}$ [Phys. Rev. Lett. \textbf{94}, 018702 (2005)], our rigorous solution shows that the average path length grows logarithmically as $\bar{d}_t \propto \ln N_t$ in the infinite limit of network size $N_t$. The extensive numerical calculations completely agree with our closed-form solution.

cond-mat.stat-mech↗

arXiv2007

Degree and component size distributions in generalized uniform recursive tree

We propose a generalized model for uniform recursive tree (URT) by introducing an imperfect growth process, which may generate disconnected components (clusters). The model undergoes an interesting phase transition from a singly connected network to a graph consisting of fully isolated nodes. We investigate the distributions of degree and component sizes by both theoretical predictions and numerical simulations. For the nontrivial cases, we show that the network has an exponential degree distribution while its component size distribution follows a power law, both of which are related to the imperfect growth process. We also predict the growth dynamics of the individual components. All analytical solutions are successfully contrasted with computer simulations.

cond-mat.stat-mech↗

arXiv2007

Evolving small-world scale-free networks consist of cliques

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.

physics.soc-ph↗

arXiv2007

A Synthetical Weights' Dynamic Mechanism for Weighted Networks

We propose a synthetical weights' dynamic mechanism for weighted networks which takes into account the influences of strengths of nodes, weights of links and incoming new vertices. Strength/Weight preferential strategies are used in these weights' dynamic mechanisms, which depict the evolving strategies of many real-world networks. We give insight analysis to the synthetical weights' dynamic mechanism and study how individual weights' dynamic strategies interact and cooperate with each other in the networks' evolving process. Power-law distributions of strength, degree and weight, nontrivial strength-degree correlation, clustering coefficients and assortativeness are found in the model with tunable parameters representing each model. Several homogenous functionalities of these independent weights' dynamic strategy are generalized and their synergy are studied.

physics.soc-ph↗

arXiv2007

Maximal planar scale-free Sierpinski networks with small-world effect and power-law strength-degree correlation

Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power-law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski networks, which are induced by the famous Sierpinski fractals and constructed in a simple iterative way. We derive analytical expressions for degree distribution, strength distribution, clustering coefficient, and strength-degree correlation, which agree well with the characterizations of various real-life networks. Moreover, we show that the introduced Sierpinski networks are maximal planar graphs.

physics.soc-ph↗

arXiv2007

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.

physics.soc-ph↗

arXiv2007

Local-world evolving networks with tunable clustering

We propose an extended local-world evolving network model including a triad formation step. In the process of network evolution, random fluctuation in the number of new edges is involved. We derive analytical expressions for degree distribution, clustering coefficient and average path length. Our model can unify the generic properties of real-life networks: scale-free degree distribution, high clustering and small inter-node separation. Moreover, in our model, the clustering coefficient is tunable simply by changing the expected number of triad formation steps after a single local preferential attachment step.

cond-mat.stat-mech↗

arXiv2007

Correlations in random Apollonian network

In this paper, by both simulations and theoretical predictions we study two and three node (or degree) correlations in random Apollonian network (RAN), which have small-world and scale-free topologies. Using the rate equation approach under the assumption of continuous degree, we first give the analytical solution for two node correlations, expressed by average nearest-neighbor degree (ANND). Then, we revisit the degree distribution of RAN using rate equation method and get the exact connection distribution, based on which we derive a more accurate result for mean clustering coefficient as an average quantity of three degree correlations than the one previously reported. Analytical results reveal that ANND has no correlations with respect to degree, while clustering coefficient is dependent on degree, showing a power-law behavior as $C(k)\sim k^{-1}$. The obtained expressions are successfully contrasted with extensive numerical simulations.

cond-mat.stat-mech↗

arXiv2007

A geometric growth model interpolating between regular and small-world networks

We propose a geometric growth model which interpolates between one-dimensional linear graphs and small-world networks. The model undergoes a transition from large to small worlds. We study the topological characteristics by both theoretical predictions and numerical simulations, which are in good accordance with each other. Our geometrically growing model is a complementarity for the static WS model.

cond-mat.stat-mech↗

arXiv2006

From regular to growing small-world networks

We propose a growing model which interpolates between one-dimensional regular lattice and small-world networks. The model undergoes an interesting phase transition from large to small world. We investigate the structural properties by both theoretical predictions and numerical simulations. Our growing model is a complementarity for the famous static WS network model.

cond-mat.stat-mech↗

arXiv2006

Self-similarity, small-world, scale-free scaling, disassortativity, and robustness in hierarchical lattices

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 $q$. 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, while the small-world phenomenon arises. Finally, the dynamical processes of intentional attacks and collective synchronization are studied and the comparisons between HLs and Barab{ási}-Albert (BA) networks as well as SWHLs are shown. 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.

cond-mat.stat-mech↗

arXiv2006

Evolving networks consist of cliques

Many real networks have cliques as their constitutional units. Here we present a family of scale-free network model consist of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and numerically. The obtained analytical solution shows that the networks follow a power-law degree distribution, with degree exponent continuously tuned between 2 and 3, coinciding with the empirically found results. 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.

cond-mat.stat-mech↗

arXiv2006

A general geometric growth model for pseudofractal scale-free web

We propose a general geometric growth model for pseudofractal scale-free web, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks: degree distribution, second moment of degree distribution, degree correlations, distribution of clustering coefficient, as well as the diameter, which are partially determined by the parameters. Analytical results show that the resulting networks are disassortative and follow power-law degree distributions, with a more general degree exponent tuned from 2 to $1+\frac{\ln3}{\ln2}$; the clustering coefficient of each individual node is inversely proportional to its degree and the average clustering coefficient of all nodes approaches to a large nonzero value in the infinite network order; the diameter grows logarithmically with the number of network nodes. All these reveal that the networks described by our model have small-world effect and scale-free topology.

cond-mat.stat-mech↗

arXiv2006

Vertex labeling and routing in expanded Apollonian networks

We present a family of networks, expanded deterministic Apollonian networks, which are a generalization of the Apollonian networks and are simultaneously scale-free, small-world, and highly clustered. We introduce a labeling of their vertices that allows to determine a shortest path routing between any two vertices of the network based only on the labels.

physics.soc-ph↗

arXiv2006

Evolving Apollonian Networks with Small-world Scale-free topologies

We propose two types of evolving networks: evolutionary Apollonian networks (EAN) and general deterministic Apollonian networks (GDAN), established by simple iteration algorithms. We investigate the two networks by both simulation and theoretical prediction. Analytical results show that both networks follow power-law degree distributions, with distribution exponents continuously tuned from 2 to 3. The accurate expression of clustering coefficient is also given for both networks. Moreover, the investigation of the average path length of EAN and the diameter of GDAN reveals that these two types of networks possess small-world feature. In addition, we study the collective synchronization behavior on some limitations of the EAN.

cond-mat.stat-mech↗