arXiv subjects

Jihong Guan

Publications and source records attributed to Jihong Guan.

81 records · Page 5Linked to original sources

arXiv2008

Transition from fractal to non-fractal scalings in growing scale-free networks

Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter $q$. We obtain the topological properties of the network including the degree distribution, average path length, diameter, fractal dimensions, and betweenness centrality distribution, which are controlled by parameter $q$. Interestingly, we show that by adjusting $q$, the networks undergo a transition from fractal to non-fractal scalings, and exhibit a crossover from `large' to small worlds at the same time. Our research may shed some light on understanding the evolution and relationships of fractal and non-fractal networks.

cond-mat.other↗

arXiv2008

Exact solution of mean geodesic distance for Vicsek fractals

The Vicsek fractals are one of the most interesting classes of fractals and the study of their structural properties is important. In this paper, the exact formula for the mean geodesic distance of Vicsek fractals is found. The quantity is computed precisely through the recurrence relations derived from the self-similar structure of the fractals considered. The obtained exact solution exhibits that the mean geodesic distance approximately increases as an exponential function of the number of nodes, with the exponent equal to the reciprocal of the fractal dimension. The closed-form solution is confirmed by extensive numerical calculations.

cond-mat.dis-nn↗

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

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↗