arXiv subjects

Jihong Guan

Publications and source records attributed to Jihong Guan.

At least 73 records · Page 4Linked to original sources

arXiv2009

Average distance in a hierarchical scale-free network: an exact solution

Various real systems simultaneously exhibit scale-free and hierarchical structure. In this paper, we study analytically average distance in a deterministic scale-free network with hierarchical organization. Using a recursive method based on the network construction, we determine explicitly the average distance, obtaining an exact expression for it, which is confirmed by extensive numerical calculations. The obtained rigorous solution shows that the average distance grows logarithmically with the network order (number of nodes in the network). We exhibit the similarity and dissimilarity in average distance between the network under consideration and some previously studied networks, including random networks and other deterministic networks. On the basis of the comparison, we argue that the logarithmic scaling of average distance with network order could be a generic feature of deterministic scale-free networks.

cond-mat.stat-mech↗

arXiv2009

Mean first-passage time for random walks on the T-graph

For random walks on networks (graphs), it is a theoretical challenge to explicitly determine the mean first-passage time (MFPT) between two nodes averaged over all pairs. In this paper, we study the MFPT of random walks in the famous T-graph, linking this important quantity to the resistance distance in electronic networks. We obtain an exact formula for the MFPT that is confirmed by extensive numerical calculations. The interesting quantity is derived through the recurrence relations resulting from the self-similar structure of the T-graph. The obtained closed-form expression exhibits that the MFPT approximately increases as a power-law function of the number of nodes, with the exponent lying between 1 and 2. Our research may shed light on the deeper understanding of random walks on the T-graph.

cond-mat.stat-mech↗

arXiv2009

Anomalous behavior of trapping on a fractal scale-free network

It is known that the heterogeneity of scale-free networks helps enhancing the efficiency of trapping processes performed on them. In this paper, we show that transport efficiency is much lower in a fractal scale-free network than in non-fractal networks. To this end, we examine a simple random walk with a fixed trap at a given position on a fractal scale-free network. We calculate analytically the mean first-passage time (MFPT) as a measure of the efficiency for the trapping process, and obtain a closed-form expression for MFPT, which agrees with direct numerical calculations. We find that, in the limit of a large network order $V$, the MFPT $ $ behaves superlinearly as $ \sim V^{3/2}$ with an exponent 3/2 much larger than 1, which is in sharp contrast to the scaling $ \sim V^θ$ with $θ\leq 1$, previously obtained for non-fractal scale-free networks. Our results indicate that the degree distribution of scale-free networks is not sufficient to characterize trapping processes taking place on them. Since various real-world networks are simultaneously scale-free and fractal, our results may shed light on the understanding of trapping processes running on real-life systems.

cond-mat.stat-mech↗

arXiv2009

Distinct scalings for mean first-passage time of random walks on scale-free networks with the same degree sequence

In general, the power-law degree distribution has profound influence on various dynamical processes defined on scale-free networks. In this paper, we will show that power-law degree distribution alone does not suffice to characterize the behavior of trapping problem on scale-free networks, which is an integral major theme of interest for random walks in the presence of an immobile perfect absorber. In order to achieve this goal, we study random walks on a family of one-parameter (denoted by $q$) scale-free networks with identical degree sequence for the full range of parameter $q$, in which a trap is located at a fixed site. We obtain analytically or numerically the mean first-passage time (MFPT) for the trapping issue. In the limit of large network order (number of nodes), for the whole class of networks, the MFPT increases asymptotically as a power-law function of network order with the exponent obviously different for different parameter $q$, which suggests that power-law degree distribution itself is not sufficient to characterize the scaling behavior of MFPT for random walks, at least trapping problem, performed on scale-free networks.

cond-mat.stat-mech↗

arXiv2009

Contact graphs of disk packings as a model of spatial planar networks

Spatially constrained planar networks are frequently encountered in real-life systems. In this paper, based on a space-filling disk packing we propose a minimal model for spatial maximal planar networks, which is similar to but different from the model for Apollonian networks [J. S. Andrade, Jr. et al., Phys. Rev. Lett. {\bf 94}, 018702 (2005)]. We present an exhaustive analysis of various properties of our model, and obtain the analytic solutions for most of the features, including degree distribution, clustering coefficient, average path length, and degree correlations. The model recovers some striking generic characteristics observed in most real networks. To address the robustness of the relevant network properties, we compare the structural features between the investigated network and the Apollonian networks. We show that topological properties of the two networks are encoded in the way of disk packing. We argue that spatial constrains of nodes are relevant to the structure of the networks.

cond-mat.stat-mech↗

arXiv2009

Standard random walks and trapping on the Koch network with scale-free behavior and small-world effect

A vast variety of real-life networks display the ubiquitous presence of scale-free phenomenon and small-world effect, both of which play a significant role in the dynamical processes running on networks. Although various dynamical processes have been investigated in scale-free small-world networks, analytical research about random walks on such networks is much less. In this paper, we will study analytically the scaling of the mean first-passage time (MFPT) for random walks on scale-free small-world networks. To this end, we first map the classical Koch fractal to a network, called Koch network. According to this proposed mapping, we present an iterative algorithm for generating the Koch network, based on which we derive closed-form expressions for the relevant topological features, such as degree distribution, clustering coefficient, average path length, and degree correlations. The obtained solutions show that the Koch network exhibits scale-free behavior and small-world effect. Then, we investigate the standard random walks and trapping issue on the Koch network. Through the recurrence relations derived from the structure of the Koch network, we obtain the exact scaling for the MFPT. We show that in the infinite network order limit, the MFPT grows linearly with the number of all nodes in the network. The obtained analytical results are corroborated by direct extensive numerical calculations. In addition, we also determine the scaling efficiency exponents characterizing random walks on the Koch network.

physics.soc-ph↗

arXiv2009

The rigorous solution for the average distance of a Sierpinski network

The closed-form solution for the average distance of a deterministic network--Sierpinski network--is found. This important quantity is calculated exactly with the help of recursion relations, which are based on the self-similar network structure and enable one to derive the precise formula analytically. The obtained rigorous solution confirms our previous numerical result, which shows that the average distance grows logarithmically with the number of network nodes. The result is at variance with that derived from random networks.

cond-mat.stat-mech↗

arXiv2009

Recursive solutions for Laplacian spectra and eigenvectors of a class of growing treelike networks

The complete knowledge of Laplacian eigenvalues and eigenvectors of complex networks plays an outstanding role in understanding various dynamical processes running on them; however, determining analytically Laplacian eigenvalues and eigenvectors is a theoretical challenge. In this paper, we study the Laplacian spectra and their corresponding eigenvectors of a class of deterministically growing treelike networks. The two interesting quantities are determined through the recurrence relations derived from the structure of the networks. Beginning from the rigorous relations one can obtain the complete eigenvalues and eigenvectors for the networks of arbitrary size. The analytical method opens the way to analytically compute the eigenvalues and eigenvectors of some other deterministic networks, making it possible to accurately calculate their spectral characteristics.

cond-mat.stat-mech↗

arXiv2009

Structural and spectral properties of a family of deterministic recursive trees: Rigorous solutions

As one of the most significant models, the uniform recursive tree (URT) has found many applications in a variety of fields. In this paper, we study rigorously the structural features and spectral properties of the adjacency matrix for a family of deterministic uniform recursive trees (DURTs) that are deterministic versions of URT. Firstly, from the perspective of complex networks, we investigate analytically the main structural characteristics of DURTs, and obtain the accurate solutions for these properties, which include degree distribution, average path length, distribution of node betweenness, and degree correlations. Then we determine the complete eigenvalues and their corresponding eigenvectors of the adjacency matrix for DURTs. Our research may shed light in better understanding of the features for URT. Also, the analytical methods used here is capable of extending to many other deterministic networks, making the precise computation of their properties (especially the full spectrum characteristics) possible.

cond-mat.stat-mech↗

arXiv2009

Influences of degree inhomogeneity on average path length and random walks in disassortative scale-free networks

Various real-life networks exhibit degree correlations and heterogeneous structure, with the latter being characterized by power-law degree distribution $P(k)\sim k^{-γ}$, where the degree exponent $γ$ describes the extent of heterogeneity. In this paper, we study analytically the average path length (APL) of and random walks (RWs) on a family of deterministic networks, recursive scale-free trees (RSFTs), with negative degree correlations and various $γ\in (2,1+\frac{\ln 3}{\ln 2}]$, with an aim to explore the impacts of structure heterogeneity on APL and RWs. We show that the degree exponent $γ$ has no effect on APL $d$ of RSFTs: In the full range of $γ$, $d$ behaves as a logarithmic scaling with the number of network nodes $N$ (i.e. $d \sim \ln N$), which is in sharp contrast to the well-known double logarithmic scaling ($d \sim \ln \ln N$) previously obtained for uncorrelated scale-free networks with $2 \leq γ<3$. In addition, we present that some scaling efficiency exponents of random walks are reliant on degree exponent $γ$.

physics.soc-ph↗

arXiv2009

A unified model for Sierpinski networks with scale-free scaling and small-world effect

In this paper, we propose an evolving Sierpinski gasket, based on which we establish a model of evolutionary Sierpinski networks (ESNs) that unifies deterministic Sierpinski network [Eur. Phys. J. B {\bf 60}, 259 (2007)] and random Sierpinski network [Eur. Phys. J. B {\bf 65}, 141 (2008)] to the same framework. We suggest an iterative algorithm generating the ESNs. On the basis of the algorithm, some relevant properties of presented networks are calculated or predicted analytically. Analytical solution shows that the networks under consideration follow a power-law degree distribution, with the distribution exponent continuously tuned in a wide range. The obtained accurate expression of clustering coefficient, together with the prediction of average path length reveals that the ESNs possess small-world effect. All our theoretical results are successfully contrasted by numerical simulations. Moreover, the evolutionary prisoner's dilemma game is also studied on some limitations of the ESNs, i.e., deterministic Sierpinski network and random Sierpinski network.

cond-mat.dis-nn↗

arXiv2009

Random walks on the Apollonian network with a single trap

Explicit determination of the mean first-passage time (MFPT) for trapping problem on complex media is a theoretical challenge. In this paper, we study random walks on the Apollonian network with a trap fixed at a given hub node (i.e. node with the highest degree), which are simultaneously scale-free and small-world. We obtain the precise analytic expression for the MFPT that is confirmed by direct numerical calculations. In the large system size limit, the MFPT approximately grows as a power-law function of the number of nodes, with the exponent much less than 1, which is significantly different from the scaling for some regular networks or fractals, such as regular lattices, Sierpinski fractals, T-graph, and complete graphs. The Apollonian network is the most efficient configuration for transport by diffusion among all previously studied structure.

cond-mat.stat-mech↗

arXiv2009

Different thresholds of bond percolation in scale-free networks with identical degree sequence

Generally, the threshold of percolation in complex networks depends on the underlying structural characterization. However, what topological property plays a predominant role is still unknown, despite the speculation of some authors that degree distribution is a key ingredient. The purpose of this paper is to show that power-law degree distribution itself is not sufficient to characterize the threshold of bond percolation in scale-free networks. To achieve this goal, we first propose a family of scale-free networks with the same degree sequence and obtain by analytical or numerical means several topological features of the networks. Then, by making use of the renormalization group technique we determine the threshold of bond percolation in our networks. We find an existence of non-zero thresholds and demonstrate that these thresholds can be quite different, which implies that power-law degree distribution does not suffice to characterize the percolation threshold in scale-free networks.

cond-mat.stat-mech↗

arXiv2009

Epidemic spreading with nonlinear infectivity in weighted scale-free networks

In this paper, we investigate the epidemic spreading for SIR model in weighted scale-free networks with nonlinear infectivity, where the transmission rate in our analytical model is weighted. Concretely, we introduce the infectivity exponent $α$ and the weight exponent $β$ into the analytical SIR model, then examine the combination effects of $α$ and $β$ on the epidemic threshold and phase transition. We show that one can adjust the values of $α$ and $β$ to rebuild the epidemic threshold to a finite value, and it is observed that the steady epidemic prevalence $R$ grows in an exponential form in the early stage, then follows hierarchical dynamics. Furthermore, we find $α$ is more sensitive than $β$ in the transformation of the epidemic threshold and epidemic prevalence, which might deliver some useful information or new insights in the epidemic spreading and the correlative immunization schemes.

q-bio.PE↗

arXiv2009

Exact solution for mean first-passage time on a pseudofractal scale-free web

The explicit determinations of the mean first-passage time (MFPT) for trapping problem are limited to some simple structure, e.g., regular lattices and regular geometrical fractals, and determining MFPT for random walks on other media, especially complex real networks, is a theoretical challenge. In this paper, we investigate a simple random walk on the the pseudofractal scale-free web (PSFW) with a perfect trap located at a node with the highest degree, which simultaneously exhibits the remarkable scale-free and small-world properties observed in real networks. We obtain the exact solution for the MFPT that is calculated through the recurrence relations derived from the structure of PSFW. The rigorous solution exhibits that the MFPT approximately increases as a power-law function of the number of nodes, with the exponent less than 1. We confirm the closed-form solution by direct numerical calculations. We show that the structure of PSFW can improve the efficiency of transport by diffusion, compared with some other structure, such as regular lattices, Sierpinski fractals, and T-graph. The analytical method can be applied to other deterministic networks, making the accurate computation of MFPT possible.

cond-mat.stat-mech↗

arXiv2008

Effects of accelerating growth on the evolution of weighted complex networks

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 extensive numerical simulations.

physics.soc-ph↗

arXiv2008

Random Sierpinski network with scale-free small-world and modular structure

In this paper, we define a stochastic Sierpinski gasket, on the basis of which we construct a network called random Sierpinski network (RSN). We investigate analytically or numerically the statistical characteristics of RSN. The obtained results reveal that the properties of RSN is particularly rich, it is simultaneously scale-free, small-world, uncorrelated, modular, and maximal planar. All obtained analytical predictions are successfully contrasted with extensive numerical simulations. Our network representation method could be applied to study the complexity of some real systems in biological and information fields.

cond-mat.stat-mech↗

arXiv2008

Topologies and Laplacian spectra of a deterministic uniform recursive tree

The uniform recursive tree (URT) is one of the most important models and has been successfully applied to many fields. Here we study exactly the topological characteristics and spectral properties of the Laplacian matrix of a deterministic uniform recursive tree, which is a deterministic version of URT. Firstly, from the perspective of complex networks, we determine the main structural characteristics of the deterministic tree. The obtained vigorous results show that the network has an exponential degree distribution, small average path length, power-law distribution of node betweenness, and positive degree-degree correlations. Then we determine the complete Laplacian spectra (eigenvalues) and their corresponding eigenvectors of the considered graph. Interestingly, all the Laplacian eigenvalues are distinct.

cond-mat.stat-mech↗