arXiv subjects

Lili Rong

Publications and source records attributed to Lili Rong.

11 recordsLinked to original sources

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↗

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↗

arXiv2005

General model for Apollonian networks

We introduce a general deterministic model for Apollonian Networks in an iterative fashion. The networks have small-world effect and scale-free topology. We calculate the exact results for the degree exponent, the clustering coefficient and the diameter. The major points of our results indicate that (a) the degree exponent can be adjusted in a wide range, (b) the clustering coefficient of each individual vertex is inversely proportional to its degree and the average clustering coefficient of all vertices approaches to a nonzero value in the infinite network order, and (c) the diameter grows logarithmically with the number of network vertices.

cond-mat.stat-mech↗

arXiv2005

Deterministic scale-free networks created in a recursive manner

In a recursive way and by including a parameter, we introduce a family of deterministic scale-free networks. The resulting networks exhibit small-world effects. We calculate the exact results for the degree exponent, the clustering coefficient and the diameter. The major points of our results indicate: the degree exponent can be adjusted; the clustering coefficient of each individual vertex is inversely proportional to its degree and the average clustering coefficient of all vertices approaches to a nonzero value in the infinite network order; and the diameter grows logarithmically with the number of network vertices.

cond-mat.stat-mech↗

arXiv2005

Evolving small-world networks with geographical attachment preference

We introduce a minimal extended evolving model for small-world networks which is controlled by a parameter. In this model the network growth is determined by the attachment of new nodes to already existing nodes that are geographically close. We analyze several topological properties for our model both analytically and by numerical simulations. The resulting network shows some important characteristics of real-life networks such as the small-world effect and a high clustering.

cond-mat.stat-mech↗

arXiv2005

A deterministic small-world network created by edge iterations

Small-world networks are ubiquitous in real-life systems. Most previous models of small-world networks are stochastic. The randomness makes it more difficult to gain a visual understanding on how do different nodes of networks interact with each other and is not appropriate for communication networks that have fixed interconnections. Here we present a model that generates a small-world network in a simple deterministic way. Our model has a discrete exponential degree distribution. We solve the main characteristics of the model.

cond-mat.stat-mech↗

arXiv2005

High Dimensional Apollonian Networks

We propose a simple algorithm which produces high dimensional Apollonian networks with both small-world and scale-free characteristics. We derive analytical expressions for the degree distribution, the clustering coefficient and the diameter of the networks, which are determined by their dimension.

cond-mat.other↗

arXiv2005

Growing Small-World Networks Generated by Attaching to Edges

We introduce a minimal model of small-world growing network generated by attaching to edges. The produced network is a plane graph which exists in real-life world. We obtain the analytic results of degree distribution decaying exponentially with degree and average clustering coefficient $C={3/2}ln3-1\approx 0.6479$, which are in good agreement with the numerical simulations. We also prove that the increasing tendency of average path length of the considered network is a little slower than the logarithm of the network order $N$.

cond-mat.stat-mech↗

arXiv2005

High dimensional random Apollonian networks

We propose a simple algorithm which produces a new category of networks, high dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and clustering coefficients which are determined by the dimension of the network. The values obtained for these parameters are in good agreement with simulation results and comparable to those coming from real networks. We prove also analitically that the average path length of the networks increases at most logarithmically with the number of vertices.

cond-mat.other↗