Nonlinear Relationship and Its Evolutionary Trace between Average Degree and Average Path Length of Edge Vertices of China Aviation Network Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the average degree and the average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 was studied.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the airline as the edge of the network.On the basis of the statistical data,the average degree and average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Through regression analysis,it was found that the average degree had a logarithmic relationship with the average path length of edge vertices and the two parameters of the logarithmic relationship had linear evolutionary trace.

Nonlinear Relationship and Its Evolutionary Trace between Node Degree and Average Path Length of China Aviation Network Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the node degree and the average path length of China aviation network in 1988,1994,2001,2008 and 2015 was studied.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the airline as the edge of the network.On the basis of the statistical data,the node average path length of China aviation network in 1988,1994,2001,2008 and 2015 was calculated.Through regression analysis,it was found that the node degree had a logarithmic relationship with the average length of node path,and the two parameters of the logarithmic relationship had linear evolutionary trace.Key word:China aviation network,complex network,node degree,average length of node path,logarithmic relationship,evolutionary trace.

A Formula of Average Path Length for Unweighted Networks

In this paper,based on the adjacency matrix of the network and its powers,the formulas are derived for theshortest path and the average path length,and an effective algorithm is presented.Furthermore,an example is providedto demonstrate the proposed method.

On the complexity of average path length for biological networks and patterns

Path length calculation is a frequent requirement in studies related to graph theoretic problems such as genetics. Standard method to calculate average path length （APL） of a graph requires traversing all nodes in the graph repeatedly, which is computationally expensive for graphs containing large number of nodes. We propose a novel method to calculate APL for graphs commonly required in the studies of genetics. The proposed method is computationally less expensive and less time-consuming compared to standard method.

Probability Distribution of Average Length of Node Path and Its Evolution Trace of Aviation Network of China Based on Complex Network

In order to reveal the complex network feature and its evolution principle of aviation network of China,probability distribution and its evolution trace of average length of node path of aviation network of China were researched according to statistics data in years 1988,1994,2001,2008 and 2015 of civil aviation of China.Floyd algorithm to calculate the path length between any two nodes of network was applied and average length of node path of aviation network was obtained according to this algorithm.It was discovered that average length of node path to other nodes had normal distribution function in each year.At meantime,the location parameter and scale parameter of normal distribution function had linear evolution trace.Airline rate was an index to describe the density of airline.It was found that average length of node path of aviation network of China evolved synchronously with airline rate and they had linear relationship.

An Ideal Assortative Network and Synchronization

This paper proposes a novel complex network with assortative property based on multi-center networks. The average path length and clustering coefficient of the network are calculated, and the impact on the network topology is investigated. A simple dynamic system established on the proposed network is used to analyze how the assortative property of the network affects synchronization.

APL-based flexibility analysis of manufacturing grid

With the characteristics of diversity, randomness, concurrency and decomposability, tasks in manufacturing field are very complicated, and so manufacturing grid (MG) should have considerable flexibility to deal with this problem. With the definition of node and arc, MG structure is converted into a small-world network. Given construction cost constraint, the problem of shortest task waiting time is transformed into the constrained optimization problem, and a corresponding ?exibility analysis model based on average path length (APL) is proposed, and the premise of arc-length and node-distance are defined. The results of application example show that the analysis model is effiective.

Small World Properties Generated by a New Algorithm Under Same Degree of All Nodes

Based on the model of the same degree of all nodes we proposed before, a new algorithm, the so-called “spread all over vertices” （SAV） algorithm, is proposed for generating small-world properties from a regular ring lattices. During randomly rewiring connections the SAV is used to keep the unchanged number of links. Comparing the SAV algorithm with the Watts-Strogatz model and the “spread all over boundaries” algorithm, three methods can have the same topological properties of the small world networks. These results offer diverse formation of small world networks. It is helpful to the research of some applications for dynamics of mutual oscillator inside nodes and interacting automata associated with networks.

An Intelligent Multi-robot Path Planning in a Dynamic Environment Using Improved Gravitational Search Algorithm

This paper proposes a new methodology to optimize trajectory of the path for multi-robots using improved gravitational search algorithm(IGSA) in clutter environment. Classical GSA has been improved in this paper based on the communication and memory characteristics of particle swarm optimization(PSO). IGSA technique is incorporated into the multi-robot system in a dynamic framework, which will provide robust performance, self-deterministic cooperation, and coping with an inhospitable environment. The robots in the team make independent decisions, coordinate, and cooperate with each other to accomplish a common goal using the developed IGSA. A path planning scheme has been developed using IGSA to optimally obtain the succeeding positions of the robots from the existing position in the proposed environment. Finally, the analytical and experimental results of the multi-robot path planning were compared with those obtained by IGSA, GSA and differential evolution(DE) in a similar environment. The simulation and the Khepera environment result show outperforms of IGSA as compared to GSA and DE with respect to the average total trajectory path deviation, average uncovered trajectory target distance and energy optimization in terms of rotation.

Impact of distance between two hubs on the network coherence of tree networks

We study the impact of the distance between two hubs on network coherence defined by Laplacian eigenvalues.Network coherence is a measure of the extent of consensus in a linear system with additive noise.To obtain an exact determination of coherence based on the distance,we choose a family of tree networks with two hubs controlled by two parameters.Using the tree’s regular structure,we obtain analytical expressions of the coherences with regard to network parameters and the network size.We then demonstrate that a shorter distance and a larger difference in the degrees of the two hubs lead to a higher coherence.With the same network size and distance,the best coherence occurs in the tree with the largest difference in the hub’s degrees.Finally,we establish a correlation between network coherence and average path length and find that they behave linearly.

Topological Properties of Fibonacci Networks

The Fibonacci numbers are the numbers defined by the linear recurrence equation, in which each subsequent number is the sum of the previous two. In this paper, we propose Fibonacci networks using Fibonacci numbers. The analyticai expressions involving degree distribution, average path lengh and mean first passage time are obtained. This kind of networks exhibits the smail-world characteristic and follows the exponential distribution. Our proposed models would provide the vaiuable insights into the deterministicaily delayed growing networks.

Research of Scalability of the Belt-Type Sensor Networks

For the large-scale application requirements of the belt-type networks,the mathematical modeling as well as quantitative analysis for the scalability of the network based on average path length is completed in this paper,and the theorem for the scale scalability of the belt-type networks is derived.The theorem provides a calculation formula for the upper limit of node scale theory of the belt-type networks and a calculation formula for the upper limit of single node load theory.