The asymptotic formula on average weighted path length for scale-free modular network

2021 ◽  
pp. 2150298
Author(s):  
Min Niu ◽  
Mengjun Shao
Keyword(s):  
Asymptotic Formula ◽  
Shortest Path ◽  
Path Length ◽  
Average Path Length ◽  
Modular Network ◽  
Scale Free ◽  
Iteration Formula ◽  
Modular Networks ◽  
Unweighted Network ◽  
Sum Of Distances

In this paper, we discuss the average path length for a class of scale-free modular networks with deterministic growth. To facilitate the analysis, we define the sum of distances from all nodes to the nearest hub nodes and the nearest peripheral nodes. For the unweighted network, we find that whether the scale-free modular network is single-hub or multiple-hub, the average path length grows logarithmically with the increase of nodes number. For the weighted network, we deduce that when the network iteration [Formula: see text] tends to infinity, the average weighted shortest path length is bounded, and the result is independent of the connection method of network.

SCALE-FREE AND SMALL-WORLD PROPERTIES OF A SPECIAL HIERARCHICAL NETWORK

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950010
Author(s):  
DAOHUA WANG ◽  
YUMEI XUE ◽  
QIAN ZHANG ◽  
MIN NIU
Keyword(s):  
Degree Distribution ◽  
Path Length ◽  
Small World ◽  
Average Path Length ◽  
Clustering Coefficient ◽  
Hierarchical Network ◽  
Scale Free

Many real systems behave similarly with scale-free and small-world structures. In this paper, we generate a special hierarchical network and based on the particular construction of the graph, we aim to present a study on some properties, such as the clustering coefficient, average path length and degree distribution of it, which shows the scale-free and small-world effects of this network.

ASYMPTOTIC FORMULA ON AVERAGE PATH LENGTH OF A SPECIAL NETWORK BASED ON SIERPINSKI CARPET

Fractals ◽  
2018 ◽  
Vol 26 (03) ◽  
pp. 1850039 ◽  
Author(s):  
YUMEI XUE ◽  
DONGXUE ZHOU
Keyword(s):  
Asymptotic Formula ◽  
Path Length ◽  
Average Path Length ◽  
The Self ◽  
Renewal Theorem ◽  
Self Similarity ◽  
Sierpinski Carpet ◽  
Sierpiński Carpet

In this paper, we construct a special network based on the construction of the Sierpinski carpet. Using the self-similarity and renewal theorem, we obtain the asymptotic formula for the average path length of our evolving network.

scholarly journals A Multilevel Simplification Algorithm for Computing the Average Shortest-Path Length of Scale-Free Complex Network

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guoyong Mao ◽  
Ning Zhang
Keyword(s):  
Complex Network ◽  
Shortest Path ◽  
Path Length ◽  
Large Scale ◽  
Computation Time ◽  
Scale Free Network ◽  
Original Network ◽  
Memory Space ◽  
Scale Free ◽  
Free Network

Computing the average shortest-path length (ASPL) of a large scale-free network needs much memory space and computation time. Based on the feature of scale-free network, we present a simplification algorithm by cutting the suspension points and the connected edges; the ASPL of the original network can be computed through that of the simplified network. We also present a multilevel simplification algorithm to get ASPL of the original network directly from that of the multisimplified network. Our experiment shows that these algorithms require less memory space and time in computing the ASPL of scale-free network, which makes it possible to analyze large networks that were previously impossible due to memory limitations.

An estimation formula for the average path length of scale-free networks

2008 ◽  
Vol 17 (7) ◽  
pp. 2327-2332 ◽  
Author(s):  
Li Ying ◽  
Cao Hong-Duo ◽  
Shan Xiu-Ming ◽  
Ren Yong
Keyword(s):  
Path Length ◽  
Average Path Length ◽  
Scale Free ◽  
Estimation Formula ◽  
Scale Free Networks

The average path length of scale free networks

2008 ◽  
Vol 13 (7) ◽  
pp. 1405-1410 ◽  
Author(s):  
Fei Chen ◽  
Zengqiang Chen ◽  
Xiufeng Wang ◽  
Zhuzhi Yuan
Keyword(s):  
Path Length ◽  
Average Path Length ◽  
Scale Free ◽  
Scale Free Networks

THE RELEVANCE-STRENGTH IN A SCALE-FREE NETWORK

2008 ◽  
Vol 22 (31) ◽  
pp. 3053-3059 ◽  
Author(s):  
HYUN-JOO KIM
Keyword(s):  
Network Model ◽  
Shortest Path ◽  
Power Law ◽  
Path Length ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network ◽  
The Mean

We introduce a new quantity, relevance-strength which describes the relevance of a node to the others in a scale-free network. We define a weight between two nodes i and j based on the shortest path length between them and the relevance-strength of a node is defined as the sum of the weights between it and others. For the Barabási and Albert model which is a well-known scale-free network model, we measure the relevance-strength of each node and study the correlations with other quantities, such as the degree, the mean degree of neighbors of a node, and the mean relevance-strength of neighbors. We find that the relevance-strength shows power law behaviors and the crossover behaviors for the degree and the mean relevance-strength of neighbors. Also, we study the scaling behaviors of the relevance-strength for various average relevance-strength for all nodes.

An improved global dynamic routing strategy for scale-free network with tunable clustering

2016 ◽  
Vol 30 (22) ◽  
pp. 1650302 ◽  
Author(s):  
Lina Sun ◽  
Ning Huang ◽  
Yue Zhang ◽  
Yannan Bai
Keyword(s):  
Shortest Path ◽  
Path Length ◽  
Network Capacity ◽  
Network Routing ◽  
Scale Free Network ◽  
Scale Free ◽  
Global Dynamic ◽  
Routing Strategy ◽  
Traffic Awareness ◽  
Free Network

An efficient routing strategy can deliver packets quickly to improve the network capacity. Node congestion and transmission path length are inevitable real-time factors for a good routing strategy. Existing dynamic global routing strategies only consider the congestion of neighbor nodes and the shortest path, which ignores other key nodes’ congestion on the path. With the development of detection methods and techniques, global traffic information is readily available and important for the routing choice. Reasonable use of this information can effectively improve the network routing. So, an improved global dynamic routing strategy is proposed, which considers the congestion of all nodes on the shortest path and incorporates the waiting time of the most congested node into the path. We investigate the effectiveness of the proposed routing for scale-free network with different clustering coefficients. The shortest path routing strategy and the traffic awareness routing strategy only considering the waiting time of neighbor node are analyzed comparatively. Simulation results show that network capacity is greatly enhanced compared with the shortest path; congestion state increase is relatively slow compared with the traffic awareness routing strategy. Clustering coefficient increase will not only reduce the network throughput, but also result in transmission average path length increase for scale-free network with tunable clustering. The proposed routing is favorable to ease network congestion and network routing strategy design.

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