scholarly journals Vertex Labeling and Routing for Farey-Type Symmetrically-Structured Graphs

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 407 ◽  
Author(s):  
Wenchao Jiang ◽  
Yinhu Zhai ◽  
Zhigang Zhuang ◽  
Paul Martin ◽  
Zhiming Zhao ◽  
...  
Keyword(s):  
Routing Protocol ◽  
Routing Algorithm ◽  
Fibonacci Numbers ◽  
Shortest Paths ◽  
Small World ◽  
Dynamic Processes ◽  
Scale Free ◽  
Structured Graphs

The generalization of Farey graphs and extended Farey graphs all originate from Farey graphs. They are simultaneously scale-free and small-world. A labeling of the vertices for them are proposed here. All of the shortest paths between any two vertices in these two graphs can be determined only on their labels. The number of shortest paths between any two vertices is the product of two Fibonacci numbers; it is increasing almost linearly with the order or size of the graphs. However, the label-based routing algorithm runs in logarithmic time O(logn). Our efficient routing protocol for Farey-type models should help contribute toward the understanding of several physical dynamic processes.

scholarly journals Vertex Labeling and Routing for Farey-Type Symmetrically-Structured Graphs

2018 ◽  
Author(s):  
Wenchao Jiang ◽  
Yinhu Zhai ◽  
Zhigang Zhuang ◽  
Paul Martin ◽  
Zhiming Zhao ◽  
...  
Keyword(s):  
Routing Protocol ◽  
Linear Time ◽  
Routing Algorithm ◽  
Fibonacci Numbers ◽  
Shortest Paths ◽  
Small World ◽  
Dynamic Processes ◽  
Scale Free ◽  
Structured Graphs

The generalization of Farey graphs and extended Farey graphs are all originated from Farey graph and scale-free and small-world simultaneously. We propose a labeling of the vertices for it that allows determining all the shortest paths routing between any two vertices only based on their labels. The maximum number of shortest paths between any two vertices is huge as the product of two Fibonacci numbers, however, the label-based routing algorithm runs in linear time O(n). The existence of an efficient routing protocol for Farey-type models should help the understanding of several physical dynamic processes on it.

scholarly journals Studies on the Decrease Mechanisms of Typical Complex Networks

2021 ◽  
Author(s):  
Yuhu Qiu ◽  
Tianyang Lyu ◽  
Xizhe Zhang ◽  
Ruozhou Wang
Keyword(s):  
Average Length ◽  
Shortest Paths ◽  
Real Life ◽  
Network Models ◽  
Small World ◽  
Clustering Coefficient ◽  
Network Growth ◽  
Scale Free ◽  
Complex Network Models ◽  
High Degree

Network decrease caused by the removal of nodes is an important evolution process that is paralleled with network growth. However, many complex network models usually lacked a sound decrease mechanism. Thus, they failed to capture how to cope with decreases in real life. The paper proposed decrease mechanisms for three typical types of networks, including the ER networks, the WS small-world networks and the BA scale-free networks. The proposed mechanisms maintained their key features in continuous and independent decrease processes, such as the random connections of ER networks, the long-range connections based on nearest-coupled network of WS networks and the tendency connections and the scale-free feature of BA networks. Experimental results showed that these mechanisms also maintained other topology characteristics including the degree distribution, clustering coefficient, average length of shortest-paths and diameter during decreases. Our studies also showed that it was quite difficult to find an efficient decrease mechanism for BA networks to withstand the continuous attacks at the high-degree nodes, because of the unequal status of nodes.

scholarly journals Complex network description of the ionosphere

2018 ◽  
Vol 25 (1) ◽  
pp. 233-240
Author(s):  
Shikun Lu ◽  
Hao Zhang ◽  
Xihai Li ◽  
Yihong Li ◽  
Chao Niu ◽  
...  
Keyword(s):  
Complex Network ◽  
Hypothesis Test ◽  
Small World ◽  
Dynamic Processes ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Total Electron ◽  
Scale Free ◽  
Probabilistic Graph ◽  
Small World Property

Abstract. Complex networks have emerged as an essential approach of geoscience to generate novel insights into the nature of geophysical systems. To investigate the dynamic processes in the ionosphere, a directed complex network is constructed, based on a probabilistic graph of the vertical total electron content (VTEC) from 2012. The results of the power-law hypothesis test show that both the out-degree and in-degree distribution of the ionospheric network are not scale-free. Thus, the distribution of the interactions in the ionosphere is homogenous. None of the geospatial positions play an eminently important role in the propagation of the dynamic ionospheric processes. The spatial analysis of the ionospheric network shows that the interconnections principally exist between adjacent geographical locations, indicating that the propagation of the dynamic processes primarily depends on the geospatial distance in the ionosphere. Moreover, the joint distribution of the edge distances with respect to longitude and latitude directions shows that the dynamic processes travel further along the longitude than along the latitude in the ionosphere. The analysis of “small-world-ness” indicates that the ionospheric network possesses the small-world property, which can make the ionosphere stable and efficient in the propagation of dynamic processes.

scholarly journals VORONOI AND FRACTAL COMPLEX NETWORKS AND THEIR CHARACTERIZATION

2004 ◽  
Vol 15 (01) ◽  
pp. 175-183 ◽  
Author(s):  
LUCIANO DA FONTOURA COSTA
Keyword(s):  
Complex Networks ◽  
Metric Spaces ◽  
Spatial Scales ◽  
Shortest Paths ◽  
Network Models ◽  
Small World ◽  
Effective Length ◽  
Scale Free ◽  
Fractal Network ◽  
Natural Means

Real world networks are often characterized by spatial constraints such as the relative position and adjacency of nodes. The present work describes how Voronoi tessellations of the space where the network is embedded provide not only a natural means for relating such networks with metric spaces, but also a natural means for obtaining fractal complex networks. A series of comprehensive measurements closely related to spatial aspects of these networks is proposed, which includes the effective length, adjacency, as well as the fractal dimension of the network in terms of the spatial scales defined by successive shortest paths starting from a specific node. The potential of such features is illustrated with respect to the random, small-world, scale-free and fractal network models.

Small world routing algorithm of wireless sensor network

2010 ◽  
Vol 30 (9) ◽  
pp. 2497-2500
Author(s):  
Xiu-li REN ◽  
Jiang-ying DONG ◽  
Jian-sheng XUE
Keyword(s):  
Wireless Sensor Network ◽  
Sensor Network ◽  
Routing Algorithm ◽  
Small World ◽  
Wireless Sensor

Top Museums on Instagram

2019 ◽  
Vol 3 (2) ◽  
pp. 18-42 ◽  
Author(s):  
Vasiliki G. Vrana ◽  
Dimitrios A. Kydros ◽  
Evangelos C. Kehris ◽  
Anastasios-Ioannis T. Theocharidis ◽  
George I. Kavavasilis
Keyword(s):  
Social Network ◽  
Network Analysis ◽  
Small World ◽  
Marketing Strategies ◽  
The Other ◽  
Small World Network ◽  
Scale Free ◽  
Centrality Metrics ◽  
Photo Sharing ◽  
Visualization Algorithms

Pictures speak louder than words. In this fast-moving world where people hardly have time to read anything, photo-sharing sites become more and more popular. Instagram is being used by millions of people and has created a “sharing ecosystem” that also encourages curation, expression, and produces feedback. Museums are moving quickly to integrate Instagram into their marketing strategies, provide information, engage with audience and connect to other museums Instagram accounts. Taking into consideration that people may not see museum accounts in the same way that the other museum accounts do, the article first describes accounts' performance of the top, most visited museums worldwide and next investigates their interconnection. The analysis uses techniques from social network analysis, including visualization algorithms and calculations of well-established metrics. The research reveals the most important modes of the network by calculating the appropriate centrality metrics and shows that the network formed by the museum Instagram accounts is a scale–free small world network.

Network Routing Mechanism Simulation Research Based on VANETs

2014 ◽  
Vol 651-653 ◽  
pp. 1868-1874
Author(s):  
Li Zhu ◽  
Lan Bai
Keyword(s):  
Routing Protocol ◽  
Vehicular Networks ◽  
Routing Algorithm ◽  
Dynamic Network ◽  
Network Routing ◽  
On Demand ◽  
Routing Mechanism ◽  
Demand Routing ◽  
On The Road ◽  
Low Efficiency

VANETs is a rapid developed wireless mobile MANETs network with special challenge nature. It is a distributed and self-organized communication network based on moving vehicle. This network has characteristics like limited bandwidth, strong mobility, strong dynamic network topology, limited node degrees freedom, equipment capacity constraints and weak physical security. These characteristics usually make typical routing protocol in mobile MANET show a low efficiency in mobile VANETs, even fail. MANET routing algorithm is roughly divided into two categories, namely table driven routing protocol and on-demand routing protocol. It is due to the particularity of driving cars on the road. So how to improve network routing protocol in the performance is now a challenging problem. The purpose of this article studies network routing mechanism based on wireless vehicular networks simulation method. On the basis of analyzing the performance of typical routing protocols in MANET, such as DSDV, AODV and DSR, the improved scheme of AODV on-demand routing algorithm is put forward.

Research and Improvement about LEACH Routing Protocol for Wireless Sensor Networks

2012 ◽  
Vol 241-244 ◽  
pp. 1028-1032
Author(s):  
Li Wang ◽  
Qi Lin Zhu
Keyword(s):  
Routing Protocol ◽  
Routing Algorithm ◽  
Cluster Head ◽  
Wireless Sensor ◽  
Cluster Head Selection ◽  
Selection Algorithm ◽  
Energy Factor ◽  
Random Cluster ◽  
Simulation Results ◽  
Node Energy

In recent years, as the development of wireless sensor network, people do some deep researches on cluster-based protocol, most around the prolongation of the lifetime of WSN and decline of energy consumed by the sensors. This paper analyses of classical clustering routing protocol based on LEACH, aiming at the node energy foot presents energy improved clustering routing algorithm, the random cluster head selection algorithm of threshold to be changed, lowering the threshold, in the original threshold increases the node's remaining energy factor, reduces the communication load of cluster nodes, and simulation. The simulation results show that the LEACH-E improved algorithm, energy saving, reducing balance node energy consumption, effectively prolongs the network lifetime.

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

A Small World Routing Protocol in Wireless Sensor Networks

2011 ◽  
Vol 474-476 ◽  
pp. 828-833
Author(s):  
Wen Jun Xu ◽  
Li Juan Sun ◽  
Jian Guo ◽  
Ru Chuan Wang
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Routing Protocol ◽  
Data Transmission ◽  
Small World ◽  
Wireless Sensor ◽  
Small World Network ◽  
Average Delay ◽  
Network Diameter ◽  
Simulation Results

In order to reduce the average path length of the wireless sensor networks (WSNs) and save the energy, in this paper, the concept of the small world is introduced into the routing designs of WSNs. So a new small world routing protocol (SWRP) is proposed. By adding a few short cut links, which are confined to a fraction of the network diameter, we construct a small world network. Then the protocol finds paths through recurrent propagations of weak and strong links. The simulation results indicate that SWRP reduces the energy consumption effectively and the average delay of the data transmission, which leads to prolong the lifetime of both the nodes and the network.

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