Survivability of public transit network based on network structure entropy

2015 ◽  
Vol 26 (09) ◽  
pp. 1550104 ◽  
Author(s):  
Bai-Bai Fu ◽  
Lin Zhang ◽  
Shu-Bin Li ◽  
Yun-Xuan Li
Keyword(s):  
Network Model ◽  
Network Structure ◽  
Public Transit ◽  
Small World ◽  
Clustering Coefficient ◽  
Statistical Characteristics ◽  
Network Efficiency ◽  
Transit Network ◽  
Scale Free ◽  
The Public

In this work, we have collected 195 bus routes and 1433 bus stations of Jinan city as sample date to build up the public transit geospatial network model by applying space L method, until May 2014. Then, by analyzing the topological properties of public transit geospatial network model, which include degree and degree distribution, average shortest path length, clustering coefficient and betweenness, we get the conclusion that public transit network is a typical complex network with scale-free and small-world characteristics. Furthermore, in order to analyze the survivability of public transit network, we define new network structure entropy based on betweenness importance, and prove its correctness by giving that the new network structure entropy has the same statistical characteristics with network efficiency. Finally, the "inflexion zone" is discovered, which can be taken as the momentous indicator to determine the public transit network failure.

scholarly journals Afrikaans as a complex network: The word co-occurrence network in André P. Brink’s Donkermaan in Afrikaans, Dutch and English

2016 ◽  
Vol 35 (1) ◽  
Author(s):  
Burgert A. Senekal ◽  
Cornelia Geldenhuys
Keyword(s):  
Complex Systems ◽  
Network Model ◽  
Network Structure ◽  
Random Network ◽  
Small World ◽  
Distribution Patterns ◽  
Small World Networks ◽  
Scale Free ◽  
Free Network ◽  
Link Distribution

Language has already been approached as a system since De Saussure, and recently the theory of complex systems has been applied within Linguistics as well. Complex systems, however, can also be modelled as complex networks, and a variety of studies investigating the network structure of language have already been undertaken worldwide. The current study follows in the footsteps of overseas studies and investigates the network structure of Afrikaans by analysing a word co-occurrence network compiled from André P. Brink’s novel Donkermaan. Link distribution patterns and the small-world phenomenon are investigated and then compared to the English and Dutch translations of this novel. The current study represents the first network study of Afrikaans. Firstly, the random network model of Erdös and Rényi and the scale-free network model by Barabási and Albert are used to indicate that the link distribution patterns in a word co-occurrence network of Afrikaans are better described according to the network model of Barabási and Albert than by that of Erdös and Rényi. Furthermore, the method proposed by Humphreys and Gurney to define smallworldedness (S) was used to quantify this phenomenon for the Afrikaans, as well as English and Dutch versions of the text. With 522 ≤ S ≤ 797, it is indicated that Afrikaans, English and Dutch are all clearly small-world networks. Suggestions are also made for further research.

scholarly journals Cross-Shareholdings Structural Characteristic and Evolution Analysis Based on Complex Network

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaohong Chang ◽  
Haiyun Wang
Keyword(s):  
Complex Network ◽  
Network Structure ◽  
Practical Importance ◽  
Small World ◽  
Clustering Coefficient ◽  
Policy Makers ◽  
Scale Free ◽  
Network Properties ◽  
The Cross ◽  
Cross Shareholdings

This study depicts the network morphology of firms which establish ties through cross-shareholdings by the theory of complex network analysis method. It calculates some complex network properties of the cross-shareholdings network and analyzes the evolution law of network structure in nearly 7 years. The network clearly displays small world properties and scale-free properties. The cross-shareholdings network average path length and clustering coefficient is with a small amplitude fluctuation; the network structure is relatively stable. Such a study is of practical importance and could provide opportunities for policy makers to improve the performance of the cross-shareholdings network.

scholarly journals Research on Optimization of Urban Public Transport Network Based on Complex Network Theory

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2436
Author(s):  
Zhongyi Lin ◽  
Yang Cao ◽  
Huasheng Liu ◽  
Jin Li ◽  
Shuzhi Zhao
Keyword(s):  
Public Transportation ◽  
Solution Method ◽  
Public Transit ◽  
Network Efficiency ◽  
Transit Network ◽  
Complex Network Theory ◽  
The Public ◽  
Passenger Travel ◽  
Public Transportation System ◽  
Travel Impedance

The urban public transportation system is an important part of urban transportation, and the rationality of public transportation routes layout plays a vital role in the transportation of the city. Improving the efficiency of public transportation can have a positive impact on the operation of the public transportation system. This paper uses complex network theory and the symmetry of the up and down bus routes and stations to establish an urban public transit network model and calculates the probability of passengers choosing different routes in the public transit network according to passenger travel impedance. Based on passenger travel impedance, travel path probability and passenger travel demand, the links are weighed, and the network efficiency calculation method is improved. Finally, the public transit network optimization model was established with network efficiency as the objective function and solved by the ant colony algorithm. In order to verify the effectiveness of the model and the solution method, this paper selects areas in Nanguan District of Changchun City for example analysis. The result shows that the efficiency of the optimized network is 8.5% higher than that of the original network, which proves the feasibility of the optimized model and solution method.

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.

The Research of Complex Network on Archives Blog

2011 ◽  
Vol 181-182 ◽  
pp. 14-18
Author(s):  
Yi He
Keyword(s):  
Information Sharing ◽  
Complex Network ◽  
Network Model ◽  
Degree Distribution ◽  
Small World ◽  
Scale Free ◽  
Set Up

At the background of archives blog on Internet, this paper constructs a directed complex network model, and analyzes the network characters such as degree distribution. To verify its efficiency, we collect blogs’ information and set up a complex network..From the analysis result of the simulation and demonstration network, we know that they have the same characters, which show that, the virtual society network has small-world effect and scale-free character compared with real society network. The results indicate that the establishment of archives blog is favor to spread rapidly archives information, improve information sharing efficiency and promote the development of archives technology.

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 Directed random geometric graphs

2019 ◽  
Vol 7 (5) ◽  
pp. 792-816
Author(s):  
Jesse Michel ◽  
Sushruth Reddy ◽  
Rikhav Shah ◽  
Sandeep Silwal ◽  
Ramis Movassagh
Keyword(s):  
Real World ◽  
Word Association ◽  
Graph Model ◽  
Small World ◽  
Geometric Graph ◽  
Clustering Coefficient ◽  
Random Geometric Graph ◽  
Random Geometric Graphs ◽  
Scale Free ◽  
Small World Property

Abstract Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet and the network of followers on Twitter among many others. The challenge, however, is to create a network model that has many of the properties of real-world networks such as power-law degree distributions and the small-world property. To meet these challenges, we introduce the Directed Random Geometric Graph (DRGG) model, which is an extension of the random geometric graph model. We prove that it is scale-free with respect to the indegree distribution, has binomial outdegree distribution, has a high clustering coefficient, has few edges and is likely small-world. These are some of the main features of aforementioned real-world networks. We also empirically observed that word association networks have many of the theoretical properties of the DRGG model.

scholarly journals Public transit network planning in small cites considering safety and convenience

2020 ◽  
Vol 12 (1) ◽  
pp. 168781402090235 ◽  
Author(s):  
Changxi Ma ◽  
Dong Yang
Keyword(s):  
Traffic Congestion ◽  
Public Transit ◽  
Network Planning ◽  
Optimization Method ◽  
Transit Oriented Development ◽  
Transit Planning ◽  
Transit Network ◽  
The Public ◽  
Traffic Generation ◽  
Interval Value

Scientific and rational public transit network planning, not only can effectively alleviate city traffic congestion, but also can reduce the risk of accidents. First, based on the data of residents’ travel survey, this article employs the multiple regression method to forecast the traffic generation and adopts the double-constrained gravity model to forecast the residents’ travel distribution of small cites. Second, by aiming at public transit planning objectives, the unsafe roads for public transit are screened, and the public transit trip-mode sharing rate is set as the interval value. According to the interval value, the public transit trip-mode sharing rate is divided into three cases, and the three alternatives of public transit network are calculated based on the network optimization method and the public transit-oriented development model. Next, the alternatives are evaluated by the set pair analysis method, and the optimal scheme is selected. Finally, this article takes the public transit network planning of Huaiyuan County in Anhui Province as an example, and the results show the proposed method is feasible.

scholarly journals Complex network theory, streamflow, and hydrometric monitoring system design

2015 ◽  
Vol 19 (7) ◽  
pp. 3301-3318 ◽  
Author(s):  
M. J. Halverson ◽  
S. W. Fleming
Keyword(s):  
Complex Network ◽  
Network Theory ◽  
Small World ◽  
Detection Algorithm ◽  
Clustering Coefficient ◽  
Network Stability ◽  
Meteorological Forcing ◽  
Complex Network Theory ◽  
Scale Free ◽  
Seasonal Flow

Abstract. Network theory is applied to an array of streamflow gauges located in the Coast Mountains of British Columbia (BC) and Yukon, Canada. The goal of the analysis is to assess whether insights from this branch of mathematical graph theory can be meaningfully applied to hydrometric data, and, more specifically, whether it may help guide decisions concerning stream gauge placement so that the full complexity of the regional hydrology is efficiently captured. The streamflow data, when represented as a complex network, have a global clustering coefficient and average shortest path length consistent with small-world networks, which are a class of stable and efficient networks common in nature, but the observed degree distribution did not clearly indicate a scale-free network. Stability helps ensure that the network is robust to the loss of nodes; in the context of a streamflow network, stability is interpreted as insensitivity to station removal at random. Community structure is also evident in the streamflow network. A network theoretic community detection algorithm identified separate communities, each of which appears to be defined by the combination of its median seasonal flow regime (pluvial, nival, hybrid, or glacial, which in this region in turn mainly reflects basin elevation) and geographic proximity to other communities (reflecting shared or different daily meteorological forcing). Furthermore, betweenness analyses suggest a handful of key stations which serve as bridges between communities and might be highly valued. We propose that an idealized sampling network should sample high-betweenness stations, small-membership communities which are by definition rare or undersampled relative to other communities, and index stations having large numbers of intracommunity links, while retaining some degree of redundancy to maintain network robustness.

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