Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 340780, 11 pages

http://dx.doi.org/10.1155/2015/340780

## Analysis on Topological Properties of Dalian Hazardous Materials Road Transportation Network

^{1}School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 610031, China^{2}Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 610031, China^{3}Kunming Hydroelectric Investigation Design and Research Institute, China Hydropower Engineering Consulting Group Corporation, Kunming 650051, China

Received 19 July 2014; Accepted 10 November 2014

Academic Editor: Hong Chen

Copyright © 2015 Pengyun Chong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

To analyze the topological properties of hazardous materials road transportation network (HMRTN), this paper proposed two different ways to construct the cyberspace of HMRTN and constructed their complex network models, respectively. One was the physical network model of HMRTN based on the primal approach and the other was the service network model of HMRTN based on neighboring nodes. The two complex network models were built by using the case of Dalian HMRTN. The physical network model contained 154 nodes and 238 edges, and the statistical analysis results showed that (1) the cumulative node degree of physical network was subjected to exponential distribution, showing the network properties of random network and that (2) the HMRTN had small characteristic path length and large network clustering coefficient, which was a typical small-world network. The service network model contained 569 nodes and 1318 edges, and the statistical analysis results showed that (1) the cumulative node degree of service network was subjected to power-law distribution, showing the network properties of scale-free network and that (2) the relationship between nodes strength and their descending order ordinal and the relationship between nodes strength and cumulative nodes strength were both subjected to power-law distribution, also showing the network properties of scale-free network.

#### 1. Introduction

Complexity science is the kind of science of the 21st century. Complex network has developed rapidly in the past few years as an important part of the complexity science [1]. Its main idea is to convert the various elements within the research system into nodes of the network, and the relationship between the elements into the edges to form a network in order to describe the relationship among the various elements within the research system. Exploring the essential properties of the real system through the studies of the topological properties of the network structure is an effective method to research complexity science.

Mathematical theory basis of complex network theory is graph theory. Euler’s study on “seven-bridge problem” of Gurney Myers in 1736 was the beginning of the studies into complex network theory. Since then people abstracted a number of complex systems into networks to describe and research from the perspective of the network topology, such as the Internet network [2], the food chain network [3], neural networks [4], and the citation network [5]. Milgram first proposed small-world phenomenon of network in 1967 in the analysis of network structure [6]. Based on this, Watts and Strogatz proposed WS small-world network in the study of small-world phenomenon generation process mechanisms and presented the network generation algorithm for the first time in 1998 [7]. Barabási and Albert found the scale-free properties of real-world networks in 1999, which called BA model, and presented the network generation algorithm [8]. The research results of Watts and Barabási et al. subverted people’s awareness of the traditional network, causing many scholars in the field of physics, economics, and computer communications to focus on complex network [9–11].

The normal operation of traffic and transportation system is an important prerequisite for the steady and rapid development of the national economic, and the complex network theory has attracted wide attention of scholars in transportation field. In current studies, scholars research the topological properties of the transportation network mainly by means of graph theory and network topology theory and so on. Transportation network has growth and irregularity; therefore, these theories can describe networks of simple structure well, but not competent for complex transportation network. The research results of application of complex network theory to the transportation network topological properties are mainly concentrated on the railway network [12–14], airport network [15–20], and urban traffic network [10, 21].

In the studies on topological properties of railway network, Sen et al. [12] studied the Indian railway network in the P space, which showed that it had a shorter average path length and large clustering coefficient, presenting small-world network properties. Li and Cai [13] researched China railway passenger transportation network, and the results showed that the physical railway network had the tree structure and the traffic flow network was a typical small-world network. Kurant and Thiran [14] made an empirical study on the three kinds of space forms P, R, and L of European and Swiss railway networks and analyzed the similarities and differences among the railway network topological properties of different space forms.

In the studies on topological properties of airport network, Guimerà et al. [15, 16] researched global airport networks, and results showed that the airline network was a small-world network, with average shortest path length of 4.4 and the network average clustering coefficient of 0.62. Chi et al. [17] constructed a directed and weighted airport network of USA, with similar research results to Guimerà et al, that is, American airport network also presenting small-world properties, with average shortest path length of 2.4 and the network average clustering coefficient of 0.618. Other scholars have conducted similar studies, such as Bagler [18] on India airport network, Guida and Maria [19] on Italy airport network, and Li and Cai [20] on Chinese airport network. Their results showed that the airport network was small-world network, and the network average clustering coefficient was similar. The only difference was that the average shortest path length of global airport network was greater than that of each national airport networks.

In the studies on topological properties of urban traffic network, Latora and Marchiori [10] researched the complex network properties of the Boston subway network by constructing an undirected and weighted subway network, and results showed that the Boston subway network presented small-world properties. Jiang and Claramunt [21] researched urban road network, and results showed that it presented small-world network properties.

In general, the studies on complex network are mainly focused on the following areas: (1) to simulate the geometrical statistics (such as the number of nodes, the number of edges, the network average node degree) of real world by using generation algorithm of random network, scale-free network, and small-world network [7, 8]; (2) to research dynamic problems of network topology structure [22]; (3) to observe the change of its properties after the implementation of different operation on the network, that is, to research network survivability at different attack strategies [23]. Studies of applying complex network theory to researching the transportation network can be divided roughly into two categories: (1) to research the topological properties of the transportation network, which mostly concentrated on the railway network [12–14], airport network [15–20], urban rail transit network [10], and urban road network [21]; (2) to study how to improve the reliability and survivability of the network under a deliberate or random attack, optimizing network structure when the topological properties of the network are known [24].

Compared with the common freight transportation, hazardous materials transportation objects are flammable, explosive, corrosive, and radioactive such as gasoline, explosive, strong acid, and peroxide. So once an accident happens during the transport process, it will cause serious damage to the environment, the surrounding residents, and the normal operation of economic activity. At present, China railway, airport, and shipping are not perfect in hazardous materials transportation infrastructure and management mechanism, so road transportation is the main way of the hazardous materials transportation. According to statistics, road transports cover about 80% of our hazardous materials [25]. In 2009, China’s annual hazardous materials transport volume is more than 4 million tons, and in the first half of 2013, the total increase in main chemicals is about 6.3%, and more than 95% of the hazardous materials relate to offsite transportation problem [25], so hazardous materials transportation in our country presents properties of having a large volume, a high growth rate, a single mode of transportation, a low safety management level, and so on. Due to the increasing transport volume of hazardous materials, both road mileage and density of road network of hazardous materials transportation network increase significantly, and also the integration and the complexity of the network are more obvious.

Compared to other transportation networks, hazardous materials road transportation network (HMRTN) is a special kind of transit network, which mainly reflected on the following points. (1) Different network planning concept: for common freight transport, the general intention of road network planning is mainly reducing running costs or shortening the distance between two places. Because of the particularity of hazardous materials, transportation risk must be minimized. So the basic principle of HMRTN planning is to minimize risk, which also leads to differences between that and the other road transportation network. (2) Different network system composing elements: edges and nodes of HMRTN should be far away from area of high network density, such as population, schools, water, bridges, and government agencies, which leads to its network structure different from other transportation network. (3) Different network scale: edges and nodes of HMRTN are composed of the city’s main roads and intersections, which is a part of urban road network but different from it. Considering the several factors above, HMRTN must present different topological properties from the other transportation network. When hazardous materials transportation vehicles encounter random attacks (such as traffic accidents) or deliberate attacks (like terrorist attacks) in the transport process, transportation network function will be impaired. In particular, when the accident locates at the network node or edge which is the most “fragile,” it may paralyze the network. Therefore, applying complex network theory to researching topological properties of HMRTN helps to improve the understanding of the properties of network and reduce the damage of the unknown risks to network function.

Based on the above analysis, this paper researches the topological properties of HMRTN. On the basis of constructing hazardous materials road transportation physical network and service network structure models, and analyzing the interaction between them, this paper constructs the physical network model of HMRTN based on the primal approach and the service network model of HMRTN based on the neighboring nodes by applying complex network theory and puts forward the research process of network topological properties. The method is applied to the Dalian HMRTN. This paper researches the complex network properties of HMRTN through the statistical average shortest path length, the network diameter, average network clustering coefficient, node degree, strength, the strength parameters, and so on and provides scientific basis for the planning and optimization of HMRTN.

#### 2. Methodology of Researching Topological Properties of HMRTN

In order to get the network topological properties, the following questions need to be focused on for the research method of hazardous materials road transportation network properties. (1) What is HMRTN? (2) What factors could be used to judge the topological properties of a network? (3) How to judge the type of a complex network? (4) How to construct a HMRTN based on complex network theory? (5) What is the research process of network topological properties? In view of the above questions, the main methods of this paper are explained through the following aspects.

##### 2.1. The Structure Model of HMRTN

HMRTN system is composed of nodes of different nature, the road network of connection among the nodes, and the OD pairs’ information with distribution tasks. Therefore, HMRTN includes physical network and service network, and it has the double attributes. Based on this, this paper constructs its network models, respectively.

*(1) Physical Network Space*. The network in urban road network represents hazardous materials road transportation physical network. is a node set of network that represents the places of actual meaning like intersections, and so forth. If , say network has nodes, ; is the edge set of network , which represents the connection path between two nodes, including expressway, national highway, and the urban road. If , representing edges in network , ; are the edge weights of network , which represents a set of path lengths between any two nodes; that is, . Therefore, the physical network constructed in this paper is an undirected, weighted, and connected network.

*(2) Service Network Space*. In hazardous materials road transportation physical network , where is the minimum risk path between any two nodes and , hazardous materials road transportation vehicles complete the distribution task along the minimum risk path. In the distribution process, transportation vehicles passing distribution center, demand center, and distribution route compose another huge service network , where is the places of actual meaning like hazardous materials distribution center, demand center, and so forth. If , which represents nodes in network , . is the network edge set formed by distribution route passing two neighboring nodes. Because the distribution is divided into upstream and downstream, the edges in network are directed edges. If , which represents edges in network , , , . Therefore, the service network in this paper is a directed, weighted, and connected network.

HMRTN model and spatial interaction are shown in Figure 1.