Article citation information:

Żochowska, R., Soczówka, P. Analysis of selected transportation network structures based on graph measures. Scientific Journal of Silesian University of Technology. Series Transport. 2018, 98, 223-233. ISSN: 0209-3324. DOI:



Renata ŻOCHOWSKA[1], Piotr SOCZÓWKA[2]






Summary. The structure of transportation networks has been the subject of analysis for many years, due to the important role that it plays in assessing the efficiency of transportation systems. One of the most common approaches to representing this structure is to use graph theory, in which elements of transportation infrastructure are depicted by a set of vertices and edges. An approach based on graph theory allows us to assess the structure of a transportation network in terms of connectivity, accessibility, density or complexity. In the paper, different transportation network structures are assessed and compared, based on graph measures.

Keywords: transportation network, graph theory, graph and topology measures





A transportation network is usually understood as a set of transportation points, with connections between them, in the form of paths or routes, designed for travel by people, cargo shipments and the passage of vehicles [20]. The spatial structure of such a network corresponds to the connections that exist between the elements of transportation infrastructure in the geographical space. This means that elements of the transportation network are also elements of land use in the area in which they are located [5]. The volume of traffic flows, expressed by the number of travelling people, as well as moving vehicles, or by the mass of carried goods in a given unit of time, is one of the measures of transportation network performance.

The efficiency of the entire transportation system in the area under analysis is largely determined by the structure of its transportation network. The denser and more consistent the network, the greater the number of connections between two selected vertices. This has a significant impact on the possibility of reducing traffic congestion by moving traffic onto alternative roads, which in turn means shorter travel time. This explains why the analysis of transportation network structures has been the subject of intensive research for many decades [1,6-9,22,24].

The article analyses the assessment of selected structures of a transportation network based on graph measures. The network models correspond to real transportation systems. The analysis is carried out in terms of the possibility of using different types of graph measures when assessing the propagation of disturbances in the transportation network.





The physical topology of a network, which is understood as the arrangement of nodes and links in the network, is based on point and linear transportation infrastructure objects. The aim of the study is to define the scope of the representation of the infrastructure’s elements and the connections between them. Therefore, the structure of the network may be both very simplified and particularly complex. Thus, depending on the adopted criteria for the classification of transportation systems, scales and aggregation level, a transportation node may be a single intersection, a bus stop, a railway station, a road junction, an airport, a logistics centre or even a whole city. In turn, the link may be a single traffic lane, a railway track, a communication route or a corridor connecting important transportation nodes. When designing a network model, the proper representation of location, direction and connections is of particular importance. It is also worth noting that the topology of a network model should be as close as possible to the structure of the real network it represents [18].

The structure of the transportation network can be mapped by using various mathematical tools. One of the most commonly and intuitive approaches is to represent the transportation system of the studied area using graph theory [12,25]. Graph methods has been used to map and study the spatial structure of transportation networks since the 1960s [10,13]. In Poland, they have been used, for example, to assess the topological accessibility of the railway network of the West Pomeranian Voivodeship [19], former Poznań Province [15,16] and Silesia [21].

The main requirement of topological analysis is to represent an existing transportation network as an abstract set of points (nodes or vertices), connected by a set of lines (segments, edges or arcs). In the graph theory approach, attention is primarily centred on the arrangement of connections between nodes, which allows for the use of undirected graphs. Metric and capacity characteristics are also often ignored [2].

Two basic approaches to the representation of a transportation network structure using graph theory are found in the literature [23]:

-          Primal, in which the nodes of the network are represented in the form of vertices, and links in the form of arcs or edges

-          Dual, in which the sections of the network are represented in the form of vertices, and nodes in the form of arcs or edges


For the purpose of analysing the values of selected graph measures for various structures of a transportation network, a set of numbers relating to the types of structures has been determined as follows:




where is the number for structure type, and is the number for all structure types under analysis. Therefore, using the primal approach to mapping the structure of the transportation network, the -th structure of the network may be described in the form of a graph:



where is the set of vertices of graph ,is the set of edges of graph . Both the vertices and the edges are sequentially numbered. Therefore, the set  contains subsequent numbers for the vertices of graph , i.e.: