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, 223233. ISSN: 02093324. DOI: https://doi.org/10.20858/sjsutst.2018.98.21.
Renata ŻOCHOWSKA[1],
Piotr SOCZÓWKA[2]
ANALYSIS
OF SELECTED TRANSPORTATION NETWORK STRUCTURES BASED ON GRAPH MEASURES
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
1. INTRODUCTION
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 [1,69,22,24].
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.
2. REPRESENTATION OF THE TRANSPORTATION NETWORK
STRUCTURE
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 infrastructures 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:
_{} (1)
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:
_{} (2)
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.:
_{} (3)
where