“When different points, whether in one-, two- or three-dimensional space, are linked together into a structure they are said to form a network. Such networks, by carrying flows of goods, people, information or anything else that is moved from place to place, give rise to regional transport systems” (Robinson and Bamford, 1978).
The term ‘network’ is basically used for the spatial pattern of transportation facilities in a given region. The description and analysis of the transport network has been a traditional concern of geographers. Among the methods used by earlier geographers, have been the preparation of maps and tables listing distances, capacities, flow and such indices as network densities and isochrones.
Similarly, the general layout of a transport network can be described in verbal terms like linear, tree-like, grid-iron, radial, web-like, etc. “This kind of description is unsatisfactory, however for at least two reasons. Firstly, it is imprecise and unsuitable for comparison among several networks. Secondly, it is possible that the visual appearance of the layout is only a superficial feature and that underlying features that can be described in terms of topological ratios or detour indices cover more meaningful aspects of the network and describe better whether it is successful and efficient” (Cole and King, 1968).
Hence, a purely qualitative approach is inadequate and the geographer seeks to examine networks in a quantitative way. Therefore, during the past several years, a more consistent set of summarising measures of network characteristics has been developed in order to provide a’ better basis for structural analysis of the transport networks. Most of these measures are based on the graph theory and the abstract concept of mathematics. Prior to the discussion on the various measures of network analysis, it is essential to describe the geometry of networks.
The analysis of transport networks has become an important part of geographical studies. Transport networks are highly complex spatial systems and their analysis is based on graph theory. A regional transport system is a combination of point- to-point movements that occur between origins and destinations. Point-to-point movements are the basis of all kinds of flows and are responsible for spatial arrangements. “When different points, whether in one-, two- or three-dimensional space, are linked together into a structure they are said to form a network. Such networks, by carrying flows of goods, people, information or anything else that is moved from place to place, give rise to regional transport systems” (Robinson and Bamford, 1978).
The regional transport network analysis is done by developing topological map. A topological map or graph reduces a transport network to its simplest form and such simplicity map helps us more easily to understand the characteristics of transport networks. In such a map, the line patterns or networks are described in terms of their topological characteristics, which do not rely so much upon distances and directions but rather upon contiguity, relative locations and systematisation of lines and junctions.
Figure 4.1 depicts topological transformation of actual routes. In order to apply graph theory to the analysis of a transport network, it is necessary to idealise the network into the form of a graph. In this graph, we are treating only the topological properties of the transportation system, not the whole range of properties of any given network. But, it provides a basis for the measures of the structural properties of the transportation system.
Network Graphs and Types:
In topological network or a graph, the following elements have been identified, which translate the observed relationships of networks into numerical and symbolic form.
Vertices or nodes (v) – The points which form the basic elements of a graph are commonly known as vertices and are sometimes designated as nodes.
Edges or links (e) – The lines connecting the vertices or nodes are called edges or links.
Regions or faces – The areas enclosed by area are referred as regions or faces.
Nodes or vertices are located at the junctions of two or more areas. According to the number of junctions affected, they are termed 2-node, 3-node, 4-node, etc. Where a node occurs at the end of an arc, i.e., at a terminus, it is called an end-node.
Arcs are lines, representing routes, which link nodes. One arc only may link two nodes. An arc leading to an end-node is termed a branch. A path is a collection of routes or, in other words, a set of consecutive arcs, which link together series of nodes, e.g., in Figure 4.2, ABCD forms a path.
Circuits are formed by a closed path, e.g., in Figure 4.2, ABCDA and ACDA are circuits. A circuit, which does not contain any other circuits, e.g., ABCA and ACDA, is called a fundamental circuit, and is different from ABCDA, which is made up of two other circuits.
A region or a face is an area bounded by a fundamental circuit thus in Figure 4.2, there are two regions.
Connected and unconnected networks:
A network is said to be connected when it is possible to reach a vertex from any other vertex by following the lines or the edges connecting the different vertices. Otherwise, the graph is considered to be unconnected.
Oriented and non-oriented graphs:
The oriented graphs recognise the direction of the link, whereas in the case of non-oriented graphs no consideration is paid to the direction of the link.
Planar and non-planar graphs:
A graph which can be mapped on a plane such that no two edges have a point in common that is not a vertex is known as a planar graph. Graphs which cannot be mapped in the manner stated above are called non-planar graphs. The pattern of transport network varies in their structure, size, connectivity and complexity. On the basis of their basic geometrical characteristics, Haggett has described the classification of networks as depicted in Figure 4.3.
The planar graphs are two-dimensional, in which, the arcs may, and frequently do, intersect, i.e., they share the same crossing point. On the other hand non-planar graphs are three-dimensional, in which two arcs may cross one another and they do so without intersecting. This is because one of the arcs is permitted to pass for a short distance into the third space dimension.
The planar nets are of four types, viz., paths, trees, circuits and cells. The single line or paths is the simplest network. There are two kinds of singe line paths: direct paths and wondering paths. The search for optimum paths can be selected by following shortest-route paths, maximum flow paths and minimum-cost paths. The second type of geographical network is the tree-like, which is similar to that of dendritic drainage system, in which every vertex is linked to the network by an arc but they are without connecting loops to make a circuit.
The circuits or loops are the complex network system in a region. In this system, there is a greater degree of connectivity and likewise, the greater the degree of connectivity, the more efficient will be a transportation network. The fourth type of geographical network is the cellular network. The cells form barrier lines across which flows move.
Cole and King (1968) have listed the following questions which are to be taken into consideration during network analysis:
(i) How many nodes are there in a network – two, three, several, many? The number of nodes is important because they determined the complexity of a network.
(ii) How many arcs are there?
(iii) Does the graphs represent a real network (it may be an abstract or imaginary network) and, if so, does it have channels?
(iv) Is the graph, directed or not – in other words, is movement one-way or two-way along the arcs?
(v) What sort of correspondence are there between nodes?
(vi) What kinds of distances are involved?
(vii) What is the orientation of the network?