International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
To measure the spatial network structure, topological 
measures of network structure based on gross characteristics 
and the cyclomatic number can be used (Lo and Yeung, 2002), 
which is represented by numbers of vertexes or nodes and those 
of edges or links in the graph. 
In general, connectivity terms the connected quantity 
between nodes in a given network, to extract overall structure 
of transportation network. It is regarded as one of important 
information to assess transportation network (Han, 1996). 
Several types of connectivity index, in which each index has its 
own applicable meaning, are developed in the domain of 
transportation geography: alpha index, gamma index, and 
shimmel index. 
Especially, it is known that alpha index and gamma index 
measure the most fundamental properties of a network. As for a 
basic application of these indices for connectivity measurement, 
periodic change of road network structure in a given boundary 
of ROI (Region of Interests) or traffic analysis zone shown in 
Fig. 1 can be significantly quantized and compared. 
As shown in Figure 1, extraction of connectivity index needs 
some requirements such as road centre-line representing road 
network structure composed of transportation nodes. A 
transportation node is point feature, composing transportation 
network or topological structure. In some cases, it can be 
processed as target-based node point, where target means a 
point-typed feature for a given application purpose. 
    
X Transportation Node 
ROI \ 
Road (Road Centerline ) 
Figure 1. Use case of degree of connectivity for 
transportation analysis 
As one of important connectivity indices, alpha(a) index is 
defined as the ratio of actual number of circuits to the number 
of maximum circuits in the network (Chou, 1999), where a 
circuit is a loop in the network and is composed of nodes and 
links (equation 1). 
This quantity is useful to evaluate network structure in terms 
of the number of the ways that proceed from one node to 
another, and can be used in comparing and differentiating the 
connectivity levels of different networks. The following 
equation in a planar graph is used to obtain Alpha index in a 
network ranging from 0 and |. 
ium v+1 | 
2v—5 D 
where a = alpha index 
e, v= number of link (or edge) and node (or vertex) 
in a circuit 
Gamma( y) index is defined as the ratio of the actual number 
of edges to the maximum possible number of edges in the 
network. In a planar graph, gamma index can be computed as 
quantity of actual number of links divided by the maximum 
number of links (equation 2). 
It is known that this is useful for comparing two or more 
network structures in transportation analysis. This index ranges 
Otol. 
— e ( 
5 3(v - 2) 
N 
where y = gamma index 
A well-developed transportation network has higher values 
on both alpha and gamma indices which correspond to higher 
levels of complexity and connectivity. But in the non-planar 
graphs of 3-dimensional case, different forms should be applied 
for these indices. 
Unlike these two fundamental indices, shimbel index, D(G), 
is summation of all the shortest path distances(d ;.) among all 
points (vertex and node) in a defined zone or a circuit (equation 
3). Especially, this is useful in evaluating concentrated levels of 
transportation networks in urban transportation analysis. 
D(G)=H Hd, 6) 
i 
where D(G) = shimmel index 
d = shortest path between i node to j node 
In this study, it is designed that these indices can be 
computed in a same user interface. For it, two types of spatial 
layer, which are most fundamental information in GIS-based 
urban applications, are needed: administrative boundary and 
road centerline. These layers can be directly obtained from 
digital map datasets, or these can generate using generic GIS 
tools or CAD tools. In any cases, it is possible to define node 
and polyline elements. 
Figure 2 represents implementation result of connectivity 
analysis's user interface, composed of Select layer, Select 
boundary type, and Extract, with IKONOS imagery. Followed 
by determining target layer in < Step 1 >, function of ‘Select 
boundary types’ of <Step 2> is to choose analysis zone to 
automatically extract nodes in <Step 3>. It shows selected name, 
coordinate, area. If selection of “Extract Road node” button in 
<Step 3>, edge(e) and vertex(v) are abstracted automatically. 
Finally, alpha, gamma, Shimbel index are calculated by 
“Calculate index” button control. 
Computed results are shown in ‘Index info’ in this dialog. In 
this process, geo-spatial imagery can be effectively used to find 
out spatial features related to analysis zone selection in an 
arbitrary polygon. Digital layers and rectified geo-spatial 
imagery of a certain city nearby Seoul are used in Figures 3 and 
  
Figure 2. User interface of extraction extension program of 
Connectivity index with IKONOS imagery 
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