Shimbel Index and Koenig Number: Accessibility Analysis

 Introduction: 

Transportation is the movement of people and goods through the pathways or Networks (rail, road, pipe line, water, air) by means of vehicles drawn by animal power, natural or mechanical power. The pathways form the network structure on the geographical space and the movement of vehicles (service) carry the people and goods. Connectivity and Accessibility are the two important  aspects of transport. These two determine the movement of people over geographic space for various purposes.  

Connectivity means the "degree of connectedness of the  settlements/ habitations as well the facility locations by means of transport networks". It is a network parameter. More the interconnectedness between the links, more connectivity is the result. 

Accessibility indicates the ‘ease of access of people to a place or facility or service locations". It is determined by many factors like, the type of road networks, distance, mode of transport and time. 

Connectivity and accessibility are measured from the network of transport routes or lines. A network is a "set of lines that join or cross each other at junctions". Individual places are physically connected and are functionally integrated into a wider regional framework. 

Fig.1 Topological Representation of Networks

Topological Map: topological network is a "simplified representation of the actual transport network where the lines or roots are shown as simple links that connect or meet at points (Nodes) with each other." In the topological map only the connections and links are considered. The orientation and actual distance of the routes are not considered. The topological representation of the transport network is called a graph. 

Properties of Graph: graph has following components:

1. Node/ Vertices
2. Links/ Edges
3. Area
4. Sub-Graph

Fig.2: Graph components

Importance of Accessibility: 

Accessibility determines the ease of access to a place from all other places. Thus within a regional framework accessibility of different points represents the most accessible places in the region. 

The location of facilities are determined based on the accessibility of points and the facilities tend to be located in the most accessible places. Different economic activities (Bank, market etc.) tend to be located in the most accessible places so that it can be accessed easily from different parts of the region. 

Measurement of Accessibility: Shimbel Index

Accessibility can be measured in a variety of ways. Among different methods of measuring accessibility, the Shimbel index is the simplest form of accessibility index. It is measured from the topological network represented as a graph. 

Shimbel index considers the number of links or edges needed to reach from a point to all other points along the shortest possible path. The matrix (Shimbel distance matrix) prepared for this purpose is called shortest path matrix. 

Equation:

Where, C1= Shimbel Index, Cij= distance between node i and j; n= number of nodes

Principle: Shimbel distance is inversely proportional to the level of accessibility. Smaller the index greater the accessibility and vice versa. 

Steps: 

1. From the transport network map identify the nodes and links.
2. Prepare simplified representation of the network and put SL numbers each of the nodes
3. Prepare Shimbel distance matrix. Put all the nodes in rows and columns.
4. Find out the number of links needed to reach different nodes from node 1.
5. Repeat the process for all nodes. 
6. Make row/Column sum. This summation for each node represents their respective Shimbel distance value. 
7. Put the values at the nodes in the map and draw isolines for accessibility zoning. 
8. Give higher density symbols/colours to lower values as lower values represent higher accessibility. 

Fig. 3: Graph Table;1: Shimbel Distance Matrix

Exercise: 1 Prepare Shimbel index from the network. 

Koenig Number:

Koenig number (or associated number, eccentricity) is a measure of farness based on the number of links needed to reach the most distant node in the graph. 

It is computed from the shimbel distance matrix. Highest value of each row is the koenig number of that node. 

The koenig number is plotted just like a shimbel index.