Jean-Paul Rodrigue (2017), New York:
Routledge, 440 pages.
Transportation and Accessibility
Author: Dr. Jean-Paul Rodrigue
1. Defining Accessibility
Accessibility is a key element to transport geography, and to geography
in general, since it is a direct expression of mobility either in terms
of people, freight or information. This mobility is a choice made by
users and is therefore a mean to evaluate the impacts of infrastructure
investment and related transport policies on regional development. Well-developed and efficient transportation
systems offer high levels of accessibility (if the impacts of congestion
are excluded), while less-developed ones have lower levels of accessibility.
Thus accessibility is
linked with an
array of economic and social opportunities.
Accessibility is defined as the measure of the capacity
of a location to be reached by, or to reach different locations.
Therefore, the capacity and the arrangement of transport infrastructure
are key elements in the determination of accessibility.
All locations are not equal because some are more accessible than
others, which implies inequalities. Thus, accessibility is a proxy
for inequalities. The notion of accessibility consequently
relies on two core concepts:
- The first is location where the relativity of space is
estimated in relation to transport infrastructures, since they offer
the mean to support movements. Each location has a set of
referential attributes, such as its population or level of
- The second is distance, which derived from the
between locations. Distance can only exist when there is a possibility
to link two locations through transportation. It expresses the friction
of distance and the location which has the least friction relatively
to others is likely to be the most accessible. Commonly, the
friction of distance
is expressed in units such as in kilometers or in time, but variables
such as cost or energy spent can also be used.
Last, accessibility is a good indicator of the
spatial structure since it takes into consideration location
as well as the inequality conferred by distance
to other locations.
2. Connectivity and Total Accessibility
The most basic measure of accessibility involves network connectivity
where a network is represented as a
(C1), which expresses the connectivity of each node with its adjacent
nodes. The number of columns and rows in this matrix is equal to the
number of nodes in the network and a value of 1 is given for each cell
where this is a connected pair and a value of 0 for each cell where
there is an unconnected pair. The summation of this matrix provides
a very basic measure of accessibility, also known as the degree of
- The first type is known as topological accessibility
and is related to measuring accessibility in a system of nodes
and paths (a transportation network). It is assumed that accessibility
is a measurable attribute significant only to specific elements
of a transportation system, such as terminals (airports, ports or
- The second type is known as contiguous accessibility
and involves measuring accessibility over a surface. Under
such conditions, accessibility is a cumulative measure of the attributes of every
location over a predefined distance, as space is considered in a contiguous manner.
It is also referred as isochrone accessibility.
The connectivity matrix does not take into account all the possible
indirect paths between nodes. Under such circumstances, two nodes could
have the same degree, but may
accessibilities. To consider this attribute, the
matrix (T) is used to calculate the total number of paths in a network,
which includes direct as well as indirect paths. Its calculation involves
the following procedure:
- C1 = degree of a node.
- cij = connectivity between node i and node j (either
1 or 0).
- n = number of nodes.
Thus, total accessibility would be a more comprehensive accessibility
measure than network connectivity.
3. The Shimbel Index and the Valued Graph
The main focus of measuring accessibility does not necessarily involve
measuring the total number of paths between locations, but rather what
are the shortest paths between them. Even if several paths between two
locations exist, the shortest one is likely to be selected. In
congested networks the shortest path may change however. Consequently,
the Shimbel index calculates the minimum number of paths necessary
to connect one node with all the nodes in a defined network. The
matrix, also known as the D-Matrix, thus includes for each
possible node pairs the shortest path.
The Shimbel index and its D-Matrix fail to consider that a topological
link between two nodes may involve variable distances. It can thus be
expanded to include the notion of distance, where a value is attributed
to each link in the network. The
valued graph matrix,
or L-Matrix, represents such an attempt. It has a very strong
similarity with the Shimbel accessibility matrix and the only difference
lies that instead of showing the minimal path in each cell, it provides
the minimal distance between each node of the network.
4. Geographic and Potential Accessibility
From the accessibility measure developed so far, it is possible to
derive two simple and highly practical measures, defined as geographic
and potential accessibility.
considers that the accessibility of a location is the summation of
all distances between other locations divided by the number of locations.
The lower its value, the more a location is accessible.
- D = the diameter of the network.
This measure (A(G)) is an adaptation of the Shimbel Index and the
Valued Graph, where the most accessible place has the lowest summation
Although geographic accessibility can be solved using a spreadsheet
(or manually for simpler problems), Geographic Information Systems
have proven to be a very useful and flexible tool to measure accessibility,
notably over a surface simplified as a matrix (raster representation).
This can be done by
generating a distance grid for each place and then summing all the
grids to form the total
summation of distances (Shimbel) grid. The cell having the lowest
value is thus the most accessible place.
Potential accessibility is a more complex measure than geographic
accessibility, since it includes simultaneously the concept of distance
weighted by the attributes of a location. All locations are not
equal and thus some are more important than others.
can be measured as follows:
- A(G) = geographical accessibility matrix.
- dij = shortest path distance between location i and
- n = number of locations.
- L = valued graph matrix.
The potential accessibility matrix is not transposable since locations
do not have the same attributes, which brings the underlying notions
of emissiveness and attractiveness:
- A(P) = potential accessibility matrix.
- dij = distance between place i and j (derived from
valued graph matrix).
- Pj = attributes of place j, such as its population,
retailing surface, parking space, etc.
- n = number of locations.
Likewise, a Geographic Information System can be used to
measure potential accessibility,
notably over a surface.
- Emissiveness is the capacity to leave a location, the
sum of the values of a row in the A(P) matrix.
- Attractiveness is the capacity to reach a location, the
sum of the values of a column in the A(P) matrix.