Accessibilityis defined as the measure ofthe 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.

- 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 economic activity. - The second is
**distance**, which derived from the physical separation 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.

- 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 subway stations). - 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.

**location**as well as the

**inequality conferred by distance to other locations**.

**network connectivity**where a network is represented as a connectivity matrix (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 a node**:

- C1 = degree of a node.
- c
_{ij}= connectivity between node i and node j (either 1 or 0). - n = number of nodes.

- D = the diameter of the network.

**minimum number of paths**necessary to connect one node with all the nodes in a defined network. The Shimbel accessibility matrix, also known as the

**D-Matrix**, thus includes for each possible node pairs the shortest path.

**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.

**summation of all distances**between other locations divided by the number of locations. The lower its value, the more a location is accessible.

- A(G) = geographical accessibility matrix.
- d
_{ij}= shortest path distance between location i and j. - n = number of locations.
- L = valued graph matrix.

**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.

**concept of distance weighted by the attributes of a location**. All locations are not equal and thus some are more important than others. Potential accessibility can be measured as follows:

- A(P) = potential accessibility matrix.
- d
_{ij}= distance between place i and j (derived from valued graph matrix). - P
_{j}= attributes of place j, such as its population, retailing surface, parking space, etc. - n = number of locations.

**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.