Distance matrix

A distance matrix is somewhat like an adjacency matrix, but instead of simply showing whether two nodes in a network are connected, it provides information about the weight (e.g. distance) between them.

It’s a way of representing a network in a table, where both the rows and columns correspond to the nodes in the network.

Structure of a distance matrix

An adjacency matrix looks like this:

Where:

• The rows and columns represent the nodes (or vertices) in the network.
• The letters A, B and $C in the matrix represent the weight (e.g. distance) between the nodes. These could also be dashes.
• A dash (-) indicates that there is no direct connection between the nodes (or that the verices are the same).

The dashes in the graph above could also be replaced with 0s to indicate that the distance from a node to itself is zero.

Example

A distance matrix looks like this, for example:

This would represent this network:

       2     
    A --- C  
  5 |     | 7
    B --- D  
       1