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:

	V1	V2	V3
V1	-	A	B
V2	A	-	C
V3	B	C	-

Where:

• The rows and columns represent the nodes (or vertices) in the network.
• The letters , 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 s to indicate that the distance from a node to itself is zero.

Example

A distance matrix looks like this, for example:

	A	B	C	D
A	0	5	2	-
B	5	0	-	1
C	2	-	0	7
D	-	1	7	0

This would represent this network:

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