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:

V1V2V3
V1-AB
V2A-C
V3BC-

Where:

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:

ABCD
A052-
B50-1
C2-07
D-170

This would represent this network:

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

flashcards

QuestionAnswer
What is a distance matrix in a network?A table where rows and columns correspond to nodes, and entries show the weight (e.g., distance) between them, rather than just whether they are connected.
How does a distance matrix differ from an adjacency matrix?An adjacency matrix shows only whether nodes are connected, while a distance matrix provides the weight (e.g., distance) of the connections.
What do the rows and columns represent in a distance matrix?They represent the nodes (vertices) in the network.
What does a dash (-) represent in a distance matrix?It indicates that there is no direct connection between the nodes, or that the vertices are the same (although same-node entries may sometimes be 0).
What might replace a dash for the distance from a node to itself?0, indicating the distance from a node to itself is zero.
In the given example distance matrix, what is the distance between node A and node B?5
In the given example distance matrix, what is the distance between node A and node C?2
In the given example distance matrix, what is the distance between node C and node D?7
In the given example network, how many edges are directly represented?There are 4 edges: A-B (5), A-C (2), B-D (1), and C-D (7).