# Connectivity Matrix

The network on the above figure can be represented as a connectivity matrix, which is rather simple to construct:

• Size of the connectivity matrix: Involves a number of rows and cells equivalent to the number of nodes in the network. A connectivity matrix is always a square matrix. Since the above network has 5 nodes, its connectivity matrix is a five by five grid.
• Connection: Each cell representing a connection between two nodes receives a value of 1 (e.g. Cell B – A).
• Non-connection: Each cell that does not represent a direct connection gets a value of 0 (e.g. Cell D – E).
• If all connections in the network are bi-directional (a movement is possible from node C to node D and vice-versa), the connectivity matrix is transposable.

Adding up a row or a column gives the degree of a node. Node C is obviously the most connected since it has the highest summation of connectivity comparatively to all other nodes. However, this assumption may not hold true on a more complex network because of a larger number of indirect paths which are not considered in the connectivity matrix.