Total Accessibility Matrix (T)

The total accessibility matrix (T) is obtained from the following procedure:

Construct the connectivity matrix (C1). On the above network node C is having the highest degree (4).
Construct the second order (two-linkages paths) connectivity matrix (C2). The total number of two-linkages paths (matrix C2) equals to C1*C1. Each cell in the C2 matrix is the result of the summation of the product of each corresponding row and column in the C1 matrix. For instance, cell A-B in matrix C2 (see above) is constructed from the following: 0*1 + 1*0 + 1*1 + 1*0 + 0*0. It indicates that there is only one possible two-paths link between node A and node B (A-C-B). Looking at the C2 matrix enable to find that there are two possible two-linkages paths between C and A (C-B-A and C-D-A).
Repeat the construction of the Nth order connectivity matrices until the number of Nth-linkages paths is equivalent to the diameter (path between the farthest nodes) of the network. A 3rd order connectivity matrix (C3) would be equal to C1*C2. A network that has a diameter of 4 would require the construction of 4 matrices (C1 to C4). Since the above network has a diameter of 2, only two matrices, C1 (1st order connectivity) and C2 (2nd order connectivity), need to be constructed.
Construct the total accessibility matrix (T). For the above network, matrix C2 (two-linkages paths) is added to matrix C1 (single paths; connectivity matrix). This summation represents for each node the total number of paths. For this network, there are thus 46 possible paths, with node C having the largest number (12); either originating from it or having it as a destination.