Count routes using powers of a connection matrix
Consider this network of teams linked by recorded matches. Each line records one match between the teams
Use the order Hawks, Blues, Tigers for the rows and columns of connection matrix \(C\). Rows name the starting vertex and columns name the ending vertex
\[C = \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{bmatrix}\]