tournament_matrix#
- tournament_matrix(G)[source]#
Returns the tournament matrix for the given tournament graph.
This function requires SciPy.
The tournament matrix of a tournament graph with edge set E is the matrix T defined by
\[\begin{split}T_{i j} = \begin{cases} +1 & \text{if } (i, j) \in E \\ -1 & \text{if } (j, i) \in E \\ 0 & \text{if } i == j. \end{cases}\end{split}\]An equivalent definition is
T = A - A^T, where A is the adjacency matrix of the graphG.- Parameters:
- GNetworkX graph
A directed graph representing a tournament.
- Returns:
- SciPy sparse array
The tournament matrix of the tournament graph
G.
- Raises:
- ImportError
If SciPy is not available.