I'm building a flow matrix of a graph and I came to realize that my matrix of size $ N \times N $ has this simple property:
$$ \sum_{n=1}^{N}{A_{ni} } = \sum_{n=1}^{N}{A_{in} } $$
for $ i \in [1, N] $.
further properties:
- Rows and columns add up to different numbers, so I excluded
Stochastic Matrix - Definitely not
symmetric
I'm not sure if there is a term for it. It seems to be one-normalization step away from being left-stochastic or right-stochastic. It also seems to be generalized form of double stochastic matrix where the sum is not the same and is not necessarily equal to one.
Intuitively, the property meant to capture the fact that number of people coming to a node is equal to number of people leaving that node, therefore, none of the nodes is a sink nor a source.