Rank properties of the arc-node incidence matrix
Recall the definition of the arc-node incidence matrix of a network.
A number of topological properties of a network with 
nodes and 
edges can be inferred from those of its node-arc incidence matrix 
, and of the reduced incidence matrix 
, which is obtained from by removing its last row. For example, the network is said to be connected if there is a path joining any two nodes. It can be shown that the network is connected if and only if the rank of is equal to 
.
