I want to check the structural controllability of a given network from a given input node.
In Matlab, controllability can be verified using Kalman rank condition (ctrb). However, function ctrb computes powers of (adjacency) matrix $A$ up to $n-1$, where $n$ is the size of $A$. This is inefficient for larger networks because of computational issues (e.g., finite word length).
My network is directed and is of order greater than $25$ nodes and I want to check the controllability (or, at least, structural controllability) of the network from each node. Input matrix $B$ is a vector of size $25$ where only one element is non-zero, i.e., I want to check the controllability from one node at a time independently.
Is there any way to check the controllability or at least structural controllability of a network if the input matrix is given?