As I am reading wikipedia and some material:
A basis for cycles of a network is a minimal collection of cycles such that any cycle in the network can be written as a sum of cycles in the basis.
Some other material also point out the cycle basis need to be linear independent and span the graph.
Given a graph (V,E). Say I already have a set of cycles C. How can I check the linear independent between these cycles?
$$C = {C_0, C_1, \cdots }$$ $$C_0 = {e_0, e_1\cdots}$$
For the example below, from my understanding, in the left it is cycle basis, but on the right it is not because there's linear dependency on the 2 cycles.
Is there any simple algorthim to do this, or any material I should look into for to this?