Rank of a graph

[Adarsh Kishore]

Hi everyone,

I was going through the concept of graphs as matroids and I came upon the rank of a graph. Wikipedia lists it as n - c, n = |V|, c = # of connected components.

I do understand rank and nullity of matrices, and graphs when expressed in their incidence matrix form have a one-to-one correspondence with the rank of its incidence matrix.

However, I am not understanding how

r(G) = |V| - c, c = # of connected components

and the definition of rank as the maximum size of a subforest of G are equivalent.

I tried looking it up on Google and StackOverFlow but found no satisfactory explanation. Any resources that would be helpful to understand the concept would be great.