I am working on analyzing an algorithm and its variance depends on the gap between largest and second largest eigenvalues of the adjacency matrix of an undirected, weighted graph. However, the adjacency matrix is unnormalized (rows do not add up to one). Is it possible to say anything about the network properties (expansion, etc. ) using this eigenvalue gap of the unnormalized adjacency matrix?
PS: I noticed that most material and questions on the internet address how the eigenvalue gap of the normalized adjacency matrix is related to the expansion. However, in my case, the adjacency matrix is unnormalized and the normalization would result in a change in the eigenvalues.
Any advice, help or suggestions would be very helpful. Thank you!