Check for similarity between networks/graphs with the same nodes, but different edge values I have two networks which involve the same entities, but the quantities around which I have built the respective networks are different. What is a good way to compare the networks?
Currently, I run the Louvain method on both graphs (I do so on Gephi), then check the overlap between the communities generated. Is this a good way to do this? Are there better alternatives?
 A: Graphs are complex objects and each measure can compare two graphs based on specific characteristics of the graph.
I would suggest to check these two approaches:


*

*Compute graph measures and compare them between your graphs: You can compute diffferent centrality measures. They would measure connectedness of your graph. Do clustering and compare clusters/communities by their overlap, size, etc. Another suggestion is to look at degree/shortest path distance distributions for each graph. Each measure looks at specific characteristics of the graph and depending on your application, can be relevant for you purpose. 

*Look at the literature around Graph kernels. They map each graph to a vector and compare the distance between two vectors

*Use direct comparison: your problem is much simpler than general comparison of graphs. You have the correspondence between nodes. You can take corresponding nodes and compare measures like degree, etc. Also take corresponding pairs and compare the edge weights/shortest path distances. If you sum over all pairwise distances between corresponding nodes/pairs, you would also get a similarity measure.

A: You can try out the tool CompNet to find similarity (and differences) between two (or more) interaction networks. The tool allows visual comparison of multiple networks based on various network metrics. CompNet allows interactive visualization of the union, intersection and/or complement regions of a selected set of networks. Different visualization features (e.g. pie-nodes, edge-pie matrix, etc.) aid in easy identification of the key nodes/interactions and their significance across the compared networks. The tool also allows one to perform network comparisons on the basis of neighbourhood architecture of constituent nodes and community compositions, a feature particularly useful while analyzing biological networks.
CompNet tool download link (with videos)
https://web.rniapps.net/compnet/
Publication link https://bmcbioinformatics.biomedcentral.com/articles/10.1186/s12859-016-1013-x
