I use R and want to apply a clustering_leading_eigen function on an undirected weighted graph G=(V,E). The wights are nonnegative integers.

If I choose **NULL** for the parameter weights in function, then does that create a multigraph by adding n-1 extra edges besides for particular an edge e (I assumed that edge e has weight of n and connects vertices v,u\in V)?

Because in a paper “*Analysis of weighted networks*”, Newman mentioned such a way of conversion for weighted graphs.

This method is defined in terms of the graph’s adjacency matrix A.

If the graph is unweighted, then A_{ij} is the number of connections between vertices i and j (or twice that number if i=j).

If the graph is weighted, then A_{ij} the sum of the weights of edges between i and j (or twice that number if i=j).

This is consistent with the paper you cite.

Just to add what Szabolcs said: if edge e has weight n, and you do *not* pass in the weights explicitly, `igraph`

will simply interpret it as a single edge. That is, it won’t *generate* n - 1 “additional” edges for you in some way. In short, if you have edge weights, you probably just want to pass them in.

In a paper “*Finding community structure in networks using the eigenvectors of matrices*”, to find a modularity, denoted as Q, the following equation was used.

So A_{ij} represents here a weight, nonnegative integer, for an edge \{i,j\}.

So if I pass **NULL** to the weights parameter, then does cluster_leading_eigenvector function treat weights in such a way for detecting a set of communities based on leading eigenvectors of a modularity matrix?

I can’t quite understand your question …

Let’s put it like this: If you pass `NULL`

, all edges will have weight `1`

.

Does this help?