[igraph] Interpretation of edge weights in the calculation of weighted diameter and weighted betweenness

[Brenn Poppe]

Dear all,

For my masterthesis I'm constructing and analyzing animal social networks. In these networks individual Great Tits (Parus major) and Blue Tits (Cyanistes caeruleus) are represented by nodes. I construct a set of daily networks that are undirected and weighted starting from adjacency matrices. The values in these adjacency matrices are used as the edge weights of the links between nodes in my graphs. These values represent an interaction strength: the more 2 individuals interacted (co-occurring on garden feeders) the higher their interaction strength and the higher the edge weight between these individuals in the graph.

I use igraph in R to construct and analyse these daily networks.

Now for each of these daily networks I calculate (among others) 2 metrics namely: the diameter (graph-level) and the betweenness centrality (node-level). Because I have weighted networks I also use the weights when implementing these functions.

Now based on my interpretation of the edge weights, being interaction strengths, I would expect the diameter to be the path that has the lowest sum of edge weights and thus a path along which all interactions are weak. Assuming that for example information travels slower along a path with weak connections opposed to a path with strong connections. However I have noticed that the calculated diameter actually gives the 'opposite' result being the path with the highest sum of edge weights and thus a path with overall strong connections. This is a path that I would consider to be the shortest rather than the longest. In some occassions the diameter is exactly the same as the highest edge weight in a network. It looks as if the edge weights are interpreted as costs/distances/resistance.

Because of this 'problem' with the calculation of diameter according to my interpretation I also have similar concerns about the calculation of weighted betweenness. I have seen this issue (a confusing interpretation of edge weights by igraph) pop up several times on this mailing list.

Although this issue has popped up several times, I have not found a clear solution in the answers as to what I should do with my data or my script to get diameter and betweenness to be interpretable according to my interpretation of the edge weights:

• Do I have to use a different function or do I have to specify certain arguments in the functions diameter() and betweenness()
• Or can I simple take the inverse (1/edge weight) of the edge weights before calling the specified functions?
• Or.....

Note: all the edge weights range between 0 and 1.

Thanks in advance,

Brenn Poppe

Masterstudent MSc in Biology (University of Ghent)