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

[Chris Watson]

Hi Brenn, this is common in analyses of brain networks, in which a
higher edge weight indicates a stronger connection. For example, they
can be represented by correlation/covariance (between signals in brain
regions A and B) so that a higher edge weight (w --> 1) indicates
greater similarity in function; or, they are (proportional to) the
"number of connections" between regions A and B so that a higher edge
weight (w --> Inf) indicates a greater amount of structural/physical
connectivity.

In the brain network literature, I have discovered that there are ~5
different edge weight transform methods (the first 3 being the most
common by far):
1. Invert the weights:    1 / w
2. Take the negative (natural) log:    -log(w)
3. Subtract from 1:    1 - w
4. Normalize by the network's maximum weight and take the log:
-log10(w / max(w))
5. Same as 4, but add 1:    -log10(w / max(w) + 1)

Since all your edge weights are 0 <= w <= 1, then subtracting from 1
might be the best. However, as Szabolcs points out, you need to
consider if this makes practical sense for your study and the type of
data you have.

Chris

P.S. I have an R package, "brainGraph", with a function called
"xfm.weights" that does this. You can see an older version of the
function at https://github.com/cwatson/brainGraph/blob/master/R/utils.R#L396

On 10/15/19, Brenn Poppe <address@hidden> wrote:
> Hi Tamás,
>
> Thank you very much for this answer!
>
> I could definitely consider using the centrality metrics you propose here.
>
> Thanks.
>
> Kindly,
> Brenn
> ________________________________
> Van: igraph-help <igraph-help-bounces+brenn.poppe=address@hidden>
> namens Tamas Nepusz <address@hidden>
> Verzonden: dinsdag 15 oktober 2019 10:30
> Aan: Help for igraph users <address@hidden>
> Onderwerp: Re: [igraph] Interpretation of edge weights in the calculation of
> weighted diameter and weighted betweenness
>
>
> My 'raw' adjacency matrices have as values these numbers of co-occurrences
> (as you say: the number of interactions) between each pair of birds. However
> for constructing my networks I do not use these absolute values (nr. of
> occurrences) as edge weights but a standardized value. This standardized
> value is actually the number of co-occurences 2 birds have divided by the
> sum of all co-occurrences both of these 2 birds had with other birds
> (including with each other) during that day.
>
> In this case the weights behave very much like "probabilities" for a random
> walker that traverses the graph (the sum of weights of each outbound edge
> incident on a node is 1); your best bet is a measure that has an underlying
> random-walker-like assumption like eigenvector centrality or PageRank.
>
> T.
>
>
>