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From: | Brenn Poppe |
Subject: | Re: [igraph] Interpretation of edge weights in the calculation of weighted diameter and weighted betweenness |
Date: | Tue, 15 Oct 2019 15:48:48 +0000 |
Hi Chris,
Thanks for this great clarification and the proposed transform methods.
Also thanks for the reference to your R package, I will definitely take note of that.
Now, I have looked at the distribution of the edge weights of all my daily networks.
The weights are indeed between 0 and 1, however they are not evenly distributed between 0 and 1.
Actually, most edge weights are below 0.2. Cases in which the edge weight is 1 is basically where 2 birds have only
interacted with each other and not with any other birds (during that day). These cases are rather outliers as it does not happen
that often that 2 birds only interact with each other and not with others.
Would this be a problem when using the method 'substracting from 1' or say the method 'taking the inverse'?
Thanks.
Kindly,
Brenn
Van: igraph-help <igraph-help-bounces+brenn.poppe=address@hidden> namens Chris Watson <address@hidden>
Verzonden: dinsdag 15 oktober 2019 16:48 Aan: Help for igraph users <address@hidden> Onderwerp: Re: [igraph] Interpretation of edge weights in the calculation of weighted diameter and weighted betweenness 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. > > > _______________________________________________ igraph-help mailing list address@hidden https://lists.nongnu.org/mailman/listinfo/igraph-help |
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