Transferred Weight Selection
In the weighted case, the switching algorithm transfers a certain amount of weight from some edges to others. The package provides two settings, which we will choose according to what type of weighted graph we are working with.
Complete graphs with a fixed upper bound
These graphs have an edge between every pair of vertices, which will usually be the result of applying some function to each pair. For example, networks resulting from computing correlations of time series (where each series corresponds to a vertex, and the edge weights are the correlations between series) fall into this category.
We show an example built from correlations of currency exchange time series . In this network vertices are pairs of exchange rates, and the edge weights are the correlations of their corresponding time series, scaled to the interval \([0,1]\). In this case, the appropriate setting is the one that keeps the variance of the edge weights constant.
data(g_forex, package="clustAnalytics")
rewireCpp(g=g_forex, weight_sel="const_var", lower_bound=0, upper_bound=1)
#> IGRAPH d1b5b62 UNW- 78 5841 --
#> + attr: name (v/c), TRUE (v/c), weight (e/n)
#> + edges from d1b5b62 (vertex names):
#> [1] JPYUSD--AUDUSD JPYUSD--SGDNZD HKDNZD--SGDSEK MXNCHF--SGDSEK JPYUSD--SGDGBP
#> [6] JPYUSD--HKDEUR JPYUSD--CADAUD JPYUSD--CNYUSD JPYUSD--NZDGBP CHFAUD--SGDSEK
#> [11] JPYUSD--CNYEUR CHFUSD--SGDCNY AUDUSD--SGDSEK GBPUSD--CNYEUR JPYUSD--JPYEUR
#> [16] GBPUSD--CADAUD JPYUSD--MXNAUD GBPUSD--SGDAUD GBPUSD--GBPEUR CADEUR--SGDSEK
#> [21] SEKUSD--SGDNZD NZDUSD--SGDSEK GBPUSD--SGDEUR GBPUSD--MXNUSD JPYUSD--SGDSEK
#> [26] JPYUSD--SGDCNY CHFUSD--SGDSEK GBPUSD--SGDSEK GBPUSD--HKDAUD JPYUSD--CADCHF
#> [31] SGDUSD--SGDNZD JPYUSD--GBPJPY JPYUSD--SEKCNY JPYUSD--SEKNZD SGDMXN--SGDNZD
#> [36] GBPUSD--NZDJPY JPYUSD--NZDCAD CHFUSD--CHFAUD CHFAUD--SGDCNY JPYUSD--NZDCNY
#> + ... omitted several edgesMore sparse graphs with weights that are non-negative but not necessarily upper bounded
This describes most commonly found weighted graphs, where the weights quantify some characteristic of the edges. Multigraphs also fit here, if we reinterpret them as weighted graphs where the edge weight is the number of parallel edges between each pair of vertices.
This is the case for the famous karate club graph from Zachary.
data(karate, package="igraphdata")
rewired_karate <- rewireCpp(karate, weight_sel="max_weight")
oldpar <- par(mfrow=c(1,2), mai=c(0,0.1,0.3,0.1)) #save original parameters
plot(karate, main="karate")
plot(rewired_karate, main="rewired_karate")
par(oldpar) #restore original parameters