BinGraph: Compute a distance bin matrix from a distance matrix

Description

In order for the Knet or Knode functions to be run on a network, it is necessary to place the raw distances between each vertex pair into discreet distance bins, as the functions are unable to handle continuous distributions of distances. This is done automatically within the Knet and Knode functions, but can also be done separately using BinGraph.

Usage

BinGraph(D, nsteps=1000, equal.bin.fill=TRUE, verbose=TRUE)

Arguments

Numeric matrix, a distance matrix output by DistGraph.

nsteps

Integer value, the desired number of bins across which the distances are to be split. If there are too few unique distances to fill each bin, then fewer bins are returned.

equal.bin.fill

Logical, if TRUE then the function attempts to fill each bin with an equal number of vertex pairs.

verbose

Logical, if TRUE messages about the progress of the function are displayed.

Value

Integer matrix with the same dimensions as D.

Details

In order for the Knet or Knode functions to be run, the vertex pair distances (as computed by DistGraph) but be split into bins. This is done as part of the Knet or Knode. However, this step is often slow for large networks and therefore the BinGraph function is provided separately, in order to avoid repeat computation.

Each vertex pair is placed into a bin, either ranging from 1 to nsteps, or from 1 to the number of unique distances.

If equal.bin.fill is FALSE, then the bin each vertex pair is placed into is directly proportional to the largest vertex pair distance. For example, if the distance between the pair is 25% of the largest distance and nsteps equals 100, then the vertex pair will be placed into bin 25. However, this can create problems when there are a small number of edges with especially large distances, as this can result in the majority of vertex pairs being placed into a small number of bins. This can reduce the effectiveness of the Knet and Knode functions. Therefore, when equal.bin.fill is TRUE, the function attempts to fill each bin with an equal number of vertex pairs. If there are a large number of tied distances, then the bins may not be filled equally.

Examples

Run this code

# create network and calculate the distance matrix using the shortest paths measure
g1 <- barabasi.game(6, directed=FALSE)
plot(g1, layout=layout.fruchterman.reingold)
D1 <- DistGraph(g1, dist.method="shortest.paths")
# place the distances into distance bins
BinGraph(D1, nsteps=100)

# create network and calculate the distance matrix using diffusion kernel-based measure
g2 <- erdos.renyi.game(6, p.or.m=0.5, directed=FALSE)
g2 <- set.edge.attribute(g2, name="distance", value=runif(ecount(g2)))
plot(g2, layout=layout.fruchterman.reingold)
# place the distances into distance bins
D2 <- DistGraph(g2, dist.method="diffusion", edge.attr="distance")
BinGraph(D2, nsteps=100)