Modularity of a partition — ntmod • crimlab

Q = sum over communities of in / 2m - res (tot / 2m)^2, where in is the weight of edges inside the community (counted from both ends), tot the summed strength of its nodes and 2m the total strength (Newman and Girvan 2004), on the undirected, weighted graph. At res = 1 it lies between -1/2 and 1 (proof("ntmod")). NaN for a graph without edges. Graph rules as in ntdeg().

Usage

ntmod(from, to, memb, w = NULL, nodes = NULL, res = 1)

Arguments

from, to: Labels of the two ends of each edge: vectors of the same length (zero when nodes gives every node) with no missing values.
memb: The community of each node: labels, either named by node (every node named once; other names are ignored) or unnamed, one per node in the order the network functions report nodes.
w: NULL, or one positive weight per edge (a tie's strength, such as the number of co-offences).
nodes: NULL, or every node's label once: the node order of the results and the way to include isolated nodes.
res: The resolution: one number, at least 0.

Value

The modularity, one number.

References

Newman, M. E. J. and Girvan, M. (2004). Finding and evaluating community structure in networks. Physical Review E, 69(2), 026113. doi:10.1103/PhysRevE.69.026113

Examples

ntmod(c(1, 1, 2, 4, 4, 5, 3), c(2, 3, 3, 5, 6, 6, 4),
      memb = c(1, 1, 1, 2, 2, 2))
#> [1] 0.3571429