`nwmodularity`

Score an existing node partition using Newman’s modularity

Syntax

nwmodularity
[netlist]
,
group(varname)
[measure(string)
SYMmetrize
resolution(real)
silent]


`group(varname)`	Stata variable holding each node’s community/group assignment
`measure(binary\\|valued)`	Whether to use tie values (valued) or only presence/absence of ties (binary); default = valued for valued networks, binary otherwise
`symmetrize`	Symmetrize a directed network before scoring (required for directed networks)
`resolution(real)`	Resolution parameter (Reichardt-Bornholdt); must be > 0; default = 1
`silent`	Suppress display of results

Description

nwmodularity computes Newman’s modularity Q of the network(s) in netlist against an ul:existing node partition given in group() — for example a partition obtained from nwcomponents, a block model, or any hand-coded grouping variable. Unlike nwcommunity, nwmodularity does not search for a partition; it only scores the one given. All calculations are performed on the undirected network; directed networks require symmetrize.

Modularity compares the fraction of ties that fall within the given groups to the fraction expected under a random network with the same degree sequence. Values near 0 indicate the grouping is no better than chance; higher (positive) values indicate a grouping that captures real community structure. Scoring a single, all-nodes-in-one-group partition always gives Q = 0, for any network.

Examples

. nwwebuse florentine, nwclear
. nwcomponents flomarriage, generate(comp)
. nwmodularity flomarriage, group(comp)

Supported network types

Binary: yes. Directed: requires symmetrize - modularity as computed here is not defined for a directed network. Weighted: yes, via measure(binary|valued); default = valued for a valued network, binary otherwise. Signed: not checked. Two-mode: not checked.

Stored results

Scalars

r(communities) number of distinct groups in group()
r(modularity) modularity Q of the given partition

Matrices

r(comm_sizeid) distribution over groups

References

Newman, M.E.J. (2006). Modularity and community structure in networks. PNAS 103(23), 8577-8582.

nwmodularity