`nwcommunity`

Detect communities via the Louvain method or label propagation

Syntax

nwcommunity
[netlist]
[,
generate(newvarname)
replace
measure(string)
SYMmetrize
resolution(real)
algorithm(louvain|labelprop|dirtlpa)
seed(int)
silent
listall
onemode
starts(#)
reps(#)
minmodules(#)]


`generate(newvarname)`	Required. Name of the Stata variable that stores community membership
`replace`	Replace existing variable
`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 detecting communities (required for directed networks)
`resolution(real)`	Resolution parameter (Reichardt-Bornholdt); must be > 0; only affects algorithm(louvain)’s own search, though it always affects the reported r(modularity) regardless of algorithm; default = 1
`algorithm(louvain\\|labelprop\\|dirtlpa)`	Community-detection algorithm; default = louvain; dirtlpa (two-mode networks only) is the label propagation of Beckett (2016) for the bipartite modularity of Barber
`seed(int)`	Set the random-number seed before detecting communities (for reproducibility with algorithm(labelprop), which uses randomized sweep order and tie-breaking)
`silent`	Suppress display of results
`listall`	Print the full table of communities; by default at most the first 30 rows are printed, with a note. Results in `r()` are unchanged
`onemode`	Two-mode network: the modularity of Newman for the bipartite graph read as a one-mode graph, instead of the bipartite modularity of Barber (the default for a two-mode network)
`starts(#)`	Two-mode network: the number of starting orders of the search for the partition with the largest bipartite modularity; default = 30; the first starts in the order of the nodes, the others in random order (`seed()`)
`reps(#)`	algorithm(dirtlpa): the number of repeated runs of the label propagation for every number of starting modules (the reps of `bipartite::DIRT_LPA_wb_plus`); default = 10
`minmodules(#)`	algorithm(dirtlpa): the smallest number of starting modules of the repeated runs (the mini of `bipartite::DIRT_LPA_wb_plus`); default = 4

Description

nwcommunity detects communities in the network(s) in netlist using one of two algorithms (algorithm()): the Louvain method (Blondel et al 2008, the default), a greedy algorithm that repeatedly moves nodes between communities and aggregates communities into a coarser network, in order to maximize Newman’s modularity Q; or label propagation (Raghavan, Albert & Kumar 2007), a much cheaper algorithm with no modularity optimization at all - each node simply, repeatedly adopts whichever community its neighbors’ total edge weight favors most, until no node wants to move. Label propagation does not optimize any global objective the way Louvain does, so its partitions are typically lower-modularity and less consistent run to run, but it scales far better to very large networks. All calculations are performed on the undirected network; directed networks require symmetrize.

algorithm(labelprop) uses genuinely randomized sweep order and tie-breaking (unlike Louvain’s own fixed, reproducible sweep order) - this is a deliberate, load-bearing part of the algorithm, not an incidental implementation detail: a fixed visiting order with deterministic tie-breaking was tried first and found to be not merely non-standard but actively wrong, systematically collapsing even simple, cleanly-separated community structure into one giant community (see Algorithm below). Use seed() for reproducible results.

On dense networks algorithm(labelprop) can collapse to a single community; compare the reported modularity with that of algorithm(louvain) before relying on it. Louvain is deterministic and ignores seed(). The two-mode search draws its random starting orders from the seed: the same seed() (or set seed) gives the same communities, whatever the platform; with a plugin of the current generation the search is about 25 times faster than the older Mata search (the Mata code is used when the plugin is older), and the two reach the same modularity up to the luck of the random starts (Southern women: identical, 0.3455).

generate() is required and names the new variable that stores, for each node, the id of the community it was assigned to.

Examples

. nwwebuse florentine, nwclear
. nwcommunity flomarriage, generate(_community)
. nwcommunity flomarriage, algorithm(labelprop) seed(12345) generate(_community) replace

Supported network types

Binary: yes. Directed: requires symmetrize - community detection as implemented here is not defined for a directed network. Weighted: yes, via measure(binary|valued); default = valued for a valued network, binary otherwise (affects both which partition is searched for and the reported r(modularity)). Signed: not checked. Two-mode: yes - Louvain-type search for the partition with the largest bipartite modularity of Barber (2007), the null model of bipartite::computeModules; onemode gives the modularity of Newman for the bipartite graph read as a one-mode graph (igraph::cluster_louvain); starts() sets the number of starting orders.

Stored results

Scalars

r(communities) number of communities
r(modularity) modularity Q of the detected partition

Matrices

r(comm_sizeid) distribution over communities

References

Blondel, V.D., Guillaume, J.-L., Lambiotte, R., Lefebvre, E. (2008). Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 2008(10), P10008.

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

Beckett, S.J. (2016). Improved community detection in weighted bipartite networks. Royal Society Open Science 3(1), 140536. doi:10.1098/rsos.140536.

Raghavan, U.N., Albert, R., Kumar, S. (2007). Near linear time algorithm to detect community structures in large-scale networks. Physical Review E 76(3), 036106.

nwcommunity