`nwfactions`

Partition nodes into a specified number of cohesive factions

Syntax

nwfactions
[netname]
[,
groups(int)
generate(newvarname)
replace
measure(binary|valued)
maxiter(int)
silent]


`groups(int)`	Number of factions to partition nodes into; must be between 2 and the number of nodes; default = 2
`generate(newvarname)`	Required. Name of the Stata variable that stores each node’s faction membership (1..`groups()`)
`replace`	Replace existing variable
`measure(binary\\|valued)`	Whether tie VALUES enter the fitness calculation, or only tie presence/absence; default follows whether the network itself is valued
`maxiter(int)`	Maximum number of full local-search sweeps; default 100
`silent`	Suppress display of results

Description

nwfactions implements UCINET’s own classical “factions” technique: partition the nodes into exactly groups() groups so as to MAXIMIZE the correlation between the observed tie matrix and the ideal “factions” block pattern (every pair of nodes in the SAME group is tied; every pair in DIFFERENT groups is not). This is the assortative-block-model sibling of nwcoreperiphery - the same fitness-correlation idea, generalized from a fixed 2-group core/periphery split (where the ideal pattern is “at least one endpoint is core”) to an arbitrary number of symmetric, equally-treated groups (where the ideal pattern is “both endpoints share a group”).

Optimized via greedy local search, the same general shape nwcommunity’s own Louvain algorithm and nwcoreperiphery both already use: seed by sorting nodes by degree (descending) and assigning them to groups round-robin (spreading high- and low-degree nodes evenly across every group, rather than an arbitrary block split), then repeatedly try moving each node (fixed 1..n order, for reproducibility) to every OTHER group, keeping whichever single move most improves the fitness correlation, until a full sweep produces no further improvement or maxiter() sweeps are reached. This is a greedy local optimum, not a guaranteed global one - the discrete factions problem is combinatorial, the same character of problem Louvain’s own greedy search already accepts for modularity.

Starting partition. Nodes with the same degree are taken in the order of their node number, so the same call always gives the same partition. (Earlier versions sorted with ties broken at random, which made the result differ from run to run on any network with equal degrees.) The fitness of a candidate move is computed from the total tie weight inside the groups and the number of same-group pairs, which takes time proportional to the node’s degree plus the number of groups, not to the square of the number of nodes; r(fitness) agrees with a direct computation of the correlation to rounding error (about 1e-15).

Examples

. nwwebuse florentine, nwclear
. nwfactions flomarriage, groups(3) generate(_faction)
. tab _faction

Supported network types

Binary: yes. Directed: yes, automatically symmetrized (the classical factions definition does not distinguish in-ties from out-ties, the same choice nwcoreperiphery already makes). Weighted: yes, via measure(valued) - tie VALUES then enter the fitness correlation directly rather than just their presence/absence. Signed: not checked. Two-mode: not supported - error 6088; the factions of the square matrix would mix the two modes; make a one-mode network of one mode first with nwproject.

Stored results

Scalars

r(fitness) correlation between the observed network and the ideal factions block pattern (1 = perfect fit)
r(groups) number of groups requested

Macros

r(netgenerate) name of the generated faction-membership variable

References

Borgatti, S.P., Everett, M.G., Freeman, L.C. (2002). UCINET for Windows: Software for Social Network Analysis. Analytic Technologies. (Factions routine)

nwfactions