`nwcohesion`

Moody-White structural cohesion hierarchy

Syntax

nwcohesion
[netlist]
[,
generate(newvarname)
replace
silent
force]


`generate(newvarname)`	Required. Name of the Stata variable that stores each node’s own highest cohesion level
`replace`	Replace existing variable
`silent`	Suppress display of results
`force`	Run the command although its estimated time is more than 2 minutes (it stops with r(484) otherwise)

Description

nwcohesion computes the full, multi-level Moody and White (2003) cohesive-blocking hierarchy: starting from the whole network, it recursively finds ever-more-cohesive nested sub-blocks, using nwkcomponents’ own single-level k-component primitive (vertex connectivity via node-splitting max-flow, Menger’s theorem) applied repeatedly at increasing connectivity levels. Where nwkcomponents answers “which nodes form a block of at least connectivity k(int)?” for one chosen k(int), nwcohesion answers the fuller question: “what is the complete nested structure, from the whole network down to its most cohesive cores, and how cohesive is each level?” - with no k(int) to choose, since every level actually present in the network is found and reported.

Each block’s own connectivity level is its network’s ACTUAL vertex connectivity (not merely the level searched for) - a disconnected network’s own top block is reported at level 0, a network joined only by a single cut vertex at level 1, and so on. Levels found deeper in the hierarchy can skip values (e.g. a level-1 block can have level-3 children directly, with no level-2 block ever appearing) - a well-documented real property of structural cohesion, not a limitation of this implementation.

Like nwkcomponents, blocks can genuinely overlap (a cutset remains a shared member of every sub-block its removal reveals) and nest (a child block’s own node set is always a strict subset of its parent’s), so the complete structure is returned via r(cohesion_matrix) (a blocks-by-nodes 0/1 membership matrix, one row per block found at ANY level of the hierarchy) and r(cohesion_levels) (a parallel column vector giving each row’s own connectivity level). generate(newvarname) (required) stores, per node, the HIGHEST level of any block that node belongs to - the standard node-level structural-cohesion summary statistic - and is always well-defined for every node (even an isolate gets its own top-block level, typically 0), unlike nwkcomponents’ own _kcompnum, which is missing for nodes that don’t qualify for the one requested k(int).

Examples

. nwwebuse florentine, nwclear
. nwcohesion flomarriage, generate(_cohesion)

Supported network types

Binary: yes. Directed: yes, automatically symmetrized (vertex connectivity has no directed generalization here, matching nwkcomponents). Weighted: not used. Signed: not checked. Two-mode: same as for the bipartite graph read as a one-mode network (valid; no mode-specific normalisation).

Stored results

Scalars

r(blocks) number of cohesive blocks found across the whole hierarchy

Matrices

r(cohesion_matrix) blocks-by-nodes 0/1 membership matrix, one row per block at any level
r(cohesion_levels) blocks-by-1 column vector of each row’s own connectivity level

References

Moody, J., White, D.R. (2003). Structural cohesion and embeddedness: a hierarchical concept of social groups. American Sociological Review 68(1), 103-127.

Kanevsky, A. (1993). Finding all minimum-size separating vertex sets in a graph. Networks 23(6), 533-541.

Even, S. (1979). Graph Algorithms. Computer Science Press. (the vertex-splitting max-flow reduction for vertex connectivity)

nwcohesion