`nwclustering`

Clustering coefficient (transitivity) of a network

Syntax

nwclustering
[netname]
[,
measure(string)
SYMmetrize
generate(newvarname)
replace
silent
level(#)
ra
onemode]


`measure(binary\\|arithmetic\\|geometric\\|maximum\\|minimum)`	How to combine the two tie values in a potential triple for a weighted network; binary ignores tie values and only checks presence/absence; arithmetic/geometric/maximum/minimum combine the two tie values via that function; default = arithmetic for a valued undirected network, binary otherwise
`symmetrize`	Symmetrize a directed network before calculating (required for any weighted `measure()` on a directed network - see Supported network types below)
`generate(newvarname)`	Required. Name of the Stata variable that stores each node’s own clustering coefficient
`replace`	Overwrite an existing `generate(newvarname)` variable; required if it already exists
`silent`	Suppress display of results
`level(#)`	Two-mode network: the mode (1 or 2) whose nodes get a coefficient; default = 1
`ra`	Two-mode network: the global coefficient of Robins and Alexander (2004), 4 C4 / L3, as `r(ra)`; `generate()` is then optional
`onemode`	Two-mode network: the one-mode coefficient of the bipartite graph (always 0, the graph has no triangles) instead of the two-mode coefficient of Opsahl (2013), the default

Description

nwclustering calculates the clustering coefficient (also known as transitivity) of a network: for each node i, the proportion of i’s own potential triples - pairs of i’s neighbors - that are themselves actually tied to each other (“the friends of my friends are themselves friends”). A node with fewer than 2 neighbors has no potential triples and its own clustering coefficient is reported as missing.

generate() is required and names the new variable that holds each node’s own clustering coefficient, and returns both the network-level average (r(cluster_avg), the mean of the per-node values) and the network-level global clustering coefficient (r(cluster_global), the ratio of the total count of closed triples to the total count of potential triples across the whole network - not the same quantity as the average of per-node ratios, since it weights every potential triple equally rather than every node equally).

If the network is a two-mode (bipartite) network, nwclustering uses the two-mode form by default: the coefficient of Opsahl (2013) (the share of four-paths that a fifth tie closes, tnet::clustering_tm), and with ra the global coefficient of Robins and Alexander (2004). An ordinary clustering coefficient is not meaningful on a bipartite network’s own inherently triangle-free structure; onemode computes it anyway. nw2clustering is the same command under its older name and takes the same options.

Examples

. nwwebuse florentine, nwclear
. nwclustering flomarriage, generate(_clustering)
. sum _clustering

Supported network types

Binary: yes (the default measure(binary) case). Directed: yes for measure(binary) (each node’s own potential triples are formed from one in-neighbor paired with one out-neighbor, matching the directed two-path a -> i -> b convention used elsewhere in this package); a weighted measure() is not defined for a directed network - either choose measure(binary) or symmetrize the network first. Weighted: yes, via measure(arithmetic|geometric|maximum|minimum), each combining the two tie values of a potential triple’s own pair of ties before testing closure; undirected networks only (see above). Signed: not checked; negative tie values are not validated or rejected. Two-mode: two-mode form by default (Opsahl 2013; ra: Robins and Alexander 2004); onemode forces the one-mode computation on the bipartite graph (nw2clustering is an alias).

Stored results

Scalars

r(cluster_avg) mean of the per-node clustering coefficients
r(cluster_global) network-level global clustering coefficient

Macros

r(measure) the measure() actually used
r(symmetrized) false, only returned when symmetrize was specified

References

Watts, D.J., Strogatz, S.H. (1998). Collective dynamics of ‘small-world’ networks. Nature 393, 440-442.

nwclustering