`nwsimmelian`

Simmelian ties

Syntax

nwsimmelian 
[netname]
[,
name(newnetname)
nwreplace]


`name(newnetname)`	Save Simmelian ties as new network; default _simmelian
`nwreplace`	Replace the network name() if it already exists

Description

Simmelian ties are concerned with more than just the strength of the relationship (see Krackhardt 1998). The original concept looks at the number of strong, reciprocated ties within a group: for a simmelian tie to exist, there must be three (a triad) or more of reciprocal strong ties in a group, viewed as even stronger than a regular strong tie. This command implements the reciprocated-triad structure only - it does not apply any tie-strength/value threshold (see Supported network types below); a weak reciprocated tie in a closed triad is flagged identically to a strong one.

For example, if Adam has a (reciprocated) tie to Betty, and both Adam and Betty share a (reciprocated) tie to Charles, this three-way tie would be a simmelian one.

The concept of a Simmelian tie is related to that of a clique; each pair of nodes (individuals) in a clique has a Simmelian tie between them. Thus a simmelian tie can be defined as a basic tie in a clique, or a co-clique relationship (between individuals who belong to a specific clique).

Examples

. nwwebuse florentine, nwclear
. nwsimmelian flomarriage
. nwplot flomarriage, edgecolor(_simmelian)

Supported network types

Binary: yes (only) - uses get_matrix_unvalued() throughout; a weak tie and a strong tie in an otherwise-identical closed triad are both flagged as Simmelian identically, despite this command’s own documentation describing the concept in “strong tie” language (the concept is often described in terms of strong ties; this command does not apply a strength threshold). Directed: yes - reciprocity is checked directly (a tie must be mutual to participate at all), matching the concept’s own directed-advice-network origin (Krackhardt 1999); on an undirected network reciprocity is automatically satisfied by every existing tie. Weighted: not applicable. Signed: not applicable. Two-mode: same as for the bipartite graph read as a one-mode network (valid; no mode-specific normalisation).

References

Krackhardt, D. (1999). The ties that torture: Simmelian tie analysis in organizations. Research in the Sociology of Organizations (16), 183-210.

nwsimmelian