`nw2degree`

Two-mode (bipartite) degree centrality

Syntax

nw2degree
[netlist]
[,
generate(newvarname)
replace
silent
alpha(#)
binary]


`generate(newvarname)`	Required. Name of the Stata variable that stores two-mode degree centrality
`replace`	Replace existing variable
`silent`	Suppress display of results
`alpha(#)`	Weighted (tie-strength-aware) degree/strength blend, Opsahl et al. (2010); default = 0 (plain unweighted degree, identical to omitting the option)
`binary`	Ignore the tie values of a valued network (by default they are used)
`raw`	The degree itself, not divided by the size of the other mode (`tnet::degree_tm`, `igraph::degree`)

Description

nw2degree is the form of nwdegree for a two-mode network: nwdegree uses it by default on a two-mode network (and onemode forces the one-mode degree). The two names give the same result with the same options.

nw2degree calculates degree centrality for a two-mode (bipartite) network, using the normalization of Borgatti and Everett (1997). A node’s ordinary (raw) degree can only ever reach as high as the size of the other mode - a mode-1 node can tie to at most every mode-2 node, never to another mode-1 node - so nwdegree’s usual n - 1 normalization does not apply here. Instead, each node’s raw degree is divided by the size of the mode it does not belong to:

C’D(i) = degree(i) / n_other, where n_other is the number of nodes in the other mode

so that a mode-1 node tied to every mode-2 node (or vice versa) scores exactly 1, matching ordinary degree centrality’s own [0,1] range and interpretation.

generate() is required and names the new variable that holds this value for every node, regardless of which mode it belongs to (mode membership itself is available via nw2set’s own mode-id variable, not duplicated here).

alpha(#) generalizes the plain tie-count formula above to a weighted (tie-strength-aware) variant, using the same Opsahl, Agneessens and Skvoretz (2010) blend nwdegree’s own alpha() already uses for one-mode degree:

degree_alpha(i) = k_i * (s_i/k_i)^alpha, then normalized by n_other exactly as above

where k_i is node i’s plain tie count and s_i is its tie-value sum (its “strength”). alpha(0) (the default) reduces this exactly to plain tie-count degree - the two formulas agree bit-for-bit, so leaving alpha() unspecified never changes existing results. alpha(1) gives pure normalized strength (tie-value sum / other-mode size), ignoring tie count entirely. Values between 0 and 1 blend the two; values above 1 emphasize a few strong ties over many weak ones, and negative values do the reverse. On a binary (unweighted) network every tie already has value 1, so s_i = k_i, alpha() has no effect at any value, and the plain formula always applies.

Examples

. nwclear
. mata: net = (1,1\1,0\0,1)
. nw2set, mat(net) name(mynet)
. nw2degree mynet, generate(_2degree)

Weighted (strength-aware) variant, on a valued two-mode network:

. nwclear
. clear
. input str10 person str10 org value
. "A" "X" 2
. "A" "Y" 4
. "B" "Z" 6
. end
. nwset person org value, twomode name(affil)
. nw2degree affil, generate(strength) alpha(1)

Supported network types

Binary: yes. Directed: not applicable - two-mode ties in this package’s storage are inherently undirected (a tie either connects a mode-1 node to a mode-2 node or it does not). Weighted: W1, native - alpha() generalizes the plain tie-count formula to a tie-strength-aware blend (Opsahl et al. 2010), the same convention nwdegree’s own alpha() uses for one-mode degree; alpha(0), the default, is bit-for-bit identical to the original unweighted formula. Signed: not checked - a negative tie value would distort the strength sum alpha() relies on, not handled distinctly from “no tie”. Two-mode: yes - a node’s degree divided by the size of the other mode (Borgatti and Everett 1997); raw gives the count itself (tnet::degree_tm).

References

Borgatti, S.P., Everett, M.G. (1997). Network analysis of 2-mode data. Social Networks 19(3), 243-269.

Opsahl, T., Agneessens, F., Skvoretz, J. (2010). Node centrality in weighted networks: Generalizing degree and shortest paths. Social Networks 32(3), 245-251.

nw2degree