`nw2project`

One-mode projection of a two-mode network

Syntax

nw2project
[netname]
,
project(1|2)
[name(newnetname)
stat(string)
xvars
replace]


`project(1\\|2)`	Mode/level to collapse to
`name(newnetname)`	Name of the new one-mode network; default = project
`stat(min\\|max\\|minmax\\|sum\\|mean\\|count\\|binary\\|jaccard\\|cosine\\|newman)`	How to combine tie values (or, for the last 5, how to score shared-neighbor structure directly; newman is the collaboration weight of Newman 2001, the sum over the shared nodes of the other mode of 1/(k - 1) with k the number of ties of the shared node, the weight of `tnet::projecting_tm`; for tie values the mean of tnet’s two directions); default = minmax
`xvars`	Generate Stata variables for the new network
`replace`	Replace an existing network of the same name

Description

Sometimes one wants to collapse a two-mode network to a one-mode network. This is called a one-mode projection. Such a projection is a simplification of the network to nodes of one level only. The level to which one wants to collapse is specified in option project().

For example, this loads a two-mode network and projects it onto level 1:

. nw2project mynet, project(1) name(myproject1)

By default, a one-mode projection on one level generates ties between nodes (on this level) when they have at least one network neighbor on the other level in common.

When the source network is unvalued, the tie value in the projection is simply the number of shared neighbors on the other level (e.g. the number of institutions two people share).

When the source network is valued, option stat() controls how the tie values of the two original ties (ego-to-shared-neighbor and alter-to-shared-neighbor) are combined, for every shared neighbor, into a single projected tie value:

stat(min)
the overall minimum across all ego/alter-to-shared-neighbor tie values
stat(max)
the overall maximum across all ego/alter-to-shared-neighbor tie values
stat(sum)
the sum across all ego/alter-to-shared-neighbor tie values
stat(mean)
the mean across all ego/alter-to-shared-neighbor tie values
stat(minmax) (default)
for each shared neighbor, take the minimum of the ego/alter tie values to that
neighbor, then take the maximum of those minima across all shared neighbors -
substantively, the strongest shared bond

The remaining four options score the shared-neighbor structure itself rather than combining tie values - they are defined the same way regardless of whether the source network is valued, and are available for a valued source network too (unlike the five above, which require one):

stat(count)
the number of shared neighbors - identical to the default behaviour on an
unvalued source network, but now requestable explicitly on a valued one too, ignoring
tie strength entirely
stat(binary)
1 whenever at least one shared neighbor exists, 0 (no tie) otherwise - a
plain co-affiliation indicator
stat(jaccard)
the Jaccard similarity of the two nodes’ neighbor sets: shared neighbors
divided by the size of the union of their neighbor sets
stat(cosine)
the cosine similarity of the two nodes’ neighbor sets: shared neighbors
divided by the geometric mean of their two degrees

For example, suppose Peter and Thomas are both affiliated with Oxford (Peter: 7 years, Thomas: 5 years) and LiU (Peter: 1 year, Thomas: 1 year). Then:

+---------------------+
| stat      | value  |
|---------------------|
| min       |   1    |
| max       |   7    |
| sum       |  14    |
| mean      | 3.5    |
| minmax    |   5    |
+---------------------+

The projected network’s provenance (which network and mode it was projected from, and with which stat()) is recorded on the new network itself, not just printed - see r(provenance) via nwname, and nwsummarize, which displays it.

Supported network types

Binary: yes. Directed: not checked - the source two-mode network’s ties are treated as undirected affiliations. Weighted: W1, native - an unvalued source network projects to a shared-neighbor count (the standard bipartite-projection tie weight); a valued source network projects using stat()’s explicit choice of combination rule (see above) - tie strength is never silently discarded or reinterpreted as a distance. Signed: not checked. Two-mode: yes - the projection onto one mode; stat() chooses the tie weight (count is the number of shared nodes of the other mode as in igraph::bipartite_projection, newman the weight 1/(k - 1) per shared node of tnet::projecting_tm).

Stored results

Scalars

r(nodes) number of nodes in the projected network
r(ties) number of edges in the projected (undirected) network, each pair counted once

nw2project

Syntax

Description

Supported network types

Stored results

See also

`nw2project`