`nwsimindex`

Common-neighbor similarity indices between all node pairs

Syntax

nwsimindex
[netname]
[,
measure(string)
name(newnetname)
xvars
replace]


`measure(common\\|jaccard\\|dice\\|cosine\\|adamicadar)`	Which similarity index to compute; default = jaccard
`name(newnetname)`	Name of the new similarity network; default = simindex
`xvars`	Generate Stata variables for the new network
`replace`	Replace an existing network of the same name

Description

nwsimindex computes a common-neighbor similarity index (Liben-Nowell and Kleinberg 2007) for every pair of nodes and stores the result as a new, valued, undirected network newnetname (default: simindex). These indices measure how much two nodes’ neighborhoods overlap - a standard building block for link prediction, structural-equivalence/role analysis, and as an input to blockmodeling or one-mode projection (see nw2project).

All calculations use the undirected neighbor sense: for directed networks, a node’s neighbor set is the union of its out- and in-neighbors (the same convention nwkcore uses), since neighborhood overlap is a direction-agnostic question. measure is one of:

common
the raw count of shared neighbors, * N(i) intersect N(j) *
jaccard (default)
- N(i) intersect N(j) / N(i) union N(j) *
dice
the Sorensen-Dice coefficient, *2 N(i) intersect N(j) / ( N(i) + N(j) )*
cosine
the Salton cosine similarity, * N(i) intersect N(j) / sqrt( N(i) * N(j) )*
adamicadar
Adamic-Adar, sum over shared neighbors k of 1/log(degree(k)) - weights rare
(low-degree) shared neighbors more heavily than common ones

The similarity of a node with itself is not defined and is set to missing, as are any pairs where the underlying formula is undefined - most notably cosine between two isolate nodes (0/0). This mirrors how nwgeodesic reports an undefined diameter/radius rather than silently coercing an undefined value to 0.

Examples

. nwwebuse florentine, nwclear
. nwsimindex flomarriage, measure(jaccard)
. nwsummarize simindex, matonly

Supported network types

Binary: yes (only) - similarity is computed from binary neighbor-set overlap; tie values are ignored. Directed: yes - each node’s neighbor set is the union of its out- and in-neighbors (the same convention nwkcore uses). Weighted: not applicable. Signed: not applicable. Two-mode: not checked.

Stored results

Scalars

r(nodes) number of nodes

Macros

r(measure) the measure used
r(netname) name of the new similarity network

References

Liben-Nowell, D., Kleinberg, J. (2007). The link-prediction problem for social networks. Journal of the American Society for Information Science and Technology 58(7), 1019-1031.

Adamic, L.A., Adar, E. (2003). Friends and neighbors on the Web. Social Networks 25(3), 211-230.

nwsimindex