`nwcloseness`

Closeness centrality

Syntax

nwcloseness 
[netlist]
[,
unconnected(int)
generate(var1 var2 var3)
nosym
replace
silent
force
binary
twomode
onemode
legacy]


`unconnected(int)`	defines the length of the (non-existent) path between two unconnected nodes
`legacy`	on an unconnected network, use (nodes - 1) / farness as in earlier releases instead of the number of reachable nodes / farness
`generate`(`var1 var2 var3`)	Required. Exactly 3 variable names to save closeness, farness and nearness scores, in that order
`nosym`	do not symmetrize network before calculation of shortest paths
`replace`	overwrite existing var1, var2, var3 (or _closeness, _farness, _nearness); required if they already exist
`silent`	Do not display the summary of the new variables
`force`	Run the command although its estimated time is more than 2 minutes (it stops with r(484) otherwise); also passed on to nwgeodesic
`binary`	Ignore the tie values of a valued network (by default they are used)
`twomode`	Two-mode network: the default; accepted as a synonym of the default (closeness is the smallest possible farness of a node of its mode divided by its farness, Borgatti and Everett 1997)
`onemode`	Two-mode network: the closeness of the bipartite graph read as a one-mode graph, without the normalisation of Borgatti and Everett (the result of earlier releases)

Description

Calculates the closeness centrality (and farness and nearness score) for each node i in a network or network list and saves the result as Stata variables.

The closeness centrality for node i is defined in the following way:

farness_i = sum(dist_ik), over all k
nearness_i = 1 / farness_i
closeness_i = nearness_i * (nodes - 1)

with: dist_ik being the length of the shortest path from node i to node k (see nwgeodesic)

Closeness as defined above ((nodes - 1) / farness) is only defined for a connected network. When the network is unconnected (or, for a directed network, not strongly connected) the command prints a warning and, as in R’s igraph, takes the sum of the distances over the nodes that i can reach and divides the number of those nodes by it: closeness_i = reach_i / farness_i. This equals the formula above for a connected network and never exceeds 1. Farness and nearness are the plain sum of finite distances and its inverse. A node that reaches no other node gets a missing closeness. Option legacy returns the (nodes - 1) / farness of releases before this correction, which can exceed 1 on an unconnected network. Scores based on all (nodes - 1) other nodes can also be obtained when option unconnected() is specified. Any integer value can be choosen; unconnected(max) assigns non-existent paths a length based on the longest shortest path length observed in the network (plus one) (see nwgeodesic).

generate() is required and must always give exactly 3 names (var1 var2 var3, for closeness, farness and nearness respectively). Existing Stata variables var1, var2, var3 require option replace to be overwritten. In case, closeness centrality is calculated for z networks at the same time (e.g. ** nwcloseness glasgow1 glasgow2, generate(clo far near)*), the command generates the variables *var1_z, var2_z, var3_z for each network.

Examples

. nwwebuse gang, nwclear
. nwcloseness gang, generate(_closeness _farness _nearness)
. sum _closeness _farness _nearness

Supported network types

Binary: yes. Directed: yes - symmetrized by default (the same “no-prefix trap” nosym convention as nwkatz/nwevcent), nosym available. Weighted: inherited entirely from whatever nwgeodesic options are passed through (this command has no weighted/alpha() of its own). Signed: not checked. Two-mode: two-mode form by default - the smallest possible farness of a node of its mode divided by its farness (Borgatti and Everett 1997; twomode is accepted as a synonym); onemode forces the one-mode closeness of the bipartite graph.

nwcloseness

Syntax

Description

Examples

Supported network types

See also

`nwcloseness`