`nwbalance`

Structural balance of a signed network

Syntax

nwbalance
[netname]
[,
generate(namelist)]

| | | |—|—| | generate(namelist) | Up to 3 names, for the per-node balance ratio, count of balanced triads, and count of closed triads a node belongs to; default = _balance _baltriad _clotriad |

Description

nwbalance evaluates a network’s ties as signed (positive/negative) and tests every closed triad against Cartwright and Harary’s (1956) strong structural balance criterion: a closed triad is balanced when the product of its three tie values is positive - equivalently, when it contains an even number (0 or 2) of negative ties (“the friend of my friend is my friend”; “the enemy of my enemy is my friend”). A triad with an odd number (1 or 3) of negative ties is unbalanced.

Ties do not need to be declared signed in any special way - any tie with a negative value is treated as negative, any positive value as positive.

For each node, nwbalance generates the number of closed triads it belongs to, the number of those that are balanced, and the ratio of the two. Network-level counts and the overall balance ratio are returned in r().

Examples

. nwset, mat((0,1,1,-1\1,0,1,-1\1,1,0,1\-1,-1,1,0)) undirected labs(A,B,C,D)
. nwbalance

hline 40
Network name: network
hline 40
Closed triad: 4
Balanced triad: 2
Unbalanced triad: 2

Of the 4 triads in this network, A-B-C (all positive) and A-B-D (two negative ties) are balanced; A-C-D and B-C-D (one negative tie each) are not.

Supported network types

Binary: yes. Directed: yes - a pair of nodes counts as tied for the purposes of triad closure when either direction has a tie; if both directions are tied (a mutual dyad), the value used for the balance product is whichever direction is checked first (i->j before j->i), which matters only when the two directions carry different signs. Weighted: yes - only the sign of each tie value is used (see Description); magnitude does not affect the closed/balanced classification. Signed: this is the command’s whole purpose - see Description. Two-mode: not checked; structural balance is not a meaningful concept for a bipartite network’s own inherently unclosable triads.

Stored results

Scalars

r(closed_triad) number of closed triads
r(balanced_triad) number of balanced closed triads
r(unbalanced_triad) number of unbalanced closed triads
r(balance) balanced_triad / closed_triad

References

Cartwright, D., Harary, F. (1956). Structural balance: a generalization of Heider’s theory. Psychological Review 63(5), 277-293.

nwbalance