triad_type

triad_type(G)

Returns the sociological triad type for a triad.

Parameters:

Gdigraph

A NetworkX DiGraph with 3 nodes

Returns:

triad_typestr

A string identifying the triad type

Notes

There can be 6 unique edges in a triad (order-3 DiGraph) (so 2^^6=64 unique triads given 3 nodes). These 64 triads each display exactly 1 of 16 topologies of triads (topologies can be permuted). These topologies are identified by the following notation:

{m}{a}{n}{type} (for example: 111D, 210, 102)

Here:

{m} = number of mutual ties (takes 0, 1, 2, 3); a mutual tie is (0,1)

AND (1,0)

{a} = number of asymmetric ties (takes 0, 1, 2, 3); an asymmetric tie

is (0,1) BUT NOT (1,0) or vice versa

{n} = number of null ties (takes 0, 1, 2, 3); a null tie is NEITHER

(0,1) NOR (1,0)

{type} = a letter (takes U, D, C, T) corresponding to up, down, cyclical

and transitive. This is only used for topologies that can have more than one form (eg: 021D and 021U).

References

[1]

Snijders, T. (2012). “Transitivity and triads.” University of Oxford. https://web.archive.org/web/20170830032057/http://www.stats.ox.ac.uk/~snijders/Trans_Triads_ha.pdf

Examples

>>> G = nx.DiGraph([(1, 2), (2, 3), (3, 1)])
>>> nx.triad_type(G)
'030C'
>>> G.add_edge(1, 3)
>>> nx.triad_type(G)
'120C'