nw2motifs

Bipartite motifs of a two-mode network

Syntax 

nw2motifs [netname] [, six:node gen:erate(stub) replace mat:rix(name) norm:alise posn:orm(type) silent]
   
six:node count the motifs of six nodes too: 44 motifs and 148 node positions instead of 17 and 46
gen:erate(stub) store the node position counts in the variables stub1, stub2, … (one per position, one row per node)
replace replace existing variables
mat:rix(name) store the node position counts in a Stata matrix (one row per node, columns np1, np2, …); only if the network has no more nodes than a matrix may have rows
norm:alise add the four normalised frequencies of bmotif::mcount to the motif table
posn:orm(type) normalise the node position counts as bmotif::node_positions: none (default), sum, position, sizeclass, sizeclass_plus1, sizeclass_NAzero, levelsize, levelsize_plus1, levelsize_NAzero, motif, motif_plus1, motif_NAzero
silent suppress the output

Description

nw2motifs is the form of nwmotifs for a two-mode network: nwmotifs uses it by default on a two-mode network (and onemode forces the 4-node census of the bipartite graph). The two names give the same result with the same options.

nw2motifs counts the bipartite motifs of a two-mode network: the small connected patterns of ties between two sets of nodes that make up the building blocks of species-by-site, plant-pollinator and membership networks (Baker et al. 2015; Simmons et al. 2019, Methods in Ecology and Evolution). There are 17 motifs of two to five nodes and 27 more of six nodes (44 in all), and each motif has one or more positions (46 for the five-node set, 148 with six nodes): the nodes of a motif that are not equivalent, such as the end and the middle of a path. The command gives two things.

    1. The motif table, the number of times each motif occurs in the network (what bmotif::mcount returns), shown on screen and returned in r(motifs).
    1. The node position counts, for every node the number of times it holds each position (what bmotif::node_positions returns), stored in variables with generate() or in a matrix with matrix(). They quantify the structural role of a node, for example in a plant-pollinator network.

A motif occurrence is a set of nodes whose subgraph, with all the ties between them, is connected and has the shape of the motif; an occurrence is counted once however many ways it can be read (the motifs are induced subgraphs, so a path of two rows and two columns and a four-cycle are two different motifs, and a set of four nodes is exactly one of them). The first mode of the network (mode 1) forms the rows of the biadjacency matrix of bmotif and the second mode the columns; the numbering of the motifs and of the positions is the one of bmotif (Simmons et al.), listed in the table below. The motif table equals bmotif::mcount and the position counts bmotif::node_positions (bmotif 2.0.2) exactly, on a toy network, the Southern women, the Swedish directors, a subsample of them and 34 random networks.

The counting runs in the compiled plugin of nwcommands and needs no matrices of the size of the network: the 5,092 directors and 455 firms of ftdirectors_se (5,669 ties) take 0.04 seconds for the motifs and positions up to five nodes, and 0.05 seconds with sixnode; a random network of 1,000 and 150 nodes with 14,800 ties takes 0.05 and 0.9 seconds. (The R function takes about a minute for the five-node set on the directors.) The time with sixnode grows quickly with the density and the number of nodes of the smaller mode. Counts are held as doubles, so they are exact up to 9 x 10^15. The command stops with a message when the plugin of the installed copy is older than the command or missing for the platform: update the installation (net install nwcommands, replace) and restart Stata.

The node position counts of a node that is in no motif (an isolate) are zero. In the variables and the matrix the nodes are in the order of the network, the rows of the matrix of bmotif being the nodes of mode 1 in that order and its columns those of mode 2; the position ids np1 to np148 are those of bmotif (stub1 holds position 1).

Options

sixnode counts the motifs of six nodes (motifs 18 to 44, positions 47 to 148) as well. Without it only the motifs up to five nodes are counted (17 motifs, 46 positions), as bmotif does by default.

generate(stub) stores the counts of the positions in double variables stub1 to stub46 (stub148 with sixnode), one row per node of the network in the order of the nodes. The data set is aligned with the network first, as in the other node-level commands. Existing variables stop the command unless replace is given.

matrix(name) stores the same table as a Stata matrix with one row per node and the columns np1, np2, … The matrix is limited by the largest matrix Stata allows (800 rows in Stata BE); for larger networks use generate().

normalise adds to r(motifs) (and to the display) the four normalisations of bmotif::mcount: normalise_sum (the frequency as a share of all motifs counted), normalise_sizeclass (as a share of the motifs with the same number of nodes), normalise_levelsize (as a share of the motifs with the same number of rows and columns; motifs that are alone in their class always give 1) and normalise_nodesets (as a share of the number of node sets that could form the motif, choose(rows, a) times choose(columns, b)). A share whose denominator is zero is missing.

posnorm(type) divides the node position counts (in the variables and the matrix) as bmotif::node_positions(normalisation = ) does: sum by the number of times the node holds any position (row sums); position by the number of times any node holds the position (column sums); sizeclass by the node’s count in the positions of motifs with the same number of nodes; levelsize by its count in the positions of motifs with the same number of rows and columns; motif by its count in the positions of the same motif. The suffix _plus1 adds one to all counts first (so that nodes outside a class are not missing); the suffix _NAzero replaces the missing values of a node that holds none of the positions of the class by 0. Without them such values are missing. It needs generate() or matrix(); the table r(motifs) is not affected.

silent suppresses the output.

Examples

  • A toy network of 6 persons (mode 1, the rows) and 4 groups (mode 2, the columns):

  • . clear
  • . input str3 p str3 g
  • . "p1" "g1"
  • . "p1" "g2"
  • . "p2" "g1"
  • . "p2" "g2"
  • . "p2" "g3"
  • . "p3" "g2"
  • . "p3" "g3"
  • . "p4" "g3"
  • . "p4" "g4"
  • . "p5" "g4"
  • . "p6" "g4"
  • . "p6" "g1"
  • . end
  • . nw2fromedge p g, name(toy)

  • . nw2motifs toy, normalise

  • Node positions of the Southern women and events, with the shares of each woman’s positions among the positions of motifs of the same size:

  • . nwuse davis, nwclear
  • . nw2motifs davis, generate(np) posnorm(sizeclass) silent

  • . summarize np1-np6

  • All 44 motifs of the toy network, with the position counts in a matrix:

  • . nw2motifs toy, sixnode matrix(P) silent
  • . matrix list r(motifs)

Supported network types

Binary: yes. Directed: not applicable (a two-mode network is undirected). Valued: a tie counts when its value is above zero; the values are ignored and the command prints the usual one-line note on a valued network (bmotif’s mean weight of the motifs is not offered). Two-mode: yes - native, the command needs a two-mode network and counts the motifs of the two modes as bmotif does (mode 1 = rows). For one-mode networks the 4-node census is nwmotifs.

Stored results

nw2motifs stores in r():

  • Scalars
  • r(sixnode) — 1 if the motifs of six nodes were counted
  • r(n_mode1) — number of nodes of mode 1 (rows)

  • r(n_mode2) — number of nodes of mode 2 (columns)

  • Matrices

  • r(motifs) — 17 x 3 (44 x 3 with sixnode): motif, nodes, frequency; 17 x 7 (44 x 7) with normalise, with the columns normalise_sum, normalise_sizeclass, normalise_levelsize and normalise_nodesets added

  • Macros
  • r(netname) — name of the network
  • r(posnorm) — the normalisation of the node position counts

References

Baker, N., R. Kaartinen, T. Roslin, and D. B. Stouffer. 2015. Species’ roles in food webs show fidelity across a highly variable oak forest. Ecography 38: 130-139.

Simmons, B. I., M. J. M. Sweering, M. Schillinger, L. V. Dicks, W. J. Sutherland, and R. Di Clemente. 2019. bmotif: A package for motif analyses of bipartite networks. Methods in Ecology and Evolution 10: 695-701.

Stouffer, D. B., M. Sales-Pardo, M. I. Sirer, and J. Bascompte. 2012. Evolutionary conservation of species’ roles in food webs. Science 335: 1489-1492.

nwcommands version 3.17.6, 9 November 2026 (check your installed version)

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nwcommands is free software under the GNU General Public License, version 3, as are the model packages nwsaom, nwergm, nwdynam and nwrem. Citing and licenses · Get help · GitHub. Issues with the core go to the nwcommands repository; issues with a model package go to that package's own repository.

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