Motif adjacency matrices

Functions for building motif adjacency matrices are in motifcluster.motifadjacency.

build_motif_adjacency_matrix(adj_mat, motif_name, motif_type='struc', mam_weight_type='unweighted', mam_method='sparse')

Build a motif adjacency matrix.

Build a motif adjacency matrix from an adjacency matrix. Entry (i, j) of a motif adjacency matrix is the sum of the weights of all motifs containing both nodes i and j.

  • The motif is specified by name and the type of motif instance can be one of:
    • Functional: motifs should appear as subgraphs.
    • Structural: motifs should appear as induced subgraphs.
  • The weighting scheme can be one of:
    • Unweighted: the weight of any motif instance is one.
    • Mean: the weight of any motif instance is the mean of its edge weights.
    • Product: the weight of any motif instance is the product of its edge weights.
Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_name (str) – Motif used for the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build. One of “func” or “struc”.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”. The sparse formulation avoids generating large dense matrices so tends to be faster for large sparse graphs.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix

Examples

>>> adj_mat = np.array(range(1, 10)).reshape((3, 3))
>>> build_motif_adjacency_matrix(adj_mat, "M1", "func", "mean")
mam_M1(adj_mat, motif_type, mam_weight_type, mam_method)

Perform the motif adjacency matrix calculations for motif M1.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_M10(adj_mat, motif_type, mam_weight_type, mam_method)

Perform the motif adjacency matrix calculations for motif M10.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_M11(adj_mat, motif_type, mam_weight_type, mam_method)

Perform the motif adjacency matrix calculations for motif M11.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_M12(adj_mat, motif_type, mam_weight_type, mam_method)

Perform the motif adjacency matrix calculations for motif M12.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_M13(adj_mat, motif_type, mam_weight_type, mam_method)

Perform the motif adjacency matrix calculations for motif M13.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_M2(adj_mat, motif_type, mam_weight_type, mam_method)

Perform the motif adjacency matrix calculations for motif M2.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_M3(adj_mat, motif_type, mam_weight_type, mam_method)

Perform the motif adjacency matrix calculations for motif M3.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_M4(adj_mat, mam_weight_type, mam_method)

Perform the motif adjacency matrix calculations for motif M4.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_M5(adj_mat, motif_type, mam_weight_type, mam_method)

Perform the motif adjacency matrix calculations for motif M5.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_M6(adj_mat, motif_type, mam_weight_type, mam_method)

Perform the motif adjacency matrix calculations for motif M6.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_M7(adj_mat, motif_type, mam_weight_type, mam_method)

Perform the motif adjacency matrix calculations for motif M7.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_M8(adj_mat, motif_type, mam_weight_type, mam_method)

Perform the motif adjacency matrix calculations for motif M8.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_M9(adj_mat, motif_type, mam_weight_type, mam_method)

Perform the motif adjacency matrix calculations for motif M9.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_Mcoll(adj_mat, motif_type, mam_weight_type, mam_method)

Perform the motif adjacency matrix calculations for motif Mcoll.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_Md(adj_mat, mam_weight_type)

Perform the motif adjacency matrix calculations for motif Md.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_Mexpa(adj_mat, motif_type, mam_weight_type, mam_method)

Perform the motif adjacency matrix calculations for motif Mexpa.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
  • mam_method (str) – Which formulation to use. One of “dense” or “sparse”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix
mam_Ms(adj_mat, motif_type, mam_weight_type)

Perform the motif adjacency matrix calculations for motif Ms.

Parameters:
  • adj_mat (matrix) – Adjacency matrix from which to build the motif adjacency matrix.
  • motif_type (str) – Type of motif adjacency matrix to build.
  • mam_weight_type (str) – The weighting scheme to use. One of “unweighted”, “mean” or “product”.
Returns:

A motif adjacency matrix.
Return type:

sparse matrix