# Source code for graspy.utils.ptr

```
# Copyright 2019 NeuroData (http://neurodata.io)
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import numpy as np
from .utils import import_graph, is_unweighted, is_symmetric, is_loopless, symmetrize
from scipy.stats import rankdata
[docs]def pass_to_ranks(graph, method="simple-nonzero"):
r"""
Rescales edge weights of an adjacency matrix based on their relative rank in
the graph.
Parameters
----------
graph: Adjacency matrix
method: {'simple-nonzero' (default), 'simple-all', 'zero-boost'} string, optional
- 'simple-nonzero'
assigns ranks to all non-zero edges, settling ties using
the average. Ranks are then scaled by
:math:`\frac{rank(\text{non-zero edges})}{\text{total non-zero edges} + 1}`
- 'simple-all'
assigns ranks to all non-zero edges, settling ties using
the average. Ranks are then scaled by
:math:`\frac{rank(\text{non-zero edges})}{n^2 + 1}`
where n is the number of nodes
- 'zero-boost'
preserves the edge weight for all 0s, but ranks the other
edges as if the ranks of all 0 edges has been assigned. If there are
10 0-valued edges, the lowest non-zero edge gets weight 11 / (number
of possible edges). Ties settled by the average of the weight that those
edges would have received. Number of possible edges is determined
by the type of graph (loopless or looped, directed or undirected).
See also
--------
scipy.stats.rankdata
Returns
-------
graph: numpy.ndarray, shape(n_vertices, n_vertices)
Adjacency matrix of graph after being passed to ranks
"""
graph = import_graph(graph) # just for typechecking
if is_unweighted(graph):
return graph
if graph.min() < 0:
raise UserWarning(
"Current pass-to-ranks on graphs with negative"
+ " weights will yield nonsensical results, especially for zero-boost"
)
if method == "zero-boost":
if is_symmetric(graph):
# start by working with half of the graph, since symmetric
triu = np.triu(graph)
non_zeros = triu[triu != 0]
else:
non_zeros = graph[graph != 0]
rank = rankdata(non_zeros)
if is_symmetric(graph):
if is_loopless(graph):
num_zeros = (len(graph[graph == 0]) - graph.shape[0]) / 2
possible_edges = graph.shape[0] * (graph.shape[0] - 1) / 2
else:
num_zeros = (
len(triu[triu == 0]) - graph.shape[0] * (graph.shape[0] - 1) / 2
)
possible_edges = graph.shape[0] * (graph.shape[0] + 1) / 2
else:
if is_loopless(graph):
# n^2 - num_nonzero - num_diagonal
num_zeros = graph.size - len(non_zeros) - graph.shape[0]
# n^2 - num_diagonal
possible_edges = graph.size - graph.shape[0]
else:
num_zeros = graph.size - len(non_zeros)
possible_edges = graph.size
# shift up by the number of zeros
rank = rank + num_zeros
# normalize by the number of possible edges for this kind of graph
rank = rank / possible_edges
# put back into matrix form (and reflect over the diagonal if necessary)
if is_symmetric(graph):
triu[triu != 0] = rank
graph = symmetrize(triu, method="triu")
else:
graph[graph != 0] = rank
return graph
elif method in ["simple-all", "simple-nonzero"]:
non_zeros = graph[graph != 0]
rank = rankdata(non_zeros)
if method == "simple-all":
normalizer = graph.size
elif method == "simple-nonzero":
normalizer = rank.shape[0]
rank = rank / (normalizer + 1)
graph[graph != 0] = rank
return graph
else:
raise ValueError("Unsuported pass-to-ranks method")
```