def overlap(input_graph, vertex_pair=None):
"""
Compute the Overlap Coefficient between each pair of vertices connected by
an edge, or between arbitrary pairs of vertices specified by the user.
Overlap Coefficient is defined between two sets as the ratio of the volume
of their intersection divided by the smaller of their two volumes. In the
context of graphs, the neighborhood of a vertex is seen as a set. The
Overlap Coefficient weight of each edge represents the strength of
connection between vertices based on the relative similarity of their
neighbors. If first is specified but second is not, or vice versa, an
exception will be thrown.
Parameters
----------
graph : cugraph.Graph
cuGraph graph descriptor, should contain the connectivity information
as an edge list (edge weights are not used for this algorithm). The
adjacency list will be computed if not already present.
vertex_pair : cudf.DataFrame
A GPU dataframe consisting of two columns representing pairs of
vertices. If provided, the overlap coefficient is computed for the
given vertex pairs, else, it is computed for all vertex pairs.
Returns
-------
df : cudf.DataFrame
GPU data frame of size E (the default) or the size of the given pairs
(first, second) containing the Overlap coefficients. The ordering is
relative to the adjacency list, or that given by the specified vertex
pairs.
df['source'] : cudf.Series
The source vertex ID (will be identical to first if specified).
df['destination'] : cudf.Series
The destination vertex ID (will be identical to second if
specified).
df['overlap_coeff'] : cudf.Series
The computed Overlap coefficient between the source and destination
vertices.
Examples
--------
>>> gdf = cudf.read_csv('datasets/karate.csv', delimiter=' ',
>>> dtype=['int32', 'int32', 'float32'], header=None)
>>> G = cugraph.Graph()
>>> G.from_cudf_edgelist(gdf, source='0', destination='1')
>>> df = cugraph.overlap(G)
"""
if (type(vertex_pair) == cudf.DataFrame):
null_check(vertex_pair[vertex_pair.columns[0]])
null_check(vertex_pair[vertex_pair.columns[1]])
elif vertex_pair is None:
pass
else:
raise ValueError("vertex_pair must be a cudf dataframe")
df = overlap_wrapper.overlap(input_graph, None, vertex_pair)
return df
def overlap(input_graph, first=None, second=None):
"""
Compute the Overlap Coefficient between each pair of vertices connected by
an edge, or between arbitrary pairs of vertices specified by the user.
Overlap Coefficient is defined between two sets as the ratio of the volume
of their intersection divided by the smaller of their two volumes. In the
context of graphs, the neighborhood of a vertex is seen as a set. The
Overlap Coefficient weight of each edge represents the strength of
connection between vertices based on the relative similarity of their
neighbors. If first is specified but second is not, or vice versa, an
exception will be thrown.
Parameters
----------
graph : cugraph.Graph
cuGraph graph descriptor, should contain the connectivity information
as an edge list (edge weights are not used for this algorithm). The
adjacency list will be computed if not already present.
first : cudf.Series
Specifies the first vertices of each pair of vertices to compute for,
must be specified along with second.
second : cudf.Series
Specifies the second vertices of each pair of vertices to compute for,
must be specified along with first.
Returns
-------
df : cudf.DataFrame
GPU data frame of size E (the default) or the size of the given pairs
(first, second) containing the Overlap coefficients. The ordering is
relative to the adjacency list, or that given by the specified vertex
pairs.
df['source'] : cudf.Series
The source vertex ID (will be identical to first if specified).
df['destination'] : cudf.Series
The destination vertex ID (will be identical to second if
specified).
df['overlap_coeff'] : cudf.Series
The computed Overlap coefficient between the source and destination
vertices.
Examples
--------
>>> M = cudf.read_csv('datasets/karate.csv', delimiter=' ',
>>> dtype=['int32', 'int32', 'float32'], header=None)
>>> sources = cudf.Series(M['0'])
>>> destinations = cudf.Series(M['1'])
>>> G = cugraph.Graph()
>>> G.add_edge_list(sources, destinations, None)
>>> df = cugraph.overlap(G)
"""
if (type(first) == cudf.dataframe.series.Series
and type(second) == cudf.dataframe.series.Series):
null_check(first)
null_check(second)
elif first is None and second is None:
pass
else:
raise ValueError("Specify first and second or neither")
df = overlap_wrapper.overlap(input_graph.graph_ptr, first, second)
return df
def overlap_w(input_graph, weights, vertex_pair=None):
"""
Compute the weighted Overlap Coefficient between each pair of vertices
connected by an edge, or between arbitrary pairs of vertices specified by
the user. Overlap Coefficient is defined between two sets as the ratio of
the volume of their intersection divided by the smaller of their volumes.
In the context of graphs, the neighborhood of a vertex is seen as a set.
The Overlap Coefficient weight of each edge represents the strength of
connection between vertices based on the relative similarity of their
neighbors. If first is specified but second is not, or vice versa, an
exception will be thrown.
Parameters
----------
input_graph : cugraph.Graph
cuGraph Graph instance, should contain the connectivity information
as an edge list (edge weights are not used for this algorithm). The
adjacency list will be computed if not already present.
weights : cudf.DataFrame
Specifies the weights to be used for each vertex.
Vertex should be represented by multiple columns for multi-column
vertices.
weights['vertex'] : cudf.Series
Contains the vertex identifiers
weights['weight'] : cudf.Series
Contains the weights of vertices
vertex_pair : cudf.DataFrame, optional (default=None)
A GPU dataframe consisting of two columns representing pairs of
vertices. If provided, the overlap coefficient is computed for the
given vertex pairs, else, it is computed for all vertex pairs.
Returns
-------
df : cudf.DataFrame
GPU data frame of size E (the default) or the size of the given pairs
(first, second) containing the overlap coefficients. The ordering is
relative to the adjacency list, or that given by the specified vertex
pairs.
df['source'] : cudf.Series
The source vertex ID
df['destination'] : cudf.Series
The destination vertex ID
df['overlap_coeff'] : cudf.Series
The computed weighted Overlap coefficient between the source and
destination vertices.
Examples
--------
>>> import random
>>> M = cudf.read_csv(datasets_path / 'karate.csv', delimiter=' ',
... dtype=['int32', 'int32', 'float32'], header=None)
>>> G = cugraph.Graph()
>>> G.from_cudf_edgelist(M, source='0', destination='1')
>>> # Create a dataframe containing the vertices with their
>>> # corresponding weight
>>> weights = cudf.DataFrame()
>>> # Sample 10 random vertices from the graph and drop duplicates if
>>> # there are any to avoid duplicates vertices with different weight
>>> # value in the 'weights' dataframe
>>> weights['vertex'] = G.nodes().sample(n=10).drop_duplicates()
>>> # Reset the indices and drop the index column
>>> weights.reset_index(inplace=True, drop=True)
>>> # Create a weight column with random weights
>>> weights['weight'] = [random.random() for w in range(
... len(weights['vertex']))]
>>> df = cugraph.overlap_w(G, weights)
"""
if type(vertex_pair) == cudf.DataFrame:
vertex_pair = renumber_vertex_pair(input_graph, vertex_pair)
elif vertex_pair is not None:
raise ValueError("vertex_pair must be a cudf dataframe")
if input_graph.renumbered:
vertex_size = input_graph.vertex_column_size()
if vertex_size == 1:
weights = input_graph.add_internal_vertex_id(
weights, 'vertex', 'vertex')
else:
cols = weights.columns[:vertex_size].to_list()
weights = input_graph.add_internal_vertex_id(
weights, 'vertex', cols)
overlap_weights = weights['weight']
overlap_weights = overlap_weights.astype('float32')
df = overlap_wrapper.overlap(input_graph, overlap_weights, vertex_pair)
if input_graph.renumbered:
df = input_graph.unrenumber(df, "source")
df = input_graph.unrenumber(df, "destination")
return df
def overlap_w(input_graph, weights, vertex_pair=None):
"""
Compute the weighted Overlap Coefficient between each pair of vertices
connected by an edge, or between arbitrary pairs of vertices specified by
the user. Overlap Coefficient is defined between two sets as the ratio of
the volume of their intersection divided by the smaller of their volumes.
In the context of graphs, the neighborhood of a vertex is seen as a set.
The Overlap Coefficient weight of each edge represents the strength of
connection between vertices based on the relative similarity of their
neighbors. If first is specified but second is not, or vice versa, an
exception will be thrown.
Parameters
----------
input_graph : cugraph.Graph
cuGraph graph descriptor, should contain the connectivity information
as an edge list (edge weights are not used for this algorithm). The
adjacency list will be computed if not already present.
weights : cudf.Series
Specifies the weights to be used for each vertex.
vertex_pair : cudf.DataFrame
A GPU dataframe consisting of two columns representing pairs of
vertices. If provided, the overlap coefficient is computed for the
given vertex pairs, else, it is computed for all vertex pairs.
Returns
-------
df : cudf.DataFrame
GPU data frame of size E (the default) or the size of the given pairs
(first, second) containing the overlap coefficients. The ordering is
relative to the adjacency list, or that given by the specified vertex
pairs.
df['source'] : cudf.Series
The source vertex ID
df['destination'] : cudf.Series
The destination vertex ID
df['overlap_coeff'] : cudf.Series
The computed weighted Overlap coefficient between the source and
destination vertices.
Examples
--------
>>> M = cudf.read_csv('datasets/karate.csv', delimiter=' ',
>>> dtype=['int32', 'int32', 'float32'], header=None)
>>> G = cugraph.Graph()
>>> G.from_cudf_edgelist(M, source='0', destination='1')
>>> df = cugraph.overlap_w(G, M[2])
"""
if type(vertex_pair) == cudf.DataFrame:
vertex_pair = renumber_vertex_pair(input_graph, vertex_pair)
elif vertex_pair is None:
pass
else:
raise ValueError("vertex_pair must be a cudf dataframe")
if input_graph.renumbered:
vertex_size = input_graph.vertex_column_size()
if vertex_size == 1:
weights = input_graph.add_internal_vertex_id(
weights, 'vertex', 'vertex')
else:
cols = weights.columns[:vertex_size].to_list()
weights = input_graph.add_internal_vertex_id(
weights, 'vertex', cols)
overlap_weights = cudf.Series(np.ones(len(weights)))
for i in range(len(weights)):
overlap_weights[weights['vertex'].iloc[i]] = weights['weight'].iloc[i]
overlap_weights = overlap_weights.astype('float32')
df = overlap_wrapper.overlap(input_graph, overlap_weights, vertex_pair)
if input_graph.renumbered:
df = input_graph.unrenumber(df, "source")
df = input_graph.unrenumber(df, "destination")
return df
