def katz_centrality(
G, alpha=None, max_iter=100, tol=1.0e-6, nstart=None, normalized=True
):
"""
Compute the Katz centrality for the nodes of the graph G. cuGraph does not
currently support the 'beta' and 'weight' parameters as seen in the
corresponding networkX call. This implementation is based on a relaxed
version of Katz defined by Foster with a reduced computational complexity
of O(n+m)
Foster, K.C., Muth, S.Q., Potterat, J.J. et al.
Computational & Mathematical Organization Theory (2001) 7: 275.
https://doi.org/10.1023/A:1013470632383
Parameters
----------
G : cuGraph.Graph
cuGraph graph descriptor with connectivity information. The graph can
contain either directed (DiGraph) or undirected edges (Graph).
alpha : float
Attenuation factor defaulted to None. If alpha is not specified then
it is internally calculated as 1/(degree_max) where degree_max is the
maximum out degree.
NOTE : The maximum acceptable value of alpha for convergence
alpha_max = 1/(lambda_max) where lambda_max is the largest eigenvalue
of the graph.
Since lambda_max is always lesser than or equal to degree_max for a
graph, alpha_max will always be greater than or equal to
(1/degree_max). Therefore, setting alpha to (1/degree_max) will
guarantee that it will never exceed alpha_max thus in turn fulfilling
the requirement for convergence.
max_iter : int
The maximum number of iterations before an answer is returned. This can
be used to limit the execution time and do an early exit before the
solver reaches the convergence tolerance.
If this value is lower or equal to 0 cuGraph will use the default
value, which is 100.
tolerance : float
Set the tolerance the approximation, this parameter should be a small
magnitude value.
The lower the tolerance the better the approximation. If this value is
0.0f, cuGraph will use the default value which is 1.0e-6.
Setting too small a tolerance can lead to non-convergence due to
numerical roundoff. Usually values between 1e-2 and 1e-6 are
acceptable.
nstart : cudf.Dataframe
GPU Dataframe containing the initial guess for katz centrality.
nstart['vertex'] : cudf.Series
Contains the vertex identifiers
nstart['values'] : cudf.Series
Contains the katz centrality values of vertices
normalized : bool
If True normalize the resulting katz centrality values
Returns
-------
df : cudf.DataFrame
GPU data frame containing two cudf.Series of size V: the vertex
identifiers and the corresponding katz centrality values.
df['vertex'] : cudf.Series
Contains the vertex identifiers
df['katz_centrality'] : cudf.Series
Contains the katz centrality of 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')
>>> kc = cugraph.katz_centrality(G)
"""
if nstart is not None:
if G.renumbered is True:
nstart = G.add_internal_vertex_id(nstart, 'vertex', 'vertex')
df = katz_centrality_wrapper.katz_centrality(
G, alpha, max_iter, tol, nstart, normalized
)
if G.renumbered:
df = G.unrenumber(df, "vertex")
return df
def katz_centrality(G,
alpha=0.1,
max_iter=100,
tol=1.0e-6,
nstart=None,
normalized=True):
"""
Compute the Katz centrality for the nodes of the graph G. cuGraph does not
currently support the 'beta' and 'weight' parameters as seen in the
corresponding networkX call. This implementation is based on a relaxed
version of Katz defined by Foster with a reduced computational complexity
of O(n+m)
Foster, K.C., Muth, S.Q., Potterat, J.J. et al.
Computational & Mathematical Organization Theory (2001) 7: 275.
https://doi.org/10.1023/A:1013470632383
Parameters
----------
G : cuGraph.Graph
cuGraph graph descriptor with connectivity information. The graph can
contain either directed or undirected edges where undirected edges are
represented as directed edges in both directions.
alpha : float
Attenuation factor with a default value of 0.1. If alpha is not less
than 1/(lambda_max) where lambda_max is the maximum degree
GDF_CUDA_ERROR is returned
max_iter : int
The maximum number of iterations before an answer is returned. This can
be used to limit the execution time and do an early exit before the
solver reaches the convergence tolerance.
If this value is lower or equal to 0 cuGraph will use the default
value, which is 100.
tolerance : float
Set the tolerance the approximation, this parameter should be a small
magnitude value.
The lower the tolerance the better the approximation. If this value is
0.0f, cuGraph will use the default value which is 1.0e-6.
Setting too small a tolerance can lead to non-convergence due to
numerical roundoff. Usually values between 1e-2 and 1e-6 are
acceptable.
nstart : cudf.Dataframe
GPU Dataframe containing the initial guess for katz centrality.
nstart['vertex'] : cudf.Series
Contains the vertex identifiers
nstart['values'] : cudf.Series
Contains the katz centrality values of vertices
normalized : bool
If True normalize the resulting katz centrality values
Returns
-------
df : cudf.DataFrame
GPU data frame containing two cudf.Series of size V: the vertex
identifiers and the corresponding katz centrality values.
df['vertex'] : cudf.Series
Contains the vertex identifiers
df['katz_centrality'] : cudf.Series
Contains the katz centrality of 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)
>>> kc = cugraph.katz_centrality(G)
"""
df = katz_centrality_wrapper.katz_centrality(G, alpha, max_iter, tol,
nstart, normalized)
return df
