Source code for graphscope.analytical.app.degree_assortativity_coefficient

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
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# Copyright 2020 Alibaba Group Holding Limited. All Rights Reserved.
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# 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
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#     http://www.apache.org/licenses/LICENSE-2.0
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# 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.
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# Author: Ning Xin
#


from graphscope.framework.app import AppAssets
from graphscope.framework.app import not_compatible_for
from graphscope.framework.app import project_to_simple

__all__ = ["degree_assortativity_coefficient"]


@project_to_simple
@not_compatible_for("arrow_property")
def degree_assortativity_coefficient(graph, x="out", y="in", weight=None):
    """Compute degree assortativity of graph.

    Assortativity measures the similarity of connections
    in the graph with respect to the node degree.

    Parameters
    ----------
    graph (:class:`graphscope.Graph`): A simple graph.

    x: string ('in','out')
       The degree type for source node (directed graphs only).

    y: string ('in','out')
       The degree type for target node (directed graphs only).

    weighted: bool (True, False)
        weighted graph or unweighted graph

    Returns
    -------
    r : float
       Assortativity of graph by degree.

    Examples

    .. code:: python

        >>> import graphscope
        >>> from graphscope.dataset import load_modern_graph
        >>> sess = graphscope.session(cluster_type="hosts", mode="eager")
        >>> g = load_modern_graph(sess)
        >>> g.schema
        >>> c = graphscope.degree_assortativity_coefficient(g, weight="weight")
        >>> sess.close()

    Notes
    -----
    This computes Eq. (21) in Ref. [1]_ , where e is the joint
    probability distribution (mixing matrix) of the degrees.  If G is
    directed than the matrix e is the joint probability of the
    user-specified degree type for the source and target.

    References
    ----------
    .. [1] M. E. J. Newman, Mixing patterns in networks,
       Physical Review E, 67 026126, 2003
    .. [2] Foster, J.G., Foster, D.V., Grassberger, P. & Paczuski, M.
       Edge direction and the structure of networks, PNAS 107, 10815-20 (2010).
    """
    weighted = False if weight is None else True
    ctx = AppAssets(algo="degree_assortativity_coefficient", context="tensor")(
        graph,
        source_degree_type=x,
        target_degree_type=y,
        weighted=weighted,
    )
    return ctx.to_numpy("r", axis=0)[0]