如何用networkx绘制社区

Question

如何使用 python networkx 绘制一个包含社区的图表，如下图：

image url

Answer 1

networkx.draw_networkx_nodes 和 networkx.draw_networkx_edges 的文档解释了如何设置节点和边缘颜色。可以通过查找每个社区的节点位置，然后绘制一个包含所有位置（然后是一些位置）的补丁（例如matplotlib.patches.Circle）来制作社区的补丁。

难点是图形布局/设置节点位置。 AFAIK，networkx 中没有“开箱即用”实现所需图形布局的例程。您要做的是：

1. 将社区相对于彼此定位：创建一个新的加权图，其中每个节点对应一个社区，权重对应于社区之间的边数。使用您最喜欢的图形布局算法（例如spring_layout）获得体面的布局。

2. 定位每个社区内的节点：为每个社区创建一个新图。找到子图的布局。

3. 结合 1) 和 3) 中的节点位置。例如。将 1) 中计算的社区位置放大 10 倍；将这些值添加到该社区内所有节点的位置（如 2 中计算的）。

我一直想实现这个。我可能会在今天晚些时候或周末这样做。

编辑：

瞧。现在你只需要在节点周围（后面）画出你最喜欢的补丁。

import numpy as np
import matplotlib.pyplot as plt
import networkx as nx

def community_layout(g, partition):
    """
    Compute the layout for a modular graph.


    Arguments:
    ----------
    g -- networkx.Graph or networkx.DiGraph instance
        graph to plot

    partition -- dict mapping int node -> int community
        graph partitions


    Returns:
    --------
    pos -- dict mapping int node -> (float x, float y)
        node positions

    """

    pos_communities = _position_communities(g, partition, scale=3.)

    pos_nodes = _position_nodes(g, partition, scale=1.)

    # combine positions
    pos = dict()
    for node in g.nodes():
        pos[node] = pos_communities[node] + pos_nodes[node]

    return pos

def _position_communities(g, partition, **kwargs):

    # create a weighted graph, in which each node corresponds to a community,
    # and each edge weight to the number of edges between communities
    between_community_edges = _find_between_community_edges(g, partition)

    communities = set(partition.values())
    hypergraph = nx.DiGraph()
    hypergraph.add_nodes_from(communities)
    for (ci, cj), edges in between_community_edges.items():
        hypergraph.add_edge(ci, cj, weight=len(edges))

    # find layout for communities
    pos_communities = nx.spring_layout(hypergraph, **kwargs)

    # set node positions to position of community
    pos = dict()
    for node, community in partition.items():
        pos[node] = pos_communities[community]

    return pos

def _find_between_community_edges(g, partition):

    edges = dict()

    for (ni, nj) in g.edges():
        ci = partition[ni]
        cj = partition[nj]

        if ci != cj:
            try:
                edges[(ci, cj)] += [(ni, nj)]
            except KeyError:
                edges[(ci, cj)] = [(ni, nj)]

    return edges

def _position_nodes(g, partition, **kwargs):
    """
    Positions nodes within communities.
    """

    communities = dict()
    for node, community in partition.items():
        try:
            communities[community] += [node]
        except KeyError:
            communities[community] = [node]

    pos = dict()
    for ci, nodes in communities.items():
        subgraph = g.subgraph(nodes)
        pos_subgraph = nx.spring_layout(subgraph, **kwargs)
        pos.update(pos_subgraph)

    return pos

def test():
    # to install networkx 2.0 compatible version of python-louvain use:
    # pip install -U git+https://github.com/taynaud/python-louvain.git@networkx2
    from community import community_louvain

    g = nx.karate_club_graph()
    partition = community_louvain.best_partition(g)
    pos = community_layout(g, partition)

    nx.draw(g, pos, node_color=list(partition.values())); plt.show()
    return

附录

虽然总体思路是合理的，但我上面的旧实现存在一些问题。最重要的是，对于规模不均的社区，实施效果并不好。具体来说，_position_communities 在画布上为每个社区提供相同数量的房地产。如果一些社区比其他社区大得多，这些社区最终会被压缩到与小社区相同的空间中。显然，这并不能很好地反映图的结构。

我编写了一个用于可视化网络的库，称为netgraph。它包括上述社区布局例程的改进版本，在安排社区时还考虑了社区的大小。它与networkx 和igraph Graph 对象完全兼容，因此制作漂亮的图形应该是容易和快速的（至少是这样的想法）。

import matplotlib.pyplot as plt
import networkx as nx

# installation easiest via pip:
# pip install netgraph
from netgraph import Graph

# create a modular graph
partition_sizes = [10, 20, 30, 40]
g = nx.random_partition_graph(partition_sizes, 0.5, 0.1)

# since we created the graph, we know the best partition:
node_to_community = dict()
node = 0
for community_id, size in enumerate(partition_sizes):
    for _ in range(size):
        node_to_community[node] = community_id
        node += 1

# # alternatively, we can infer the best partition using Louvain:
# from community import community_louvain
# node_to_community = community_louvain.best_partition(g)

community_to_color = {
    0 : 'tab:blue',
    1 : 'tab:orange',
    2 : 'tab:green',
    3 : 'tab:red',
}
node_color = {node: community_to_color[community_id] for node, community_id in node_to_community.items()}

Graph(g,
      node_color=node_color, node_edge_width=0, edge_alpha=0.1,
      node_layout='community', node_layout_kwargs=dict(node_to_community=node_to_community),
      edge_layout='bundled', edge_layout_kwargs=dict(k=2000),
)

plt.show()