子图

将节点标记为 supported（支持）和 unsupported（不支持）的有向图划分到只包含完全 supported 或完全 unsupported 节点的子图列表中的示例。改编自 lobpcg/python_examples

import networkx as nx
import matplotlib.pyplot as plt


def graph_partitioning(G, plotting=True):
    """Partition a directed graph into a list of subgraphs that contain
    only entirely supported or entirely unsupported nodes.
    """
    # Categorize nodes by their node_type attribute
    supported_nodes = {n for n, d in G.nodes(data="node_type") if d == "supported"}
    unsupported_nodes = {n for n, d in G.nodes(data="node_type") if d == "unsupported"}

    # Make a copy of the graph.
    H = G.copy()
    # Remove all edges connecting supported and unsupported nodes.
    H.remove_edges_from(
        (n, nbr, d)
        for n, nbrs in G.adj.items()
        if n in supported_nodes
        for nbr, d in nbrs.items()
        if nbr in unsupported_nodes
    )
    H.remove_edges_from(
        (n, nbr, d)
        for n, nbrs in G.adj.items()
        if n in unsupported_nodes
        for nbr, d in nbrs.items()
        if nbr in supported_nodes
    )

    # Collect all removed edges for reconstruction.
    G_minus_H = nx.DiGraph()
    G_minus_H.add_edges_from(set(G.edges) - set(H.edges))

    if plotting:
        # Plot the stripped graph with the edges removed.
        _node_colors = [c for _, c in H.nodes(data="node_color")]
        _pos = nx.spring_layout(H)
        plt.figure(figsize=(8, 8))
        nx.draw_networkx_edges(H, _pos, alpha=0.3, edge_color="k")
        nx.draw_networkx_nodes(H, _pos, node_color=_node_colors)
        nx.draw_networkx_labels(H, _pos, font_size=14)
        plt.axis("off")
        plt.title("The stripped graph with the edges removed.")
        plt.show()
        # Plot the edges removed.
        _pos = nx.spring_layout(G_minus_H)
        plt.figure(figsize=(8, 8))
        ncl = [G.nodes[n]["node_color"] for n in G_minus_H.nodes]
        nx.draw_networkx_edges(G_minus_H, _pos, alpha=0.3, edge_color="k")
        nx.draw_networkx_nodes(G_minus_H, _pos, node_color=ncl)
        nx.draw_networkx_labels(G_minus_H, _pos, font_size=14)
        plt.axis("off")
        plt.title("The removed edges.")
        plt.show()

    # Find the connected components in the stripped undirected graph.
    # And use the sets, specifying the components, to partition
    # the original directed graph into a list of directed subgraphs
    # that contain only entirely supported or entirely unsupported nodes.
    subgraphs = [
        H.subgraph(c).copy() for c in nx.connected_components(H.to_undirected())
    ]

    return subgraphs, G_minus_H

创建示例有向图。

此有向图有一个标记为 in（蓝色）的输入节点，一个标记为 out（品红色）的输出节点。其余六个节点被分为四个标记为 supported（绿色）的节点和两个标记为 unsupported（红色）的节点。目标是计算一个只包含完全 supported 或 unsupported 节点的子图列表。

G_ex = nx.DiGraph()
G_ex.add_nodes_from(["In"], node_type="input", node_color="b")
G_ex.add_nodes_from(["A", "C", "E", "F"], node_type="supported", node_color="g")
G_ex.add_nodes_from(["B", "D"], node_type="unsupported", node_color="r")
G_ex.add_nodes_from(["Out"], node_type="output", node_color="m")
G_ex.add_edges_from(
    [
        ("In", "A"),
        ("A", "B"),
        ("B", "C"),
        ("B", "D"),
        ("D", "E"),
        ("C", "F"),
        ("E", "F"),
        ("F", "Out"),
    ]
)

绘制原始图。

node_color_list = [nc for _, nc in G_ex.nodes(data="node_color")]
pos = nx.spectral_layout(G_ex)
plt.figure(figsize=(8, 8))
nx.draw_networkx_edges(G_ex, pos, alpha=0.3, edge_color="k")
nx.draw_networkx_nodes(G_ex, pos, alpha=0.8, node_color=node_color_list)
nx.draw_networkx_labels(G_ex, pos, font_size=14)
plt.axis("off")
plt.title("The original graph.")
plt.show()

计算子图并绘制所有中间步骤的结果。

subgraphs_of_G_ex, removed_edges = graph_partitioning(G_ex, plotting=True)

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绘制结果：列表中的每个子图。

for subgraph in subgraphs_of_G_ex:
    _pos = nx.spring_layout(subgraph)
    plt.figure(figsize=(8, 8))
    nx.draw_networkx_edges(subgraph, _pos, alpha=0.3, edge_color="k")
    node_color_list_c = [nc for _, nc in subgraph.nodes(data="node_color")]
    nx.draw_networkx_nodes(subgraph, _pos, node_color=node_color_list_c)
    nx.draw_networkx_labels(subgraph, _pos, font_size=14)
    plt.axis("off")
    plt.title("One of the subgraphs.")
    plt.show()

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将子图列表重新组合成图

G_ex_r = nx.DiGraph()
# Composing all subgraphs.
for subgraph in subgraphs_of_G_ex:
    G_ex_r = nx.compose(G_ex_r, subgraph)
# Adding the previously stored edges.
G_ex_r.add_edges_from(removed_edges.edges())

检查原始图和重构图是否同构。

assert nx.is_isomorphic(G_ex, G_ex_r)

绘制重构图。

node_color_list = [nc for _, nc in G_ex_r.nodes(data="node_color")]
pos = nx.spectral_layout(G_ex_r)
plt.figure(figsize=(8, 8))
nx.draw_networkx_edges(G_ex_r, pos, alpha=0.3, edge_color="k")
nx.draw_networkx_nodes(G_ex_r, pos, alpha=0.8, node_color=node_color_list)
nx.draw_networkx_labels(G_ex_r, pos, font_size=14)
plt.axis("off")
plt.title("The reconstructed graph.")
plt.show()