如何使用 `networkx` 中的 `pos` 参数创建流程图样式的图表？ (Python 3)

Question

我正在尝试使用Python（最好使用matplotlib 和networkx，尽管对bokeh 感兴趣）创建一个线性网络图，其概念类似于下面的。

如何在 Python 中使用 networkx 有效地构造此图表（pos？）？ 我想将其用于更复杂的示例，因此我觉得为此很难对位置进行编码简单的例子不会有用:(。networkx 有解决方案吗？

pos (dictionary, optional) – A dictionary with nodes as keys and positions as values. If not specified a spring layout positioning will be computed. See networkx.layout for functions that compute node positions.

我在networkx 中没有看到任何关于如何实现这一点的教程，这就是为什么我相信这个问题将成为社区的可靠资源。我已经广泛地浏览了networkx tutorials，但那里没有这样的东西。如果不仔细使用 pos 参数，networkx 的布局将使这种类型的网络无法解释......我相信这是我唯一的选择。 https://networkx.github.io/documentation/networkx-1.9/reference/drawing.html 文档中的预计算布局似乎都不能很好地处理这种类型的网络结构。

简单示例：

(A) 每个外键是图中从左向右移动的迭代（例如，迭代 0 表示样本，迭代 1 具有组 1-3，与迭代 2 相同，迭代 3 具有组 1-2，等等.)。 (B) 内部字典包含该特定迭代中的当前分组，以及表示当前组的先前组合并的权重（例如，iteration 3 具有 Group 1 和 Group 2 以及 iteration 4 的所有 @987654346 @Group 2 已进入 iteration 4's Group 2 但 iteration 3's Group 1 已拆分。权重总和为 1。

我的连接代码与上图的权重：

D_iter_current_previous =    {
        1: {
            "Group 1":{"sample_0":0.5, "sample_1":0.5, "sample_2":0, "sample_3":0, "sample_4":0},
            "Group 2":{"sample_0":0, "sample_1":0, "sample_2":1, "sample_3":0, "sample_4":0},
            "Group 3":{"sample_0":0, "sample_1":0, "sample_2":0, "sample_3":0.5, "sample_4":0.5}
            },
        2: {
            "Group 1":{"Group 1":1, "Group 2":0, "Group 3":0},
            "Group 2":{"Group 1":0, "Group 2":1, "Group 3":0},
            "Group 3":{"Group 1":0, "Group 2":0, "Group 3":1}
            },
        3: {
            "Group 1":{"Group 1":0.25, "Group 2":0, "Group 3":0.75},
            "Group 2":{"Group 1":0.25, "Group 2":0.75, "Group 3":0}
            },
        4: {
            "Group 1":{"Group 1":1, "Group 2":0},
            "Group 2":{"Group 1":0.25, "Group 2":0.75}
            }
        }

这是我在networkx制作图表时发生的事情：

import networkx
import matplotlib.pyplot as plt

# Create Directed Graph
G = nx.DiGraph()

# Iterate through all connections
for iter_n, D_current_previous in D_iter_current_previous.items():
    for current_group, D_previous_weights in D_current_previous.items():
        for previous_group, weight in D_previous_weights.items():
            if weight > 0:
                # Define connections using `|__|` as a delimiter for the names
                previous_node = "%d|__|%s"%(iter_n - 1, previous_group)
                current_node = "%d|__|%s"%(iter_n, current_group)
                connection = (previous_node, current_node)
                G.add_edge(*connection, weight=weight)

# Draw Graph with labels and width thickness
nx.draw(G, with_labels=True, width=[G[u][v]['weight'] for u,v in G.edges()])

注意：我能想到的唯一其他方法是在matplotlib 创建一个散点图，每个刻度代表一次迭代（5 个包括初始样本），然后用不同的权重将这些点相互连接.这将是一些非常混乱的代码，特别是试图将标记的边缘与连接对齐......但是，我不确定这和 networkx 是否是最好的方法或者是否有一个工具（例如bokeh 或plotly）专为此类绘图而设计。

Answer 1

Networkx 为探索性数据提供了不错的绘图工具 分析，它不是制作出版质量数据的工具， 由于各种原因，我不想进入这里。我因此 从头开始重写了代码库的那部分，并制作了一个 可以找到名为 netgraph 的独立绘图模块 here （就像纯粹基于 matplotlib 的原版一样）。 API 是 非常非常相似并且有据可查，所以不应该太 很难根据您的目的进行塑造。

在此基础上，我得到以下结果：

我尽可能选择颜色来表示边缘强度
1) 表示负值，并且
2) 更好地区分小值。
但是，您也可以将边缘宽度传递给 netgraph（请参阅netgraph.draw_edges()）。

分支的不同顺序是您的数据结构（字典）的结果，这表明没有固有的顺序。你必须修改你的数据结构和下面的函数_parse_input() 来解决这个问题。

代码：

import itertools
import numpy as np
import matplotlib.pyplot as plt
import netgraph; reload(netgraph)

def plot_layered_network(weight_matrices,
                         distance_between_layers=2,
                         distance_between_nodes=1,
                         layer_labels=None,
                         **kwargs):
    """
    Convenience function to plot layered network.

    Arguments:
    ----------
        weight_matrices: [w1, w2, ..., wn]
            list of weight matrices defining the connectivity between layers;
            each weight matrix is a 2-D ndarray with rows indexing source and columns indexing targets;
            the number of sources has to match the number of targets in the last layer

        distance_between_layers: int

        distance_between_nodes: int

        layer_labels: [str1, str2, ..., strn+1]
            labels of layers

        **kwargs: passed to netgraph.draw()

    Returns:
    --------
        ax: matplotlib axis instance

    """
    nodes_per_layer = _get_nodes_per_layer(weight_matrices)

    node_positions = _get_node_positions(nodes_per_layer,
                                         distance_between_layers,
                                         distance_between_nodes)

    w = _combine_weight_matrices(weight_matrices, nodes_per_layer)

    ax = netgraph.draw(w, node_positions, **kwargs)

    if not layer_labels is None:
        ax.set_xticks(distance_between_layers*np.arange(len(weight_matrices)+1))
        ax.set_xticklabels(layer_labels)
        ax.xaxis.set_ticks_position('bottom')

    return ax

def _get_nodes_per_layer(weight_matrices):
    nodes_per_layer = []
    for w in weight_matrices:
        sources, targets = w.shape
        nodes_per_layer.append(sources)
    nodes_per_layer.append(targets)
    return nodes_per_layer

def _get_node_positions(nodes_per_layer,
                        distance_between_layers,
                        distance_between_nodes):
    x = []
    y = []
    for ii, n in enumerate(nodes_per_layer):
        x.append(distance_between_nodes * np.arange(0., n))
        y.append(ii * distance_between_layers * np.ones((n)))
    x = np.concatenate(x)
    y = np.concatenate(y)
    return np.c_[y,x]

def _combine_weight_matrices(weight_matrices, nodes_per_layer):
    total_nodes = np.sum(nodes_per_layer)
    w = np.full((total_nodes, total_nodes), np.nan, np.float)

    a = 0
    b = nodes_per_layer[0]
    for ii, ww in enumerate(weight_matrices):
        w[a:a+ww.shape[0], b:b+ww.shape[1]] = ww
        a += nodes_per_layer[ii]
        b += nodes_per_layer[ii+1]

    return w

def test():
    w1 = np.random.rand(4,5) #< 0.50
    w2 = np.random.rand(5,6) #< 0.25
    w3 = np.random.rand(6,3) #< 0.75

    import string
    node_labels = dict(zip(range(18), list(string.ascii_lowercase)))

    fig, ax = plt.subplots(1,1)
    plot_layered_network([w1,w2,w3],
                         layer_labels=['start', 'step 1', 'step 2', 'finish'],
                         ax=ax,
                         node_size=20,
                         node_edge_width=2,
                         node_labels=node_labels,
                         edge_width=5,
    )
    plt.show()
    return

def test_example(input_dict):
    weight_matrices, node_labels = _parse_input(input_dict)
    fig, ax = plt.subplots(1,1)
    plot_layered_network(weight_matrices,
                         layer_labels=['', '1', '2', '3', '4'],
                         distance_between_layers=10,
                         distance_between_nodes=8,
                         ax=ax,
                         node_size=300,
                         node_edge_width=10,
                         node_labels=node_labels,
                         edge_width=50,
    )
    plt.show()
    return

def _parse_input(input_dict):
    weight_matrices = []
    node_labels = []

    # initialise sources
    sources = set()
    for v in input_dict[1].values():
        for s in v.keys():
            sources.add(s)
    sources = list(sources)

    for ii in range(len(input_dict)):
        inner_dict = input_dict[ii+1]
        targets = inner_dict.keys()

        w = np.full((len(sources), len(targets)), np.nan, np.float)
        for ii, s in enumerate(sources):
            for jj, t in enumerate(targets):
                try:
                    w[ii,jj] = inner_dict[t][s]
                except KeyError:
                    pass

        weight_matrices.append(w)
        node_labels.append(sources)
        sources = targets

    node_labels.append(targets)
    node_labels = list(itertools.chain.from_iterable(node_labels))
    node_labels = dict(enumerate(node_labels))

    return weight_matrices, node_labels

# --------------------------------------------------------------------------------
# script
# --------------------------------------------------------------------------------

if __name__ == "__main__":

    # test()

    input_dict =   {
        1: {
            "Group 1":{"sample_0":0.5, "sample_1":0.5, "sample_2":0, "sample_3":0, "sample_4":0},
            "Group 2":{"sample_0":0, "sample_1":0, "sample_2":1, "sample_3":0, "sample_4":0},
            "Group 3":{"sample_0":0, "sample_1":0, "sample_2":0, "sample_3":0.5, "sample_4":0.5}
            },
        2: {
            "Group 1":{"Group 1":1, "Group 2":0, "Group 3":0},
            "Group 2":{"Group 1":0, "Group 2":1, "Group 3":0},
            "Group 3":{"Group 1":0, "Group 2":0, "Group 3":1}
            },
        3: {
            "Group 1":{"Group 1":0.25, "Group 2":0, "Group 3":0.75},
            "Group 2":{"Group 1":0.25, "Group 2":0.75, "Group 3":0}
            },
        4: {
            "Group 1":{"Group 1":1, "Group 2":0},
            "Group 2":{"Group 1":0.25, "Group 2":0.75}
            }
        }

    test_example(input_dict)

    pass