python - 如何使用 `pos` 中的 `networkx` 参数创建流程图样式的 Graph？ ( python 3)

Question

我正在尝试使用 Python 创建一个线性网络图(最好使用 matplotlib 和 networkx 虽然会对 bokeh 感兴趣)在概念上与下面的相似。

如何使用 networkx 在 Python 中高效地构建此图表(pos？)？我想将其用于更复杂的示例所以我觉得对这个简单示例的位置进行硬编码不会有用 :( 。 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.

我还没有看到任何关于如何在 networkx 中实现这一点的教程，这就是为什么我相信这个问题将成为社区的可靠资源。我已经广泛浏览了 networkx tutorials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 上没有预先计算好的布局文档似乎很好地处理了这种类型的网络结构。

简单示例:

(A) 每个外键都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的当前分组，以及代表当前组的先前组合并的权重(例如，iteration 3 有 Group 1 和第 2 组 和迭代 4 所有迭代 3 第 2 组 已进入迭代 4 Group 2 但 iteration 3's Group 1 已拆分。权重之和始终为 1。

我的上图权重连接代码:

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 中制作图形时发生的情况:

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 中创建一个散点图，每个刻度代表一个迭代(5 个包括初始样本)，然后将这些点连接到彼此有不同的权重。这将是一些非常困惑的代码，尤其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如果有专为此类绘图设计的工具(例如 bokeh 或 plotly)。

Answer 1

Networkx 具有用于探索性数据的不错的绘图工具 分析，它不是制作出版质量数字的工具， 由于各种原因，我不想进入这里。我因此 从头开始重写了那部分代码库，并做了一个 可以找到名为 netgraph 的独立绘图模块 here (就像纯粹基于 matplotlib 的原始版本)。 API是 非常非常相似并且有据可查，所以不应该太 很难按照您的目的进行塑造。

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，您也可以将边宽传递给 netgraph(参见 netgraph.draw_edges())。

分支的不同顺序是您的数据结构(字典)的结果，这表明没有内在顺序。您必须修改数据结构和下面的函数 _parse_input() 才能解决该问题。

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