Multi-layer Graph In Networkx

I want to create a multi-layered graph (like in the attached image), by connecting the two graphs written with the following code, using networkx #Graph１ g1 = nx.read_edgelist('s

Solution 1:

There is no functionality within networkx that currently supports a layered layout, much less a visualization as shown. So we need to roll our own.

The following implementation LayeredNetworkGraph assumes that you have a list of graphs [g1, g2, ..., gn] that represent the different layers. Within a layer, the corresponding (sub-) graph defines the connectivity. Between layers, nodes in subsequent layers are connected if they have the same node ID.

As there are no layout functions (AFAIK) that would compute node positions in three dimensions with the planarity constraint imposed on nodes within a layer, we use a small hack: we create a graph composition across all layers, compute the positions in two dimensions, and then apply these positions to nodes in all layers. One could compute a true force directed layout with the planarity constraints, but that would be a lot of work and since your example only used a shell layout (which would be unaffected), I haven't bothered. The differences would be small in many cases.

If you want to change aspects of the visualisation (sizes, widths, colours), have a look at the draw method. Most changes that you might require can probably be made there.

#!/usr/bin/env python"""
Plot multi-graphs in 3D.
"""import numpy as np
import matplotlib.pyplot as plt
import networkx as nx

from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Line3DCollection


classLayeredNetworkGraph(object):

    def__init__(self, graphs, node_labels=None, layout=nx.spring_layout, ax=None):
        """Given an ordered list of graphs [g1, g2, ..., gn] that represent
        different layers in a multi-layer network, plot the network in
        3D with the different layers separated along the z-axis.

        Within a layer, the corresponding graph defines the connectivity.
        Between layers, nodes in subsequent layers are connected if
        they have the same node ID.

        Arguments:
        ----------
        graphs : list of networkx.Graph objects
            List of graphs, one for each layer.

        node_labels : dict node ID : str label or None (default None)
            Dictionary mapping nodes to labels.
            If None is provided, nodes are not labelled.

        layout_func : function handle (default networkx.spring_layout)
            Function used to compute the layout.

        ax : mpl_toolkits.mplot3d.Axes3d instance or None (default None)
            The axis to plot to. If None is given, a new figure and a new axis are created.

        """# book-keeping
        self.graphs = graphs
        self.total_layers = len(graphs)

        self.node_labels = node_labels
        self.layout = layout

        if ax:
            self.ax = ax
        else:
            fig = plt.figure()
            self.ax = fig.add_subplot(111, projection='3d')

        # create internal representation of nodes and edges
        self.get_nodes()
        self.get_edges_within_layers()
        self.get_edges_between_layers()

        # compute layout and plot
        self.get_node_positions()
        self.draw()


    defget_nodes(self):
        """Construct an internal representation of nodes with the format (node ID, layer)."""
        self.nodes = []
        for z, g inenumerate(self.graphs):
            self.nodes.extend([(node, z) for node in g.nodes()])


    defget_edges_within_layers(self):
        """Remap edges in the individual layers to the internal representations of the node IDs."""
        self.edges_within_layers = []
        for z, g inenumerate(self.graphs):
            self.edges_within_layers.extend([((source, z), (target, z)) for source, target in g.edges()])


    defget_edges_between_layers(self):
        """Determine edges between layers. Nodes in subsequent layers are
        thought to be connected if they have the same ID."""
        self.edges_between_layers = []
        for z1, g inenumerate(self.graphs[:-1]):
            z2 = z1 + 1
            h = self.graphs[z2]
            shared_nodes = set(g.nodes()) & set(h.nodes())
            self.edges_between_layers.extend([((node, z1), (node, z2)) for node in shared_nodes])


    defget_node_positions(self, *args, **kwargs):
        """Get the node positions in the layered layout."""# What we would like to do, is apply the layout function to a combined, layered network.# However, networkx layout functions are not implemented for the multi-dimensional case.# Futhermore, even if there was such a layout function, there probably would be no straightforward way to# specify the planarity requirement for nodes within a layer.# Therefor, we compute the layout for the full network in 2D, and then apply the# positions to the nodes in all planes.# For a force-directed layout, this will approximately do the right thing.# TODO: implement FR in 3D with layer constraints.

        composition = self.graphs[0]
        for h in self.graphs[1:]:
            composition = nx.compose(composition, h)

        pos = self.layout(composition, *args, **kwargs)

        self.node_positions = dict()
        for z, g inenumerate(self.graphs):
            self.node_positions.update({(node, z) : (*pos[node], z) for node in g.nodes()})


    defdraw_nodes(self, nodes, *args, **kwargs):
        x, y, z = zip(*[self.node_positions[node] for node in nodes])
        self.ax.scatter(x, y, z, *args, **kwargs)


    defdraw_edges(self, edges, *args, **kwargs):
        segments = [(self.node_positions[source], self.node_positions[target]) for source, target in edges]
        line_collection = Line3DCollection(segments, *args, **kwargs)
        self.ax.add_collection3d(line_collection)


    defget_extent(self, pad=0.1):
        xyz = np.array(list(self.node_positions.values()))
        xmin, ymin, _ = np.min(xyz, axis=0)
        xmax, ymax, _ = np.max(xyz, axis=0)
        dx = xmax - xmin
        dy = ymax - ymin
        return (xmin - pad * dx, xmax + pad * dx), \
            (ymin - pad * dy, ymax + pad * dy)


    defdraw_plane(self, z, *args, **kwargs):
        (xmin, xmax), (ymin, ymax) = self.get_extent(pad=0.1)
        u = np.linspace(xmin, xmax, 10)
        v = np.linspace(ymin, ymax, 10)
        U, V = np.meshgrid(u ,v)
        W = z * np.ones_like(U)
        self.ax.plot_surface(U, V, W, *args, **kwargs)


    defdraw_node_labels(self, node_labels, *args, **kwargs):
        for node, z in self.nodes:
            if node in node_labels:
                ax.text(*self.node_positions[(node, z)], node_labels[node], *args, **kwargs)


    defdraw(self):

        self.draw_edges(self.edges_within_layers,  color='k', alpha=0.3, linestyle='-', zorder=2)
        self.draw_edges(self.edges_between_layers, color='k', alpha=0.3, linestyle='--', zorder=2)

        for z inrange(self.total_layers):
            self.draw_plane(z, alpha=0.2, zorder=1)
            self.draw_nodes([node for node in self.nodes if node[1]==z], s=300, zorder=3)

        if self.node_labels:
            self.draw_node_labels(self.node_labels,
                                  horizontalalignment='center',
                                  verticalalignment='center',
                                  zorder=100)


if __name__ == '__main__':

    # define graphs
    n = 5
    g = nx.erdos_renyi_graph(4*n, p=0.1)
    h = nx.erdos_renyi_graph(3*n, p=0.2)
    i = nx.erdos_renyi_graph(2*n, p=0.4)

    node_labels = {nn : str(nn) for nn inrange(4*n)}

    # initialise figure and plot
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    LayeredNetworkGraph([g, h, i], node_labels=node_labels, ax=ax, layout=nx.spring_layout)
    ax.set_axis_off()
    plt.show()