networkx edge weights not mapping to arrow width properly?

Question

I'm trying to plot a graph using the following code:

import networkx as nx
import matplotlib.pyplot as plt


u = ['SAC', 'SAC', 'SAC', 'SAC', 'SAC', 'SAC', 'SAC', 'REDES SOCIAIS', 'REDES SOCIAIS', 
     'REDES SOCIAIS', 'PROCON', 'PROCON', 'PROCON', 'BACEN', 'BACEN', 'BACEN', 'BACEN',
     'OUVIDORIA', 'OUVIDORIA', 'OUVIDORIA', 'OUVIDORIA', 'OUVIDORIA', 'CHAT', 'CHAT', 
     'CHAT']
v = ['RECLAME AQUI', 'SAC', 'REDES SOCIAIS', 'PROCON', 'BACEN', 'OUVIDORIA', 'CHAT', 
     'RECLAME AQUI', 'SAC', 'REDES SOCIAIS', 'RECLAME AQUI', 'SAC', 'PROCON',
     'RECLAME AQUI', 'SAC', 'BACEN', 'OUVIDORIA', 'RECLAME AQUI', 'SAC', 
     'REDES SOCIAIS', 'BACEN', 'OUVIDORIA', 'RECLAME AQUI', 'SAC', 'REDES SOCIAIS']
w = [437, 207, 13, 1, 7, 13, 2, 70, 10, 12, 5, 
     1, 2, 23, 1, 4, 2, 16, 2, 2, 2, 4, 4, 1, 1]

G = nx.DiGraph()
for ui, vi, wi in zip(u, v, w):
    G.add_edges_from([(ui, vi)], weight=wi)
pos = nx.circular_layout(G)
edge_labels = dict([((u, v,), d['weight']) for u, v, d in G.edges(data=True)])
weights = [G[u][v]['weight'] for u, v in G.edges()]
weights = list(map(lambda x: (x - min(weights)) /
                   (max(weights) - min(weights)), weights))
weights = list(map(lambda x: (x * 4) + 1, weights))
i = 0
for u, v in G.edges():
    print(u, v, G[u][v]['weight'], weights[i])
    i += 1

fig = plt.figure(figsize=(25, 15))
plt.axis('off')
nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels)
nx.draw_networkx_nodes(G, pos,
                       nodelist=G.nodes(),
                       node_color='r',
                       node_size=500)
nx.draw_networkx_edges(G, pos,
                       edgelist=G.edges(),
                       alpha=0.5, edge_color='#5cce40', width=weights)
nx.draw_networkx_labels(G, pos, font_size=16, font_color='white')

fig.set_facecolor("#262626")
plt.show()

It creates a dictionary of edges from a pandas data frame, but the important part start when I declare G = nx.DiGraph(). At this point I have all my weighted edges and I normalize them between [1, 5].

The print statement gives me this:

SAC RECLAME AQUI 437 5.0
SAC SAC 207 2.8899082568807337
SAC REDES SOCIAIS 13 1.110091743119266
SAC PROCON 1 1.0
SAC BACEN 7 1.0550458715596331
SAC OUVIDORIA 13 1.110091743119266
SAC CHAT 2 1.0091743119266054
REDES SOCIAIS RECLAME AQUI 70 1.6330275229357798
REDES SOCIAIS SAC 10 1.0825688073394495
REDES SOCIAIS REDES SOCIAIS 12 1.1009174311926606
PROCON RECLAME AQUI 5 1.036697247706422
PROCON SAC 1 1.0
PROCON PROCON 2 1.0091743119266054
BACEN RECLAME AQUI 23 1.2018348623853212
BACEN SAC 1 1.0
BACEN BACEN 4 1.0275229357798166
BACEN OUVIDORIA 2 1.0091743119266054
OUVIDORIA RECLAME AQUI 16 1.1376146788990826
OUVIDORIA SAC 2 1.0091743119266054
OUVIDORIA REDES SOCIAIS 2 1.0091743119266054
OUVIDORIA BACEN 2 1.0091743119266054
OUVIDORIA OUVIDORIA 4 1.0275229357798166
CHAT RECLAME AQUI 4 1.0275229357798166
CHAT SAC 1 1.0
CHAT REDES SOCIAIS 1 1.0

I.e,

• SAC -> RECLAME AQUI has the possible highest weight of 5.0
• The following high weighted edge (not self looped, which I didn't find how to draw) is REDES SOCIAIS -> RECLAME AQUI with 1.6330275229357798.

However, this is my plot:

As can be seen, the edge with the second highest width is SAC -> REDES SOCIAIS, while REDES SOCIAIS -> RECLAME AQUI, with an original weight of 70, is presented thinner than the the first. I can't understand why. The print shows that my mapping is correct. Am I passing the wrong arguments to some function?

Answer 1

nx.draw_networkx_edges does not draw arrows for self-loops. So when the DiGraph contains self-loops, the weights passed to nx.draw_networkx_edges must skip the self-loop weights. Otherwise, the weights get out of sync with the edges drawn.

Thus, if you change

weights = [G[u][v]['weight'] for u, v in G.edges()]

to

weights = [G[u][v]['weight'] for u, v in G.edges() if u != v]

then

import networkx as nx
import matplotlib.pyplot as plt


u = ['SAC', 'SAC', 'SAC', 'SAC', 'SAC', 'SAC', 'SAC', 'REDES SOCIAIS', 'REDES SOCIAIS', 
     'REDES SOCIAIS', 'PROCON', 'PROCON', 'PROCON', 'BACEN', 'BACEN', 'BACEN', 'BACEN',
     'OUVIDORIA', 'OUVIDORIA', 'OUVIDORIA', 'OUVIDORIA', 'OUVIDORIA', 'CHAT', 'CHAT', 
     'CHAT']
v = ['RECLAME AQUI', 'SAC', 'REDES SOCIAIS', 'PROCON', 'BACEN', 'OUVIDORIA', 'CHAT', 
     'RECLAME AQUI', 'SAC', 'REDES SOCIAIS', 'RECLAME AQUI', 'SAC', 'PROCON',
     'RECLAME AQUI', 'SAC', 'BACEN', 'OUVIDORIA', 'RECLAME AQUI', 'SAC', 
     'REDES SOCIAIS', 'BACEN', 'OUVIDORIA', 'RECLAME AQUI', 'SAC', 'REDES SOCIAIS']
w = [437, 207, 13, 1, 7, 13, 2, 70, 10, 12, 5, 
     1, 2, 23, 1, 4, 2, 16, 2, 2, 2, 4, 4, 1, 1]

G = nx.DiGraph()
for ui, vi, wi in zip(u, v, w):
    G.add_edges_from([(ui, vi)], weight=wi)
pos = nx.circular_layout(G)
edge_labels = dict([((u, v,), d['weight']) for u, v, d in G.edges(data=True)])
weights = [G[u][v]['weight'] for u, v in G.edges() if u != v]
weights = list(map(lambda x: (x - min(weights)) /
                   (max(weights) - min(weights)), weights))
weights = list(map(lambda x: (x * 4) + 1, weights))
i = 0
for u, v in G.edges():
    if u != v:
        print(u, v, G[u][v]['weight'], weights[i])
        i += 1

fig = plt.figure(figsize=(25, 15))
plt.axis('off')
nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels)
nx.draw_networkx_nodes(G, pos,
                       nodelist=G.nodes(),
                       node_color='r',
                       node_size=500)
nx.draw_networkx_edges(G, pos,
                       edgelist=G.edges(),
                       alpha=0.5, edge_color='#5cce40', width=weights)
nx.draw_networkx_labels(G, pos, font_size=16, font_color='white')

fig.set_facecolor("#262626")
plt.show()

yields

---

The shape and thickness of the arrows in a DiGraph are currently set by this code. To replace the rectangular "arrows" with pointy arrows requires replacing nx.draw_networkx_edges with a custom draw_networkx_edges_with_arrows function:

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

def draw_networkx_edges_with_arrows(G, pos,
                        edgelist=None,
                        width=1.0,
                        edge_color='k',
                        style='solid',
                        alpha=1.0,
                        edge_cmap=None,
                        edge_vmin=None,
                        edge_vmax=None,
                        ax=None,
                        arrows=True,
                        label=None,
                        arrow_width=1.0,
                        **kwds):
    """
    Most of this code comes from https://github.com/networkx/networkx/blob/master/networkx/drawing/nx_pylab.py#L575, except that the arrow LineCollection 
    has been replaced by mpatches.Arrows below.
    """
    try:
        import matplotlib
        import matplotlib.pyplot as plt
        import matplotlib.cbook as cb
        from matplotlib.colors import colorConverter, Colormap
        from matplotlib.collections import LineCollection
        import matplotlib.patches as mpatches
        import numpy
        import itertools as IT
    except ImportError:
        raise ImportError("Matplotlib required for draw()")
    except RuntimeError:
        print("Matplotlib unable to open display")
        raise

    if ax is None:
        ax = plt.gca()

    if edgelist is None:
        edgelist = G.edges()

    if not edgelist or len(edgelist) == 0:  # no edges!
        return None

    # set edge positions
    edge_pos = numpy.asarray([(pos[e[0]], pos[e[1]]) for e in edgelist])

    if not cb.iterable(width):
        lw = (width,)
    else:
        lw = width

    if not cb.is_string_like(edge_color) \
           and cb.iterable(edge_color) \
           and len(edge_color) == len(edge_pos):
        if numpy.alltrue([cb.is_string_like(c)
                         for c in edge_color]):
            # (should check ALL elements)
            # list of color letters such as ['k','r','k',...]
            edge_colors = tuple([colorConverter.to_rgba(c, alpha)
                                 for c in edge_color])
        elif numpy.alltrue([not cb.is_string_like(c)
                           for c in edge_color]):
            # If color specs are given as (rgb) or (rgba) tuples, we're OK
            if numpy.alltrue([cb.iterable(c) and len(c) in (3, 4)
                             for c in edge_color]):
                edge_colors = tuple(edge_color)
            else:
                # numbers (which are going to be mapped with a colormap)
                edge_colors = None
        else:
            raise ValueError('edge_color must consist of either color names or numbers')
    else:
        if cb.is_string_like(edge_color) or len(edge_color) == 1:
            edge_colors = (colorConverter.to_rgba(edge_color, alpha), )
        else:
            raise ValueError('edge_color must be a single color or list of exactly m colors where m is the number or edges')

    edge_collection = LineCollection(edge_pos,
                                     colors=edge_colors,
                                     linewidths=lw,
                                     antialiaseds=(1,),
                                     linestyle=style,
                                     transOffset = ax.transData,
                                     )

    edge_collection.set_zorder(1)  # edges go behind nodes
    edge_collection.set_label(label)
    ax.add_collection(edge_collection)

    # Note: there was a bug in mpl regarding the handling of alpha values for
    # each line in a LineCollection.  It was fixed in matplotlib in r7184 and
    # r7189 (June 6 2009).  We should then not set the alpha value globally,
    # since the user can instead provide per-edge alphas now.  Only set it
    # globally if provided as a scalar.
    if cb.is_numlike(alpha):
        edge_collection.set_alpha(alpha)

    if edge_colors is None:
        if edge_cmap is not None:
            assert(isinstance(edge_cmap, Colormap))
        edge_collection.set_array(numpy.asarray(edge_color))
        edge_collection.set_cmap(edge_cmap)
        if edge_vmin is not None or edge_vmax is not None:
            edge_collection.set_clim(edge_vmin, edge_vmax)
        else:
            edge_collection.autoscale()

    arrow_collection = None

    if G.is_directed() and arrows:

        # a directed graph hack
        # draw thick line segments at head end of edge
        # waiting for someone else to implement arrows that will work
        arrow_colors = edge_colors
        # a_pos = []
        p = 1.0-0.25  # make head segment 25 percent of edge length
        for (src, dst), lwi, color in zip(edge_pos, lw, IT.cycle(arrow_colors)):
            x1, y1 = src
            x2, y2 = dst
            dx = x2-x1   # x offset
            dy = y2-y1   # y offset
            d = numpy.sqrt(float(dx**2 + dy**2))  # length of edge
            if d == 0:   # source and target at same position
                continue
            if dx == 0:  # vertical edge
                xa = x2
                ya = dy*p+y1
            if dy == 0:  # horizontal edge
                ya = y2
                xa = dx*p+x1
            else:
                theta = numpy.arctan2(dy, dx)
                xa = p*d*numpy.cos(theta)+x1
                ya = p*d*numpy.sin(theta)+y1
            dx, dy = x2-xa, y2-ya
            patch = mpatches.Arrow(xa, ya, dx, dy, 
                                   width=arrow_width, 
                                   color=color,
                                   transform=ax.transData)
            ax.add_patch(patch)

    # update view
    minx = numpy.amin(numpy.ravel(edge_pos[:, :, 0]))
    maxx = numpy.amax(numpy.ravel(edge_pos[:, :, 0]))
    miny = numpy.amin(numpy.ravel(edge_pos[:, :, 1]))
    maxy = numpy.amax(numpy.ravel(edge_pos[:, :, 1]))

    w = maxx-minx
    h = maxy-miny
    padx,  pady = 0.05*w, 0.05*h
    corners = (minx-padx, miny-pady), (maxx+padx, maxy+pady)
    ax.update_datalim(corners)
    ax.autoscale_view()

    return edge_collection


u = ['SAC', 'SAC', 'SAC', 'SAC', 'SAC', 'SAC', 'SAC', 'REDES SOCIAIS', 'REDES SOCIAIS', 
     'REDES SOCIAIS', 'PROCON', 'PROCON', 'PROCON', 'BACEN', 'BACEN', 'BACEN', 'BACEN',
     'OUVIDORIA', 'OUVIDORIA', 'OUVIDORIA', 'OUVIDORIA', 'OUVIDORIA', 'CHAT', 'CHAT', 
     'CHAT']
v = ['RECLAME AQUI', 'SAC', 'REDES SOCIAIS', 'PROCON', 'BACEN', 'OUVIDORIA', 'CHAT', 
     'RECLAME AQUI', 'SAC', 'REDES SOCIAIS', 'RECLAME AQUI', 'SAC', 'PROCON',
     'RECLAME AQUI', 'SAC', 'BACEN', 'OUVIDORIA', 'RECLAME AQUI', 'SAC', 
     'REDES SOCIAIS', 'BACEN', 'OUVIDORIA', 'RECLAME AQUI', 'SAC', 'REDES SOCIAIS']
w = [437, 207, 13, 1, 7, 13, 2, 70, 10, 12, 5, 
     1, 2, 23, 1, 4, 2, 16, 2, 2, 2, 4, 4, 1, 1]

G = nx.DiGraph()
for ui, vi, wi in zip(u, v, w):
    G.add_edges_from([(ui, vi)], weight=wi)
pos = nx.circular_layout(G)
edge_labels = dict([((u, v,), d['weight']) for u, v, d in G.edges(data=True)])
weights = [G[u][v]['weight'] for u, v in G.edges()]
weights = np.log(weights)
weights = list(map(lambda x: (x - min(weights)) /
                   (max(weights) - min(weights)), weights))
weights = list(map(lambda x: (x * 10) + 1, weights))

fig = plt.figure(figsize=(25, 15))
plt.axis('off')
nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels)
nx.draw_networkx_nodes(G, pos,
                       nodelist=G.nodes(),
                       node_color='r',
                       node_size=500)
draw_networkx_edges_with_arrows(G, pos,
                       width=weights, arrow_width=0.05,
                       alpha=0.5, edge_color='#5cce40')
nx.draw_networkx_labels(G, pos, font_size=16, font_color='white')

fig.set_facecolor("#262626")
plt.savefig('/tmp/out.pdf', format='pdf', facecolor=fig.get_facecolor(), 
            bbox_inches='tight')

yields