label nodes outside with minimum overlap with other nodes/edges in networkx

Question

I am trying to create a graph with node labels printed outside of nodes. I am able to generate 'offset' as shown below that solve the purpose. However, Sometimes the labels overlaps with edges (Which is undesirable as there are lots of empty spaces around nodes where the corresponding labels can be printed). I need to label these nodes in such a way that the labels does not overlap any edge or at least try to minimize overlap as much as possible.

import networkx as nx
from networkx.utils import is_list_of_ints, flatten
import matplotlib.pyplot as plt

G=nx.Graph()

G = nx.complete_graph(5)
mapping = {0:'aaaaaaa',1:'bbbbbbb',2:'ccccccc', 3:'dddddddd', 4:'eeeeeeeee'}
G = nx.relabel_nodes(G,mapping)

plt.figure(figsize=(10,10), facecolor="w", frameon=False)
pos = nx.graphviz_layout(G, prog="fdp") #calculate position (x,y) coordinates
nx.draw_networkx_nodes(G,pos,node_size=1200,node_shape='o',node_color='0.75')
nx.draw_networkx_edges(G,pos, width=2,edge_color='b')


#for labeling outside the node
offset =10
pos_labels = {}
keys = pos.keys()
for key in keys:
    x, y = pos[key]
    pos_labels[key] = (x, y+offset)
nx.draw_networkx_labels(G,pos=pos_labels,fontsize=2)
plt.show()

Is there any function in networkx that can deal with such situation. I googled for long with no success.

Answer 1

I have previously attempted something similar with the main idea being to keep out of the way of the edges mostly.

Assuming that the edges are straight lines, there are two simple and similar ways to achieve this:

1. On the basis of the angles that the edges of a node's neighbourhood are making with respect to the node itself.

2. On the basis of the centroid of the neighbourhood's nodes.

So, find the angles that the edges departing from a node towards its neighbourhood form and try to position the label AWAY from the majority of the edges; OR estimate the centroid of a node's neighbourhood and position the label along the opposite direction.

The first solution can be a little bit problematic, primarily because of the way that the atan2 function operates (which essentially determines the edge angles) but it does provide some flexibility in terms of positioning the label.

The second solution is the simplest and works as follows:

import networkx as nx
import matplotlib.pyplot as plt

#Build the graph
#Please note, the code here is as per the original post
G=nx.Graph()
G = nx.complete_graph(5)
mapping = {0:'aaaaaaa',1:'bbbbbbb',2:'ccccccc', 3:'dddddddd', 4:'eeeeeeeee'}
G = nx.relabel_nodes(G,mapping)

plt.figure(figsize=(10,10), facecolor="w", frameon=False)
#Get a graph layout
pos = nx.graphviz_layout(G, prog="fdp") #calculate position (x,y) coordinates
#Here is an alternative layout, please see below.
#pos = nx.layout.spring_layout(G)
nx.draw_networkx_nodes(G,pos,node_size=1200,node_shape='^',node_color='0.75')
nx.draw_networkx_edges(G,pos, width=2,edge_color='r')
#Show the original position of the labels using a Green colour.
nx.draw_networkx_labels(G,pos,font_color='g')

#Please note, the code below uses the original idea of re-calculating a dictionary of adjusted label positions per node.
label_ratio = 1.0/8.0
pos_labels = {} 
#For each node in the Graph
for aNode in G.nodes():
    #Get the node's position from the layout
    x,y = pos[aNode]
    #Get the node's neighbourhood
    N = G[aNode]
    #Find the centroid of the neighbourhood. The centroid is the average of the Neighbourhood's node's x and y coordinates respectively.
    #Please note: This could be optimised further
    cx = sum(map(lambda x:pos[x][0], N)) / len(pos)
    cy = sum(map(lambda x:pos[x][1], N)) / len(pos)
    #Get the centroid's 'direction' or 'slope'. That is, the direction TOWARDS the centroid FROM aNode.
    slopeY = (y-cy)
    slopeX = (x-cx)
    #Position the label at some distance along this line. Here, the label is positioned at about 1/8th of the distance.
    pos_labels[aNode] = (x+slopeX*label_ratio, y+slopeY*label_ratio)

#Finally, redraw the labels at their new position.
nx.draw_networkx_labels(G,pos=pos_labels,fontsize=2)
#Show the figure
plt.show()

This works, mostly, for nodes that are largely in the periphery of the Graph but is challenging for nodes that are positioned towards the centre of the graph because the centroid will not provide a reliable direction that avoids the majority of the edges.

Here is the output for graphviz's fdp layout...

...and here is the output for networkx' spring layout.

Please note the proximity of the green and black coloured labels on the second figure. Essentially, the centroid of ddddddd's neighbourhood is relatively close to the node's actual position.

For a more complex solution, you might want to check more complex algorithms such as the one that is used by Wordle in order to adapt the initial position of the label if it intersects an edge.

Hope this helps.