Massimo Nocentini

February 3, 2017: refactoring
September 15, 2016: promoted as tutorial, doc
September 14, 2016: refactoring, nodes zooming
September 13, 2016: loading and storing big graphs as JSON streams
September 9, 2016: asynchronous fetching, cleaning
September 8, 2016: synchronous fetching, drawing

Abstract
Drawing graphs according to cross-references among sequences in the OEIS.

The following cell import the function oeis_search in order to query the Online Encyclopedia of Integer Sequences and render search results directly in the current notebook; for details, see the tutorial.



In [1]:

    
import graphing, commons

on the other hand, for develop sessions:



In [2]:

    
%run ../src/graphing.py









    



usage: graphing.py [-h] [--directed] [--cache-dir CACHE_DIR]
                   [--graphs-dir GRAPHS_DIR] [--dpi DPI] [--layout LAYOUT]
                   F
graphing.py: error: the following arguments are required: F






    



An exception has occurred, use %tb to see the full traceback.

SystemExit: 2

finally, setup matplotlib plotting stuff:



In [3]:

    
%matplotlib inline



In [4]:

    
import networkx as nx
import matplotlib.pyplot as plt
from pylab import rcParams
rcParams['figure.figsize'] = 20, 20

Grapher

A link to the official documentation with many graph algorithms provided by networkx module: https://networkx.readthedocs.io/en/stable/reference/algorithms.html
A link to the drawing algorithm behind spring_layout: https://en.wikipedia.org/wiki/Force-directed_graph_drawing#cite_note-1



In [28]:

    
graph = graphing.graph_load(cache_dir='../src/fetched/')



In [29]:

    
G, nodes, edges = graphing.make_nx_graph(graph)#, node_remp=lambda n, G: G.out_degree(n) > 2)



In [20]:

    
G, nodes, edges = graphing.make_nx_graph(graph, node_remp=lambda n, G: 'nice' not in graph[n]['keyword'])



In [34]:

    
fibonacci_seq_id, catalan_seq_id = 'A000045', 'A000108'
graphing.draw_nx_graph(G, nodes_labels={'draw':True, fibonacci_seq_id:r'$\alpha$', catalan_seq_id:r'$\beta$'},
                       layout=lambda l: l.circular_layout)

Dominating set



In [32]:

    
dom_set = nx.dominating_set(G, start_with=fibonacci_seq_id)



In [37]:

    
graphing.draw_nx_graph(G, 
                       nodes_colors={n:'r' for n in dom_set},
                       nodes_labels={'draw':True, fibonacci_seq_id:r'$\alpha$', catalan_seq_id:r'$\beta$'},
                       layout=lambda l: l.circular_layout)



In [46]:

    
%%bash 
python3.6 ../src/crawling.py --cache-dir ../src/fetched/









    



419 sequences in cache ../src/fetched/
1716 sequences in fringe for restarting

`networkx` example

Taken from the official documentation.



In [3]:

    
G=nx.cubical_graph()
pos=nx.spring_layout(G) # positions for all nodes

# nodes
nx.draw_networkx_nodes(G,pos,
                       nodelist=[0,1,2,3],
                       node_color='r',
                       node_size=500,
                   alpha=0.8)
nx.draw_networkx_nodes(G,pos,
                       nodelist=[4,5,6,7],
                       node_color='b',
                       node_size=500,
                   alpha=0.8)

# edges
nx.draw_networkx_edges(G,pos,width=1.0,alpha=0.5)
nx.draw_networkx_edges(G,pos,
                       edgelist=[(0,1),(1,2),(2,3),(3,0)],
                       width=8,alpha=0.5,edge_color='r')
nx.draw_networkx_edges(G,pos,
                       edgelist=[(4,5),(5,6),(6,7),(7,4)],
                       width=8,alpha=0.5,edge_color='b')


# some math labels
labels={}
labels[0]=r'$a$'
labels[1]=r'$b$'
labels[2]=r'$c$'
labels[3]=r'$d$'
labels[4]=r'$\alpha$'
labels[5]=r'$\beta$'
labels[6]=r'$\gamma$'
labels[7]=r'$\delta$'
nx.draw_networkx_labels(G,pos,labels,font_size=16)

plt.axis('off')
plt.savefig("labels_and_colors.png") # save as png
plt.show() # display

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Grapher

Dominating set

networkx example

`networkx` example