A "square-plus-two" digraph

squareplus2graph.py

# This Python script generates a directed graph with
# vertex set V = {0, 1, 2, ..., m-1} and edge set
# E = {(n, f(n)) : n in V} where f(n) = n*n + c (mod m).
#
# Requires the python-igraph package (http://igraph.org/python/)
#
# Author: David Radcliffe (14 February 2014)
# Based on an idea of James Tanton
# https://twitter.com/jamestanton/status/549558473868849152
#
# Output: https://pbs.twimg.com/media/B91mPp_CEAAYscj.png

m = 1000
c = 2

from igraph import *

g = Graph(directed=True)
g.add_vertices(m)
for n in xrange(m):
    g.add_edge(n, (n*n+c) % m)
plot(g, vertex_size=4, edge_arrow_width=0.5)