Each of the three functions uses a different approach to solving the same problem:
networkx.pagerank()
is a pure-Python implementation of the power-method to compute the largest eigenvalue/eigenvector or the Google matrix. It has two parameters that control the accuracy - tol
and max_iter
.
networkx.pagerank_scipy()
is a SciPy sparse-matrix implementation of the power-method. It has the same two accuracy parameters.
networkx.pagerank_numpy()
is a NumPy (full) matrix implementation that calls the numpy.linalg.eig()
function to compute the largest eigenvalue and eigenvector. That function is an interface to the LAPACK dgeev function which is uses a matrix decomposition (direct) method with no tunable parameters.
All three should produce the same answer (within numerical roundoff) for well-behaved graphs if the tol
parameter is small enough and the max_iter
parameter is large enough. Which one is faster depends on the size of your graph and how well the power method works on your graph.
In [12]: import networkx as nx
In [13]: G=nx.gnp_random_graph(1000,0.01,directed=True)
In [14]: %timeit nx.pagerank(G,tol=1e-10)
10 loops, best of 3: 157 ms per loop
In [15]: %timeit nx.pagerank_scipy(G,tol=1e-10)
100 loops, best of 3: 14 ms per loop
In [16]: %timeit nx.pagerank(G)
10 loops, best of 3: 137 ms per loop