Networkx: Differences between pagerank, pagerank_numpy, and pagerank_scipy?
networkx, numpy, pagerank, python, scipy
Solution
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
Problem
Does anyone know about the differences in accuracy between the three different pagerank functions in Networkx? I have a graph of 1000 nodes and 139732 edges, and the "plain" `pagerank` function didn't seem to work at all -- all but two of the nodes had the same PG, so I'm assuming this function doesn't work quite as well for large graphs? `pagerank_numpy`'s values also seemed to be a little bit more spread out than `pagerank_scipy`'s values. The documentation for this function says that "This will be the fastest and most accurate for small graphs." What is meant by "small" graphs? Also, why doesn't pagerank_numpy allow for `max_iter` and `tol` arguments?