pagerank.py

# Copyright (C) 2011 by Peter Goodman
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.


def page_rank(links, num_iterations=20, initial_pr=1.0):
    from collections import defaultdict
    import numpy as np

    page_rank = defaultdict(lambda: float(initial_pr))
    num_outgoing_links = defaultdict(float)
    incoming_link_sets = defaultdict(set)
    incoming_links = defaultdict(lambda: np.array([]))
    damping_factor = 0.85

    # collect the number of outbound links and the set of all incoming documents
    # for every document
    for (from_id, to_id) in links:
        num_outgoing_links[int(from_id)] += 1.0
        incoming_link_sets[to_id].add(int(from_id))

    # convert each set of incoming links into a numpy array
    for doc_id in incoming_link_sets:
        incoming_links[doc_id] = np.array([from_doc_id for from_doc_id in incoming_link_sets[doc_id]])

    num_documents = float(len(num_outgoing_links))
    lead = (1.0 - damping_factor) / num_documents
    partial_PR = np.vectorize(lambda doc_id: page_rank[doc_id] / num_outgoing_links[doc_id])

    for _ in range(num_iterations):
        for doc_id in num_outgoing_links:
            tail = 0.0
            if len(incoming_links[doc_id]):
                tail = damping_factor * partial_PR(incoming_links[doc_id]).sum()
            page_rank[doc_id] = lead + tail

    return page_rank


if __name__ == "__main__":
    print
    page_rank([(1, 2), (2, 4), (4, 3)])
    print
    page_rank([(1, 2), (2, 4), (4, 3), (3, 1), (3, 2)])