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fixed the documentation

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Luca Lombardo 2 years ago
parent 6024b9eb75
commit 560bf58612
1 changed files with 58 additions and 37 deletions
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src/algo.py
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@ -10,8 +10,6 @@ import numpy as np
import pandas as pd
import networkx as nx
from os.path import exists
from scipy.sparse import *
import plotly.graph_objs as go
from typing import Literal
def load_data(dataset: Literal["Stanford", "NotreDame", "BerkStan"]) -> nx.Graph:
@ -19,15 +17,28 @@ def load_data(dataset: Literal["Stanford", "NotreDame", "BerkStan"]) -> nx.Graph
Parameters
----------
dataset : Literal["Stanford", "BerkStan"]
dataset : Literal["Stanford", "BerkStan", "NotreDame"]
The dataset to load.
Returns
-------
nx.Graph
The graph of the dataset.
data/web-Stanford.txt
The graph of the dataset loaded.
Raises
------
ValueError
If the dataset is not valid.
Notes
-----
The datasets are downloaded from the following link:
http://snap.stanford.edu/data/web-NotreDame.html
http://snap.stanford.edu/data/web-Stanford.html
http://snap.stanford.edu/data/web-BerkStan.html
If the dataset is already downloaded, it is not downloaded again.
"""
# check if there is a data folder
@ -61,8 +72,7 @@ def load_data(dataset: Literal["Stanford", "NotreDame", "BerkStan"]) -> nx.Graph
def google_matrix(G, alpha=0.85, personalization=None, nodelist=None, weight="weight", dangling=None) -> np.matrix:
"""Returns the Google matrix of the graph.
"""Returns the Google matrix of the graph. NetworkX implementation.
Parameters
----------
@ -103,6 +113,8 @@ def google_matrix(G, alpha=0.85, personalization=None, nodelist=None, weight="we
Notes
-----
DO NOT USE THIS FUNCTION FOR LARGE GRAPHS. It's memory intensive.
The matrix returned represents the transition matrix that describes the
Markov chain used in PageRank. For PageRank to converge to a unique
solution (i.e., a unique stationary distribution in a Markov chain), the
@ -147,33 +159,32 @@ def google_matrix(G, alpha=0.85, personalization=None, nodelist=None, weight="we
def google_matrix_sparse(G, alpha=0.85, personalization=None, nodelist=None, weight="weight", dangling=None) -> np.matrix:
""" Revised NetworkX implementation for sparse matrices. Returns the Ptilde matrix of the graph instead of the Google matrix.
"""Returns the Google matrix of the graph.
Parameters
----------
G : graph
Parameters
----------
G : graph
A NetworkX graph. Undirected graphs will be converted to a directed
graph with two directed edges for each undirected edge.
alpha : float
alpha : float
The damping factor.
personalization: dict, optional
personalization: dict, optional
The "personalization vector" consisting of a dictionary with a
key some subset of graph nodes and personalization value each of those.
At least one personalization value must be non-zero.
If not specfiied, a nodes personalization value will be zero.
By default, a uniform distribution is used.
nodelist : list, optional
nodelist : list, optional
The rows and columns are ordered according to the nodes in nodelist.
If nodelist is None, then the ordering is produced by G.nodes().
weight : key, optional
weight : key, optional
Edge data key to use as weight. If None weights are set to 1.
dangling: dict, optional
dangling: dict, optional
The outedges to be assigned to any "dangling" nodes, i.e., nodes without
any outedges. The dict key is the node the outedge points to and the dict
value is the weight of that outedge. By default, dangling nodes are given
@ -182,19 +193,19 @@ def google_matrix_sparse(G, alpha=0.85, personalization=None, nodelist=None, wei
matrix (see notes below). It may be common to have the dangling dict to
be the same as the personalization dict.
Returns
-------
A : NumPy matrix
Google matrix of the graph
Returns
-------
A : NumPy matrix
Google matrix of the graph
Notes
-----
This matrix i strictly speaking not the Google matrix, but the Ptilde matrix, described in the paper [1]
Notes
-----
The matrix returned represents the transition matrix that describes the
Markov chain used in PageRank. For PageRank to converge to a unique
solution (i.e., a unique stationary distribution in a Markov chain), the
transition matrix must be irreducible. In other words, it must be that
there exists a path between every pair of nodes in the graph, or else there
is the potential of "rank sinks."
References
----------
[1] Zhao-Li Shen, Meng Su, Bruno Carpentieri, and Chun Wen. Shifted power-gmres method accelerated by extrapolation for solving pagerank with multiple damping factors. Applied Mathematics and Computation, 420:126799, 2022
"""
if nodelist is None:
@ -243,7 +254,7 @@ def google_matrix_sparse(G, alpha=0.85, personalization=None, nodelist=None, wei
return A, p
def pagerank_numpy(G, alpha=0.85, personalization=None, weight="weight", dangling=None):
"""Returns the PageRank of the nodes in the graph.
"""Returns the PageRank of the nodes in the graph. NetworkX implementation.
PageRank computes a ranking of the nodes in the graph G based on
the structure of the incoming links. It was originally designed as
@ -306,7 +317,7 @@ def pagerank_numpy(G, alpha=0.85, personalization=None, weight="weight", danglin
def pagerank(G, alpha=0.85, personalization=None, max_iter=10000, tol=1.0e-9, nstart=None, weight="weight", dangling=None,):
"""
Returns the PageRank of the nodes in the graph.
Returns the PageRank of the nodes in the graph. Slighly modified NetworkX implementation.
PageRank computes a ranking of the nodes in the graph G based on
the structure of the incoming links. It was originally designed as
@ -415,15 +426,16 @@ def pagerank(G, alpha=0.85, personalization=None, max_iter=10000, tol=1.0e-9, ns
if err < N * tol: # if the error is small enough, stop iterating
return dict(zip(nodelist, map(float, x))), iter, tol # return the current vector of PageRank values'
# other wise, return a Null dictionary, the number of iterations, and the tolerance
# this is a failure to convergeS
# this is a failure to converges
raise nx.PowerIterationFailedConvergence(max_iter)
return {}, iter, tol
def shifted_pow_pagerank(G, alphas=[0.85, 0.9, 0.95, 0.99], max_iter=10000, tol=1.0e-9):
"""
Compute the PageRank of each node in the graph G.
Compute the PageRank of each node in the graph G. Algorithm 1 in the paper [1].
Parameters
----------
@ -441,8 +453,8 @@ def shifted_pow_pagerank(G, alphas=[0.85, 0.9, 0.95, 0.99], max_iter=10000, tol=
Returns
-------
pagerank : dictionary
Dictionary of nodes with PageRank as value
pagerank : sparse matrix
Each column of the sparse matrix is a pagerank vector for a different alpha value.
mv : integer
The number of matrix-vector multiplications used in the power method
@ -451,6 +463,15 @@ def shifted_pow_pagerank(G, alphas=[0.85, 0.9, 0.95, 0.99], max_iter=10000, tol=
-----
The eigenvector calculation uses power iteration with a SciPy sparse matrix representation. The shifted power method is described as Algorithm 1 in the paper located in the sources folders.
Raises
------
PowerIterationFailedConvergence
If the algorithm fails to converge to the specified tolerance
References
----------
[1] Zhao-Li Shen, Meng Su, Bruno Carpentieri, and Chun Wen. Shifted power-gmres method accelerated by extrapolation for solving pagerank with multiple damping factors. Applied Mathematics and Computation, 420:126799, 2022
"""
N = len(G)

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