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