graphrs 0.12.0

graphrs is a Rust package for the creation, manipulation and analysis of graphs.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142

use crate::{Error, ErrorKind, Graph};
use rayon::prelude::*;
use std::collections::HashMap;
use std::fmt::Display;
use std::hash::Hash;

/**
Compute PageRank centrality for nodes.

PageRank models a random walk over the graph. At each step, the walker follows
an outgoing edge with probability `alpha`, or teleports to a uniformly chosen
node with probability `1 - alpha`. Nodes without outgoing edges distribute
their rank uniformly across all nodes.

When `weighted` is `true`, outgoing edge weights are used as transition
weights. Unweighted edges contribute a weight of `1.0`. Multiple edges
contribute independently to the transition weight.

# Arguments

* `graph`: a [Graph](../../../struct.Graph.html) instance
* `weighted`: set to `true` to use edge weights
* `alpha`: damping factor; use `None` for the default value of `0.85`
* `max_iter`: maximum number of power iterations; use `None` for `100`
* `tolerance`: convergence tolerance; use `None` for `1.0e-6`

The computation uses Rayon automatically for graphs with more than 20 nodes
when more than one Rayon thread is available.
*/
pub fn pagerank<T, A>(
    graph: &Graph<T, A>,
    weighted: bool,
    alpha: Option<f64>,
    max_iter: Option<u32>,
    tolerance: Option<f64>,
) -> Result<HashMap<T, f64>, Error>
where
    T: Hash + Eq + Clone + Ord + Display + Send + Sync,
    A: Clone + Send + Sync,
{
    let alpha = alpha.unwrap_or(0.85);
    let max_iter = max_iter.unwrap_or(100);
    let tolerance = tolerance.unwrap_or(1.0e-6);
    if !(0.0 < alpha && alpha < 1.0) || max_iter == 0 || !(tolerance > 0.0 && tolerance.is_finite())
    {
        return Err(Error {
			kind: ErrorKind::InvalidArgument,
			message: "alpha must be between 0 and 1, max_iter must be greater than 0, and tolerance must be greater than 0.".to_string(),
		});
    }

    let nodes = graph.get_all_nodes();
    let node_count = nodes.len();
    if node_count == 0 {
        return Ok(HashMap::new());
    }

    let mut outgoing_sums = Vec::with_capacity(node_count);
    for source in 0..node_count {
        let edges = graph.get_successor_nodes_by_index(&source);
        if weighted
            && edges.iter().any(|edge| {
                !edge.weight.is_nan() && (!edge.weight.is_finite() || edge.weight < 0.0)
            })
        {
            return Err(Error {
                kind: ErrorKind::InvalidArgument,
                message: "PageRank weights must be finite and non-negative.".to_string(),
            });
        }
        outgoing_sums.push(
            edges
                .iter()
                .map(|edge| edge_weight(edge.weight, weighted))
                .sum::<f64>(),
        );
    }

    let teleport = (1.0 - alpha) / node_count as f64;
    let mut ranks = vec![1.0 / node_count as f64; node_count];
    let parallel = node_count > 20 && rayon::current_num_threads() > 1;

    for _ in 0..max_iter {
        let dangling_rank: f64 = ranks
            .iter()
            .enumerate()
            .filter(|(index, _)| outgoing_sums[*index] == 0.0)
            .map(|(_, rank)| rank)
            .sum();
        let dangling_share = alpha * dangling_rank / node_count as f64;

        let mut next = vec![0.0; node_count];
        let calculate = |(destination, score): (usize, &mut f64)| {
            let incoming = graph
                .get_predecessor_nodes_by_index(&destination)
                .iter()
                .map(|edge| {
                    let weight = edge_weight(edge.weight, weighted);
                    if outgoing_sums[edge.node_index] == 0.0 {
                        0.0
                    } else {
                        ranks[edge.node_index] * weight / outgoing_sums[edge.node_index]
                    }
                })
                .sum::<f64>();
            *score = teleport + dangling_share + alpha * incoming;
        };
        if parallel {
            next.par_iter_mut().enumerate().for_each(calculate);
        } else {
            next.iter_mut().enumerate().for_each(calculate);
        }

        let difference: f64 = next
            .iter()
            .zip(ranks.iter())
            .map(|(new, old)| (new - old).abs())
            .sum();
        ranks = next;
        if difference < node_count as f64 * tolerance {
            return Ok(nodes
                .iter()
                .enumerate()
                .map(|(index, node)| (node.name.clone(), ranks[index]))
                .collect());
        }
    }

    Err(Error {
		kind: ErrorKind::PowerIterationFailedConvergence,
		message: "failed to converge to the specified tolerance within the specified number of iterations.".to_string(),
	})
}

#[inline]
fn edge_weight(weight: f64, weighted: bool) -> f64 {
    if weighted && !weight.is_nan() {
        weight
    } else {
        1.0
    }
}