Function pagerank 

pub fn pagerank(
    graph: &SqliteGraph,
    damping: f64,
    iterations: usize,
) -> Result<Vec<(i64, f64)>, SqliteGraphError>

Computes PageRank scores for all nodes in the graph.

PageRank measures node importance based on link structure. Nodes with many incoming links from important nodes receive higher scores. Originally developed by Google for ranking web pages.

Arguments

• graph - The graph to analyze
• damping - Damping factor (typically 0.85), representing probability of continuing random walk
• iterations - Number of power iteration iterations (20-50 recommended, fixed not convergence-based)

Returns

Vector of (node_id, score) tuples sorted by score descending. Scores sum to approximately 1.0.

Complexity

Time: O(k * |E|) where k = iterations Space: O(|V|) for score storage

Algorithm Details

Uses power iteration method (fixed iteration count for determinism):

1. Initialize all nodes with equal score (1.0 / node_count)
2. For each iteration:
   • new_score = (1-d)/n + d * sum(incoming_scores / outgoing_count)
   • Handle dangling nodes (no outgoing edges) by redistributing their score equally
3. Sort results by score descending

References

• Page, L., Brin, S., Motwani, R., & Winograd, T. (1999). “The PageRank Citation Ranking: Bringing Order to the Web.”

Example

use sqlitegraph::{SqliteGraph, algo::pagerank};
let graph = SqliteGraph::open_in_memory()?;
// ... add nodes and edges ...
let scores = pagerank(&graph, 0.85, 20)?;