Function rustworkx_core::centrality::katz_centrality

source · 
pub fn katz_centrality<G, F, E>(
    graph: G,
    weight_fn: F,
    alpha: Option<f64>,
    beta_map: Option<HashMap<usize, f64>>,
    beta_scalar: Option<f64>,
    max_iter: Option<usize>,
    tol: Option<f64>
) -> Result<Option<Vec<f64>>, E>where
    G: NodeIndexable + IntoNodeIdentifiers + IntoNeighbors + IntoEdges + NodeCount,
    G::NodeId: Eq + Hash,
    F: FnMut(G::EdgeRef) -> Result<f64, E>,
Expand description

Compute the Katz centrality of a graph

For details on the Katz centrality refer to:

Leo Katz. “A New Status Index Derived from Sociometric Index.” Psychometrika 18(1):39–43, 1953 https://link.springer.com/content/pdf/10.1007/BF02289026.pdf

This function uses a power iteration method to compute the eigenvector and convergence is not guaranteed. The function will stop when max_iter iterations is reached or when the computed vector between two iterations is smaller than the error tolerance multiplied by the number of nodes. The implementation of this algorithm is based on the NetworkX katz_centrality() function.

In the case of multigraphs the weights of any parallel edges will be summed when computing the eigenvector centrality.

Arguments:

  • graph - The graph object to run the algorithm on
  • weight_fn - An input callable that will be passed the EdgeRef for an edge in the graph and is expected to return a Result<f64> of the weight of that edge.
  • alpha - Attenuation factor. If set to None, a default value of 0.1 is used.
  • beta_map - Immediate neighbourhood weights. Must contain all node indices or be None.
  • beta_scalar - Immediate neighbourhood scalar that replaces beta_map in case beta_map is None. Defaults to 1.0 in case None is provided.
  • max_iter - The maximum number of iterations in the power method. If set to None a default value of 100 is used.
  • tol - The error tolerance used when checking for convergence in the power method. If set to None a default value of 1e-6 is used.

Example

use rustworkx_core::Result;
use rustworkx_core::petgraph;
use rustworkx_core::petgraph::visit::{IntoEdges, IntoNodeIdentifiers};
use rustworkx_core::centrality::katz_centrality;

let g = petgraph::graph::UnGraph::<i32, ()>::from_edges(&[
    (0, 1), (1, 2)
]);
// Calculate the eigenvector centrality
let output: Result<Option<Vec<f64>>> = katz_centrality(&g, |_| {Ok(1.)}, None, None, None, None, None);
let centralities = output.unwrap().unwrap();
assert!(centralities[1] > centralities[0], "Node 1 is more central than node 0");
assert!(centralities[1] > centralities[2], "Node 1 is more central than node 2");