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Katz Centrality, Docs, Examples (#19)
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‎examples/centrality.rs

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//
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// -----------------------------
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// Degree Centrality
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// -----------------------------
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//
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fn degree_centrality_example() {
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use graphina::core::types::Graph;
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use graphina::centrality::algorithms::degree_centrality;
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let mut g: Graph<i32, ()> = Graph::new();
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let nodes = [g.add_node(1), g.add_node(2), g.add_node(3)];
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g.add_edge(nodes[0], nodes[1], ());
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g.add_edge(nodes[0], nodes[2], ());
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let centrality = degree_centrality(&g);
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println!("{:?}", centrality); // [2.0, 1.0, 1.0]
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}
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fn in_degree_centrality_example() {
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use graphina::core::types::Digraph;
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use graphina::centrality::algorithms::in_degree_centrality;
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let mut g: Digraph<i32, ()> = Digraph::new();
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let nodes = [g.add_node(1), g.add_node(2), g.add_node(3)];
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g.add_edge(nodes[0], nodes[1], ());
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g.add_edge(nodes[0], nodes[2], ());
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let centrality = in_degree_centrality(&g);
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println!("{:?}", centrality); // [0.0, 1.0, 1.0]
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}
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fn out_degree_centrality_example() {
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use graphina::core::types::Digraph;
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use graphina::centrality::algorithms::out_degree_centrality;
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let mut g: Digraph<i32, ()> = Digraph::new();
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let nodes = [g.add_node(1), g.add_node(2), g.add_node(3)];
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g.add_edge(nodes[0], nodes[1], ());
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g.add_edge(nodes[0], nodes[2], ());
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let centrality = out_degree_centrality(&g);
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println!("{:?}", centrality); // [2.0, 0.0, 0.0]
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}
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//
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// -----------------------------
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// Eigen Vector Centrality
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// -----------------------------
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//
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fn eigenvector_centrality_example() {
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use graphina::core::types::Graph;
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use graphina::centrality::algorithms::eigenvector_centrality;
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let mut g = Graph::new();
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let nodes = [g.add_node(1), g.add_node(2), g.add_node(3)];
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g.add_edge(nodes[0], nodes[1], 1.0);
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g.add_edge(nodes[0], nodes[2], 2.0);
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let centrality = eigenvector_centrality(&g, 1000, false);
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println!("{:.5?}", centrality); // [0.70711, 0.50000, 0.50000]
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let centrality = eigenvector_centrality(&g, 1000, true);
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println!("{:.5?}", centrality); // [0.70711, 0.31623, 0.63246]
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}
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fn eigenvector_centrality_numpy_example() {
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use graphina::centrality::algorithms::eigenvector_centrality_numpy;
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use graphina::core::types::Graph;
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let mut g = Graph::new();
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let nodes = [g.add_node(1), g.add_node(2), g.add_node(3)];
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g.add_edge(nodes[0], nodes[1], 1.0);
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g.add_edge(nodes[0], nodes[2], 2.0);
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let centrality = eigenvector_centrality_numpy(&g, 1000, 1e-6_f64, false);
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println!("{:.5?}", centrality); // [0.70711, 0.50000, 0.50000]
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let centrality = eigenvector_centrality_numpy(&g, 1000, 1e-6_f64, true);
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println!("{:.5?}", centrality); // [0.70711, 0.31623, 0.63246]
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}
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fn eigenvector_centrality_impl_example() {
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use graphina::centrality::algorithms::eigenvector_centrality_impl;
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use graphina::core::types::Graph;
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let mut g: Graph<i32, (f64, f64)> = Graph::new();
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// ^^^^^^^^^^
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// L arbitrary type as edge
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let nodes = [g.add_node(1), g.add_node(2), g.add_node(3)];
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g.add_edge(nodes[0], nodes[1], (0.0, 1.0));
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g.add_edge(nodes[0], nodes[2], (1.0, 0.0));
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let centrality = eigenvector_centrality_impl(
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&g,
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1000,
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1e-6_f64,
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|w| w.0 * 10.0 + w.1, // <-- custom evaluation for edge weight
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);
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println!("{:.5?}", centrality); // [0.70711, 0.07036, 0.70360]
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}
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//
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// -----------------------------
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// Katz Centrality
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// -----------------------------
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//
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fn katz_centrality_example() {
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use graphina::centrality::algorithms::katz_centrality;
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use graphina::core::types::Graph;
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let mut g = Graph::new();
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let nodes = [g.add_node(1), g.add_node(2), g.add_node(3)];
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g.add_edge(nodes[0], nodes[1], 1.0);
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g.add_edge(nodes[0], nodes[2], 2.0);
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let centrality = katz_centrality(&g, 0.1, 1.0, 1000, false, true);
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println!("{:.5?}", centrality); // [0.61078, 0.55989, 0.55989]
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let centrality = katz_centrality(&g, 0.01, 0.5, 1000, true, true);
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println!("{:.5?}", centrality); // [0.58301, 0.57158, 0.57741]
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}
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fn katz_centrality_numpy_example() {
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use graphina::centrality::algorithms::katz_centrality_numpy;
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use graphina::core::types::Graph;
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let mut g = Graph::new();
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let nodes = [g.add_node(1), g.add_node(2), g.add_node(3)];
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g.add_edge(nodes[0], nodes[1], 1.0);
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g.add_edge(nodes[0], nodes[2], 2.0);
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let centrality = katz_centrality_numpy(&g, 0.1, 1.0, false, true);
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println!("{:.5?}", centrality); // [0.61078, 0.55989, 0.55989]
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let centrality = katz_centrality_numpy(&g, 0.01, 0.5, true, true);
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println!("{:.5?}", centrality); // [0.58301, 0.57158, 0.57741]
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}
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fn katz_centrality_impl_example() {
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use graphina::centrality::algorithms::katz_centrality_impl;
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use graphina::core::types::Graph;
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let mut g: Graph<(i32, f64), (f64, f64)> = Graph::new();
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// ^^^^^^^^^^ ^^^^^^^^^^
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// | L arbitrary type as edge
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// L arbitrary type as node
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let nodes = [
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g.add_node((1, 2.0)),
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g.add_node((2, 3.0)),
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g.add_node((3, 2.0)),
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];
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g.add_edge(nodes[0], nodes[1], (0.0, 1.0));
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g.add_edge(nodes[0], nodes[2], (1.0, 0.0));
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let centrality = katz_centrality_impl(
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&g,
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|_n| 0.01, // <-- custom alpha depend on node attribute
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|(i, f): &(i32, f64)| f.powi(*i), // <-- custom beta depend on node attribute
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1_000,
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1e-6_f64,
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true,
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|w| w.0 * 10.0 + w.1, // <-- custom evaluation for edge weight
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);
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println!("{:.5?}", centrality); // [0.23167, 0.71650, 0.65800]
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}
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macro_rules! run_examples {
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($($func:ident),* $(,)?) => {
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$(
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println!("<{}>", stringify!($func));
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$func();
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println!();
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)*
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};
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}
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fn main() {
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run_examples!(
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// degree centrality
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degree_centrality_example,
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in_degree_centrality_example,
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out_degree_centrality_example,
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// eigen vector centrality
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eigenvector_centrality_example,
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eigenvector_centrality_numpy_example,
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eigenvector_centrality_impl_example,
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// katz centrality
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katz_centrality_example,
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katz_centrality_numpy_example,
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katz_centrality_impl_example
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);
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}

‎examples/centrality_eigenvector.py

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import networkx as nx
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G = nx.Graph()
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for i in range(5):
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G.add_node(i)
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edges = [
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(0, 1, 1.0),
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(0, 2, 2.0),
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(1, 3, 1.0),
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]
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for src, dst, weight in edges:
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G.add_edge(src, dst, weight=weight)
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centrality = nx.eigenvector_centrality(G, weight=None)
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print("Unweighted: ")
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for v, c in centrality.items():
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print(f">> {v} : {c:.5f}")
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centrality = nx.eigenvector_centrality(G, weight="weight")
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print("Weighted: ")
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for v, c in centrality.items():
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print(f">> {v} : {c:.5f}")

‎examples/centrality_eigenvector.rs

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use graphina::core::types::Graph;
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use graphina::centrality::algorithms::eigenvector_centrality;
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fn main() {
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let mut graph = Graph::new();
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let ids = (0..5).map(|i| graph.add_node(i)).collect::<Vec<_>>();
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let edges = [(0, 1, 1.0), (0, 2, 2.0), (1, 3, 1.0)];
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for (s, d, w) in edges {
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graph.add_edge(ids[s], ids[d], w);
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}
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let centrality = eigenvector_centrality(&graph, 1000, false);
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println!("Unweighted",);
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for (n, attr) in graph.nodes() {
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println!(">> {} : {:.5}", attr, centrality[n.index()])
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}
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println!();
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let centrality = eigenvector_centrality(&graph, 1000, true);
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println!("Weighted",);
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for (n, attr) in graph.nodes() {
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println!(">> {} : {:.5}", attr, centrality[n.index()])
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}
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println!();
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}

‎examples/centrality_katz.py

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import networkx as nx
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G = nx.DiGraph()
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for i in range(5):
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G.add_node(i)
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edges = [
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(0, 1, 1.0),
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(0, 2, 2.0),
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(1, 3, 1.0),
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]
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for src, dst, weight in edges:
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G.add_edge(src, dst, weight=weight)
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params = [
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(0.1, 1.0, 1000, None, True),
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(0.1, 1.0, 1000, None, False),
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(0.01, 0.5, 1000, "weight", False),
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(0.01, 0.5, 1000, "weight", True),
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]
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for alpha, beta, max_iter, weight, normalized in params:
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centrality = nx.katz_centrality(
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G,
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alpha=alpha,
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beta=beta,
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max_iter=max_iter,
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weight=weight,
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normalized=normalized,
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)
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print(f"alpha: {alpha:.3f}, beta: {beta:.3f}, max iter: {max_iter:>5}, ", end="")
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print(f"weighted: {weight=='weight'}, normalized: {normalized}".lower())
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for k, v in centrality.items():
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print(f">> {k} : {v:>.5f}")
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print()

‎examples/centrality_katz.rs

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use graphina::core::types::Digraph;
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use graphina::centrality::algorithms::katz_centrality;
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fn main() {
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let mut graph = Digraph::new();
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let ids = (0..5).map(|i| graph.add_node(i)).collect::<Vec<_>>();
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let edges = [(0, 1, 1.0), (0, 2, 2.0), (1, 3, 1.0)];
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for (s, d, w) in edges {
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graph.add_edge(ids[s], ids[d], w);
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}
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let params = [
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(0.1, 1.0, 1000, false, true),
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(0.1, 1.0, 1000, false, false),
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(0.01, 0.5, 1000, true, false),
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(0.01, 0.5, 1000, true, true),
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];
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for (alpha, beta, max_iter, weighted, normalized) in params {
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let centrality = katz_centrality(&graph, alpha, beta, max_iter, weighted, normalized);
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println!(
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"alpha: {:.3}, beta: {:.3}, max iter: {:>5}, weighted: {}, normalized: {}",
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alpha, beta, max_iter, weighted, normalized
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);
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for (n, attr) in graph.nodes() {
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println!(">> {} : {:.5}", attr, centrality[n.index()])
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}
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println!();
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}
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}

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