Centrality (yog-fsharp) | Yog.FSharp

Getting Started Examples API Reference GitHub

Centrality Module

Namespace: Yog
Assembly: Yog.FSharp.dll

Centrality measures for identifying important nodes in graphs.

Provides degree, closeness, harmonic, betweenness, PageRank, eigenvector, Katz, and alpha centrality measures. All functions return a Map mapping nodes to their centrality scores.

Overview

Measure	Function	Best For	Complexity
Degree	degree	Local connectivity	O(V + E)
Closeness	closeness	Distance to all others	O(V(V+E)logV)
Harmonic	harmonicCentrality	Disconnected graphs	O(V(V+E)logV)
Betweenness	betweenness	Bridge/gatekeeper detection	O(VE)
PageRank	pagerank	Link-quality importance	O(iterations×(V+E))
Eigenvector	eigenvector	Neighbor importance	O(iterations×(V+E))
Katz	katz	Attenuated paths	O(iterations×(V+E))
Alpha	alphaCentrality	Directed influence	O(iterations×(V+E))

Types

Type	Description
Centrality	A mapping of Node IDs to their calculated centrality scores.
DegreeMode	Specifies which edges to consider for directed graphs.
PageRankOptions	PageRank options for convergence.

Functions and values

Function or value	Description
`alphaCentrality alpha initial maxIterations tolerance graph` Full Usage: `alphaCentrality alpha initial maxIterations tolerance graph` Parameters: alpha : `float` initial : `float` maxIterations : `int` tolerance : `float` graph : `Graph<'n, 'e>` Returns: `Map<NodeId, float>`	Calculates Alpha Centrality for all nodes. Alpha centrality is a generalization of Katz centrality for directed graphs. Unlike Katz, it does not include a constant beta term. Formula: C(v) = α * Σ C(u) for all predecessors u (or neighbors for undirected) Time Complexity: O(max_iterations * (V + E)) Parameters: - alpha: Attenuation factor (typically 0.1-0.5) - initial: Initial centrality value for all nodes alpha : `float` initial : `float` maxIterations : `int` tolerance : `float` graph : `Graph<'n, 'e>` Returns: `Map<NodeId, float>`
`betweenness zero add compare graph` Full Usage: `betweenness zero add compare graph` Parameters: zero : `'e` add : `'e -> 'e -> 'e` compare : `'e -> 'e -> int` graph : `Graph<'n, 'e>` Returns: `Centrality`	Calculates Betweenness Centrality using Brandes' Algorithm. zero : `'e` add : `'e -> 'e -> 'e` compare : `'e -> 'e -> int` graph : `Graph<'n, 'e>` Returns: `Centrality`
`betweennessFloat graph` Full Usage: `betweennessFloat graph` Parameters: graph : `Graph<'a, float>` Returns: `Centrality`	graph : `Graph<'a, float>` Returns: `Centrality`
`betweennessInt graph` Full Usage: `betweennessInt graph` Parameters: graph : `Graph<'a, int>` Returns: `Centrality`	graph : `Graph<'a, int>` Returns: `Centrality`
`closeness zero add compare toFloat graph` Full Usage: `closeness zero add compare toFloat graph` Parameters: zero : `'e` add : `'e -> 'e -> 'e` compare : `'e -> 'e -> int` toFloat : `'e -> float` graph : `Graph<'n, 'e>` Returns: `Centrality`	Calculates Closeness Centrality for all nodes. Closeness centrality measures how close a node is to all other nodes. Formula: C(v) = (n - 1) / Σ d(v, u) for all u ≠ v Note: In disconnected graphs, nodes that cannot reach all others get 0.0. Consider using harmonicCentrality for disconnected graphs. Time Complexity: O(V * (V + E) log V) using Dijkstra from each node zero : `'e` add : `'e -> 'e -> 'e` compare : `'e -> 'e -> int` toFloat : `'e -> float` graph : `Graph<'n, 'e>` Returns: `Centrality`
`closenessFloat graph` Full Usage: `closenessFloat graph` Parameters: graph : `Graph<'a, float>` Returns: `Centrality`	graph : `Graph<'a, float>` Returns: `Centrality`
`closenessInt graph` Full Usage: `closenessInt graph` Parameters: graph : `Graph<'a, int>` Returns: `Centrality`	graph : `Graph<'a, int>` Returns: `Centrality`
`defaultPageRankOptions` Full Usage: `defaultPageRankOptions` Returns: `PageRankOptions`	Returns: `PageRankOptions`
`degree mode graph` Full Usage: `degree mode graph` Parameters: mode : `DegreeMode` graph : `Graph<'n, 'e>` Returns: `Centrality`	Calculates the Degree Centrality for all nodes in the graph. mode : `DegreeMode` graph : `Graph<'n, 'e>` Returns: `Centrality`
`degreeTotal graph` Full Usage: `degreeTotal graph` Parameters: graph : `Graph<'a, 'b>` Returns: `Centrality`	graph : `Graph<'a, 'b>` Returns: `Centrality`
`eigenvector maxIterations tolerance graph` Full Usage: `eigenvector maxIterations tolerance graph` Parameters: maxIterations : `int` tolerance : `float` graph : `Graph<'n, 'e>` Returns: `Map<NodeId, float>`	Calculates Eigenvector Centrality for all nodes. Node importance is based on the importance of its neighbors. maxIterations : `int` tolerance : `float` graph : `Graph<'n, 'e>` Returns: `Map<NodeId, float>`
`harmonicCentrality zero add compare toFloat graph` Full Usage: `harmonicCentrality zero add compare toFloat graph` Parameters: zero : `'e` add : `'e -> 'e -> 'e` compare : `'e -> 'e -> int` toFloat : `'e -> float` graph : `Graph<'n, 'e>` Returns: `Centrality`	Calculates Harmonic Centrality for all nodes. Harmonic centrality is a variation of closeness that handles disconnected graphs gracefully. It sums the reciprocals of shortest path distances. Formula: H(v) = Σ (1 / d(v, u)) / (n - 1) for all reachable u ≠ v Time Complexity: O(V * (V + E) log V) zero : `'e` add : `'e -> 'e -> 'e` compare : `'e -> 'e -> int` toFloat : `'e -> float` graph : `Graph<'n, 'e>` Returns: `Centrality`
`harmonicCentralityFloat graph` Full Usage: `harmonicCentralityFloat graph` Parameters: graph : `Graph<'a, float>` Returns: `Centrality`	graph : `Graph<'a, float>` Returns: `Centrality`
`harmonicCentralityInt graph` Full Usage: `harmonicCentralityInt graph` Parameters: graph : `Graph<'a, int>` Returns: `Centrality`	graph : `Graph<'a, int>` Returns: `Centrality`
`katz alpha beta maxIterations tolerance graph` Full Usage: `katz alpha beta maxIterations tolerance graph` Parameters: alpha : `float` beta : `float` maxIterations : `int` tolerance : `float` graph : `Graph<'n, 'e>` Returns: `Map<NodeId, float>`	Calculates Katz Centrality for all nodes. Katz centrality adds an attenuation factor (alpha) to prevent infinite accumulation in cycles, plus a constant term (beta) for base centrality. Formula: C(v) = α * Σ C(u) + β for all neighbors u Time Complexity: O(max_iterations * (V + E)) Parameters: - alpha: Attenuation factor (must be < 1/largest_eigenvalue, typically 0.1-0.3) - beta: Base centrality (typically 1.0) alpha : `float` beta : `float` maxIterations : `int` tolerance : `float` graph : `Graph<'n, 'e>` Returns: `Map<NodeId, float>`
`pagerank options graph` Full Usage: `pagerank options graph` Parameters: options : `PageRankOptions` graph : `Graph<'n, 'e>` Returns: `Centrality`	Calculates PageRank Centrality for all nodes. options : `PageRankOptions` graph : `Graph<'n, 'e>` Returns: `Centrality`