package prbnmcn-stats

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Parameters
Signature

prbnmcn-stats
- Stats
  - Binning
  - Combi
  - Emp
    
    Empirical_statistics
    
    Float
    
    Rational
  - Fin
    
    Float
    
    Dist
    
    Rational
    
    Dist
  - Finbij
    
    Make
    
    Elt
    
    S
  - Gen
    
    Infix
    
    Rational
  - Graph
    
    Dist
    
    Graph_statistics
    
    Table
    
    Undirected_edge
    
    Vertex_bij
    
    Make
    
    Graph
    
    V
    
    Table
    
    Undirected_edge
    
    Vertex_bij
  - Log_space
  - Mh
    
    MH_parameters
    
    Make
    
    X
    
    Make_core_sampling_loop
    
    X
  - Pdfs
  - Stats_intf
    
    Fin_dist
    
    Fin_fun
    
    V
    
    Basis
    
    R
    
    Fin_kernel
    
    V
    
    Basis
    
    R
    
    Gen
    
    Infix
    
    Rational
    
    Graph
    
    V
    
    Sampling_monad
    
    Infix

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Library
Module
Module type
Parameter
Class
Class type

Graph statistics generic on an undirected Graph implementation.

Parameters

module Graph : Stats_intf.Graph

Signature

type t = Graph.t

t is the type of (undirected) graphs.

type vertex = Graph.vertex

vertex is the type of vertices.

module Undirected_edge : 
  Basic_structures.Basic_intf.Std with type t = vertex * vertex

Undirected edges. The equal and hash function are invariant under permutation of the vertices in the pair encoding the edge.

module Table : Hashtbl.S with type key = Undirected_edge.t

module Vertex_bij : Finbij.S with type elt = vertex

Finite bijections between vertices and integers.

val adjacency_matrix : t -> (int * int) Linalg.Mat.Float.t * Vertex_bij.t

adjacency_matrix g computes the adjacency matrix of g as well as a bijection between the matrix dimensions and the vertices. The matrix is dense. Since the graph is undirected, it is also symmetric.

val laplacian : t -> (int * int) Linalg.Mat.Float.t * Vertex_bij.t

laplacian g computes the laplacian of the adjacency matrix, following the definition in 'Spectral Graph Theory', by Fan Chung Graham. The dimensions are the same as the adjacency matrix. A finite bijection is returned as well.

type distance_table = (vertex * vertex, Dist.t) Hashtbl.t

val floyd_warshall : t -> Dist.t Table.t

Floyd-warshall algorithm. Complexity is O(V^3) where V is the number of vertices of the graph. Returns a table of all distances between pairs of vertices.

val diameter : t -> Dist.t

Computes the diameter of the graph, ie the maximum over all pair of vertices of the shortest-path distance between those vertices.

val volume : t -> int

volume g computes the sum over all vertices of their degree.

val degree_dist : t -> (int, float) Stats_intf.fin_prb

degree_dist g computes the degree distribution of g.