persistence (version 0.2.0)

global_persistence: global persistence

Description

Given a partition of the graph vertices, it calculates the global persistence as the sum of the persistences of the single clusters. Persistence can be referred to the null-adjusted o to the probability.

Usage

global_persistence(vertex, edge_list, weights, membership, H0 = TRUE)

Value

value A list containing the following:

value

The global persistence of the partition.

clusters_value

The local persistence of each cluster. If for some k we have v_k = NaN, then C_k is empty in the input membership.

Arguments

vertex

the vertices of the graph, whose label are integers and they must be consistent with the edge sets.

edge_list

the graph edge list in the form of an integer matrix with two columns.

weights

the graph edge weights.

membership

An integer vector representing the vertex membership: x_i = k if i in C_k.

H0

If true, it calculates the null-adjusted persistence, if false, the persistence probability.

Examples

library(persistence)
library(igraph)

edg = c(1, 2, 1, 3, 1, 4, 2, 3, 3, 4, 4, 5, 5, 6, 5, 7, 5, 8, 5, 9, 6, 7, 6, 8, 7, 9, 8, 9)
vertex = unique(edg)
edg = t(matrix(as.integer(edg), nrow = 2 ))
rete <- graph_from_edgelist(edg, directed = FALSE) # I graph this matrix
plot(rete)

membership = c(1, 1, 1, 1, 2, 2, 2, 2, 2)
v1 = global_persistence(vertex, edg, weights=NULL, membership, H0=TRUE)
print(paste("global null-adjusted persistence: ", v1$value))
print(paste("null-adjusted persistence per cluster: ", v1$clusters_value))