| Type: | Package |
| Title: | Optimal Graph Partition using the Persistence |
| Version: | 0.1.0 |
| Description: | Calculate the optimal vertex partition of a graph using the persistence as objective function. These subroutines have been used in Avellone et al. <doi:10.1007/s10288-023-00559-z>. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| SystemRequirements: | C++20 |
| Suggests: | igraph |
| RoxygenNote: | 7.3.2 |
| NeedsCompilation: | yes |
| Collate: | 'persistence-exports.R' 'cluster_milano.R' 'global_persistence.R' 'local_persistence.R' |
| Packaged: | 2025-05-17 08:08:47 UTC; ale |
| Author: | Alessandro Avellone [aut, cre], Paolo Bartesaghi [aut], Stefano Benati [aut], Rosanna Grassi [aut] |
| Maintainer: | Alessandro Avellone <alessandro.avellone@unimib.it> |
| Repository: | CRAN |
| Date/Publication: | 2025-05-21 08:30:02 UTC |
Persistence
Description
Given a non-oriented graph, calculates the optimal vertex partition using the persistence as the objective function.
Details
See manual entries.
Author(s)
Maintainer: Alessandro Avellone alessandro.avellone@unimib.it
Authors:
Paolo Bartesaghi paolo.bartesaghi@unimi.it
Stefano Benati stefano.benati@unitn.it
Rosanna Grassi rosanna.grassi@unimib.it
cluster Milano
Description
Calculates the partition with maximum global null-adjuted persistence.
Usage
cluster_milano(vertex, edge_list, seed = NULL)
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. |
seed |
As some steps of the algorithm are random, users may experiments with different seeds of random numbers. |
Value
A list containing:
- membeship
The optimal vertex partition.
- value
The null-adjusted persistence of the partition.
- seed
The used seed to generate random numbers.
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)
print(length(edg) / 2.0)
vertex = unique(edg)
edg = t(matrix(as.integer(edg), nrow = 2 ))
rete <- graph_from_edgelist(edg, directed = FALSE)
plot(rete)
seed <- sample(1:as.integer(.Machine$integer.max),1, replace= FALSE)
r = cluster_milano(vertex, edg, seed=seed)
print(paste("The optimal null-adjusted persistence is: ", r$measure))
print(paste("The optimal persistence probability is: ", r$measure + 1))
global persistence
Description
Given a partition of the graph vertices, it calculates the global persistence as the sum of the persistences of the single clusters. Persistence can be referred to the null-adjusted o to the probability.
Usage
global_persistence(vertex, edge_list, membership, H0 = TRUE)
Arguments
vertex |
the vertices of the graph, whose label are integers and they must be consistent with the edge sets. |
edge_list |
the graph edge list in the form of an integer matrix with two columns. |
membership |
An integer vector representing the vertex membership: x_i = k if i in C_k. |
H0 |
If true, it calculates the null-adjusted persistence, if false, the persistence probability. |
Value
value A list containing the following:
- value
The global persistence of the partition.
- clusters_value
The local persistence of each cluster. If for some k we have v_k = NaN, then C_k is empty in the input membership.
Examples
library(persistence)
library(igraph)
edg = c(1, 2, 1, 3, 1, 4, 2, 3, 3, 4, 4, 5, 5, 6, 5, 7, 5, 8, 5, 9, 6, 7, 6, 8, 7, 9, 8, 9)
print(length(edg) / 2.0)
vertex = unique(edg)
edg = t(matrix(as.integer(edg), nrow = 2 ))
rete <- graph_from_edgelist(edg, directed = FALSE) # I graph this matrix
plot(rete)
membership = c(1, 1, 1, 1, 2, 2, 2, 2, 2)
v1 = global_persistence(vertex, edg, membership, H0=TRUE)
print(paste("global null-adjusted persistence: ", v1$value))
print(paste("null-adjusted persistence per cluster: ", v1$clusters_value))
local_persistence
Description
Given the incidence vector of a vertex subset, it calculates the persistence probability or the null-adjusted persistence of C.
Usage
local_persistence(vertex, edge_list, cluster, H0 = TRUE)
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 |
cluster |
A binary vector representing the incidence vector of the cluster: x_i = 1 if i in C, 0 otherwise. |
H0 |
if true, it calculates the null-adjusted persistence, if false, the persistence probability. |
Value
the value of the null-adjusted persistence if H0 = T, the value of the persistence probability if H0 = F
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)
print(length(edg) / 2.0)
vertex = unique(edg)
edg = t(matrix(as.integer(edg), nrow = 2 ))
rete <- graph_from_edgelist(edg, directed = FALSE) # I graph this matrix
plot(rete)
cluster = rep(0, length(vertex))
v1 = c(1, 2, 3, 4)
cluster[v1] = 1
f1 = local_persistence(vertex, edg, cluster, H0 = TRUE)
f2 = local_persistence(vertex, edg, cluster, H0 = FALSE)