R: Functions to find weighted cliques, ie. weighted complete...

weighted_cliques {igraph} | R Documentation

## Functions to find weighted cliques, ie. weighted complete subgraphs in a graph

### Description

These functions find all, the largest or all the maximal weighted cliques in an undirected graph. The weight of a clique is the sum of the weights of its edges.

### Usage

    weighted_cliques(
      graph,
      vertex.weights = NULL,
      min.weight = 0,
      max.weight = 0,
      maximal = FALSE
    )

### Arguments

`graph` | The input graph, directed graphs will be considered as undirected ones, multiple edges and loops are ignored.
`vertex.weights` | Vertex weight vector. If the graph has a `weight` vertex attribute, then this is used by default. If the graph does not have a `weight` vertex attribute and this argument is `NULL`, then every vertex is assumed to have a weight of 1. Note that the current implementation of the weighted clique finder supports positive integer weights only.
`min.weight` | Numeric constant, lower limit on the weight of the cliques to find. `NULL` means no limit, ie. it is the same as 0.
`max.weight` | Numeric constant, upper limit on the weight of the cliques to find. `NULL` means no limit.
`maximal` | Specifies whether to look for all weighted cliques (`FALSE`) or only the maximal ones (`TRUE`).

### Details

`weighted_cliques` find all complete subgraphs in the input graph, obeying the weight limitations given in the `min` and `max` arguments.

`largest_weighted_cliques` finds all largest weighted cliques in the input graph. A clique is largest if there is no other clique whose total weight is larger than the weight of this clique.

`max_weighted_cliques` finds all maximal weighted cliques in the input graph. A weighted clique is maximal if it cannot be extended to a clique with larger total weight. The largest weighted cliques are always maximal, but a maximal weighted clique is not necessarily the largest.

`count_max_weighted_cliques` counts the maximal weighted cliques.

`weighted_clique_num` calculates the weight of the largest weighted clique(s).

### Value

`weighted_cliques` and `largest_weighted_cliques` return a list containing numeric vectors of vertex IDs. Each list element is a weighted clique, i.e. a vertex sequence of class `igraph.vs`.

`weighted_clique_num` and `count_max_weighted_cliques` return an integer scalar.

### Author(s)

Tamas Nepusz ntamas@gmail.com and Gabor Csardi csardi.gabor@gmail.com

### See Also

`ivs`

### Examples

    g <- make_graph("zachary")
    V(g)$weight <- 1
    V(g)[c(1,2,3,4,14)]$weight <- 3
    weighted_cliques(g)
    weighted_cliques(g, maximal=TRUE)
    largest_weighted_cliques(g)
    weighted_clique_num(g)

[Package igraph version 1.3.1 Index]