Graph density

The density of a graph is the ratio of the actual number of edges and the largest possible number of edges in the graph, assuming that no multi-edges are present.

Usage

edge_density(graph, loops = FALSE)

Arguments

graph

The input graph.

loops

Logical constant, whether loop edges may exist in the graph. This affects the calculation of the largest possible number of edges in the graph. If this parameter is set to FALSE yet the graph contains self-loops, the result will not be meaningful.

Value

A real constant. This function returns NaN (=0.0/0.0) for an empty graph with zero vertices.

Details

The concept of density is ill-defined for multigraphs. Note that this function does not check whether the graph has multi-edges and will return meaningless results for such graphs.

References

Wasserman, S., and Faust, K. (1994). Social Network Analysis: Methods and Applications. Cambridge: Cambridge University Press.

See also

vcount(), ecount(), simplify() to get rid of the multiple and/or loop edges.

Other structural.properties: bfs(), component_distribution(), connect(), constraint(), coreness(), degree(), dfs(), distance_table(), feedback_arc_set(), girth(), is_acyclic(), is_dag(), is_matching(), k_shortest_paths(), knn(), reciprocity(), subcomponent(), subgraph(), topo_sort(), transitivity(), unfold_tree(), which_multiple(), which_mutual()

Author

Gabor Csardi csardi.gabor@gmail.com

Related documentation in the C library

igraph_density().

Examples

edge_density(make_empty_graph(n = 10)) # empty graphs have density 0
#> [1] 0
edge_density(make_full_graph(n = 10)) # complete graphs have density 1
#> [1] 1
edge_density(sample_gnp(n = 100, p = 0.4)) # density will be close to p
#> [1] 0.3921212

# loop edges
g <- make_graph(c(1, 2, 2, 2, 2, 3)) # graph with a self-loop
edge_density(g, loops = FALSE) # this is wrong!!!
#> [1] 0.5
edge_density(g, loops = TRUE) # this is right!!!
#> [1] 0.3333333
edge_density(simplify(g), loops = FALSE) # this is also right, but different
#> [1] 0.3333333