Exploring Graph Structure with igraph

graph_properties.R

# You'll need igraph. If you don't have it, run install.packages("igraph")
library(igraph)

# First load the function moore_lattice_2d()

bulky <- moore_lattice_2d(rows=100, columns=100)
slender <- moore_lattice_2d(rows=4, columns=2500)

# Other generators: sample_k_regular, make_ring, sample_smallworld, etc...

# Calculate the longest shortest paths between any two vertices
ebulky <- eccentricity(graph=bulky)
eslender <- eccentricity(graph=slender)

# What are the shortest and longest longest shortest paths (wow!) in the graph (radius and diameter, respectively)
range(ebulky)
range(eslender)

# What is the average shortest path length (characteristic path length)?
average.path.length(graph=bulky)
average.path.length(graph=slender)

# What is the probability that two of my neighbors are also neighbors? (aka clustering coefficient, transitivity)
transitivity(graph=bulky, type="global", vids=NA)
transitivity(graph=slender, type="global", vids=NA)

moore_lattice_2d.R

moore_lattice_2d <- function(rows, columns) {
    g <- make_lattice(dimvector=c(columns,rows), circular=TRUE, directed=FALSE)
 
    b <- function(x, X) ((x - 2 + X) %% X) + 1
    a <- function(x, X) (x %% X) + 1
    vid <- function(r, c) c + (columns * (r-1))

    for (r in seq_len(rows))
    {
        next_r <- a(r, rows)

        for (c in seq_len(columns))
        {
            prev_c <- b(c, columns)
            next_c <- a(c, columns)
            v <- vid(r,c)
            g <- g + edge(v, vid(next_r, prev_c), v, vid(next_r, next_c)) 
        }
    }
    g
}