common.neighbours

# Computes number of neighbours in common between first degree neighbourhood of each vertex in an igraph network
# Not sure if this is meaningful metric yet but seems like it could be interesting!

# FUNCTION --------------------------------------------------------------------

common.neighbours <- function(graph) {
  
  lapply(unique(V(graph)), function(v) {
    
    # get vertices of 1st-order neighbourhood for focal vertex (and omit self)
    n1 <- ego(graph, 1, v)[[1]] %>% as.vector()
    n1 <- n1[!n1 %in% v]
    
    # get vertices of 1st-order neighbourhood for each neighbour (and omit self from each)
    n1n <- ego(graph, 1, n1) %>% lapply(as.vector)
    n1n <- mapply(setdiff, n1n, n1, SIMPLIFY = FALSE)
    
    # count vertices in common between neighbourhood and focal vertex
    x <- lapply(n1n, function(x) x %in% n1 %>% sum)
    
    Reduce("+", x) / 2
    
  }) %>% 
    
    unlist(use.names = F)
}


# EXAMPLES --------------------------------------------------------------------

# 1. No common vertices in 1st order neighbourhood of each vertex
nodes0 <- data.frame(id = 1:10)
edges0 <- data.frame(to = c(10,10,10,10,3,1,4,4,1),
                    from = c(1,2,3,4,5,6,7,8,9))
g0 <- graph_from_data_frame(edges0, nodes0, directed = F)

plot(g0)
common.neighbours(g0)


# 2. Several common vertices in 1st order neighbourhood of each vertex
nodes1 <- data.frame(id = 1:10)
edges1 <- data.frame(to = c(10,10,10,10,3,3,1,4,4,1,2,6),
                    from = c(1,2,3,4,4,5,6,7,8,9,3,9))
g1 <- graph_from_data_frame(edges1, nodes1, directed = F)

plot(g1)
common.neighbours(g1)