get_theoretical_conn_probs: Connection probabilities in the PS model
In galanisl/NetHypGeom: Hyperbolic geometry of complex networks

Description Usage Arguments Value Author(s) References Examples

Given a a set of network properties, compute connection probabilities according to the Popularity-Similarity model [Papadopoulos et al. 2012, Nature 489(7417):537-40].

1	get_theoretical_conn_probs(bins, N, avg.k, gma, Temp)

`bins`	vector; The hyperbolic distance bins or steps in which theoretical connection probabilities are to be computed.
`N`	integer; Number of network nodes.
`avg.k`	numeric; Network's average node degree.
`gma`	numeric; The network's scaling exponent gamma.
`Temp`	numeric; The network temperature.

A data frame with the two following elements:

`dist`	The considered distance bins.
`prob`	the connection probabilities within each bin.

Gregorio Alanis-Lobato galanisl@uni-mainz.de

Papadopoulos, F. et al. (2012) Popularity versus similarity in growing networks. Nature 489(7417):537-40.

# Generate an artificial network with the PS model
net <- ps_model(500, 6, 2.5, 0.1)

# Get the real and theoretical connection probability curves and plot them
conn <- get_conn_probs(net$network, net$polar, 15)
theo <- get_theoretical_conn_probs(conn$dist, vcount(net$network), 6, 2.5, 0.1)

plot(conn$dist, conn$prob, pch = 16, 
     xlab = "Hyperbolic distance", ylab = "Connection probability")
points(theo$dist, theo$prob, pch = 16, 
     xlab = "Hyperbolic distance", ylab = "Connection probability", col = "red")
legend("topright", c("Real", "Theory"), pch = c(16, 16), col = c("black", "red"))