greedy_route_packets: Analyse the navigability of a complex network

In galanisl/NetHypGeom: Hyperbolic geometry of complex networks

Description

Given a network and source and destination nodes, greedy route packets in hyperbolic space and record successful deliveries. If the packet visits any of the nodes in faulty, it is dropped and the delivery flagged as unsuccessful (unless the faulty node is a target).

Usage

greedy_route_packets(net, polar, source, target, faulty = c())

Arguments

net	igraph; A complex network with N nodes.
polar	data frame; Polar coordinates (r, theta) of all nodes in the network.
source	vector; A vector with one or more node indices representing sources.
target	vector; A vector, the same size as source, with one or more node indices representing targets.
faulty	vector; A vector with one or more node indices representing faulty system components (default = c()).

Value

A vector, the same size as source or target, with the hop stretch required to deliver the packet from each source to each target, or 0 if the packet was dropped.

Author(s)

Gregorio Alanis-Lobato [e-mail]

References

Boguna, M. and Krioukov, D. (2009) Navigating Ultrasmall Worlds in Ultrashort Time. Physical Review Letters 102(5).

Krioukov, D. et al. (2010) Hyperbolic geometry of complex networks. Physical Review E 82(3).

Examples

# Generate an artificial network with the PS model
N <- 500
net <- ps_model(N, 6, 2.5, 0)

# Form vectors of random non-redundant source-target pairs
st <- 1000
# We subtract 1, because the formulae to go from linear upper 
# diagonal indexing to (i,j) are zero-based
k <- sample(N*(N-1)/2, st) - 1
sources <- (N - 2 - floor(sqrt(-8*k + 4*N*(N-1)-7)/2.0 - 0.5))
targets <- (k + sources + 1 - N*(N-1)/2 + (N-sources)*((N-sources)-1)/2)

# Back to 1-based indexing
sources <- sources + 1
targets <- targets + 1

# Analyse the network's navigability
hop.stretch <- greedy_route_packets(net$network, net$polar, sources, targets)

# Compute the fraction of succesfully delivered packets
sum(hop.stretch > 0)/st

galanisl/NetHypGeom documentation built on May 16, 2019, 5:36 p.m.