make_Mixture {netcom}

Make a Mixture Mechanism Network

Description

Creates a network by iteratively adding or rewiring nodes, each capable of attaching to existing nodes according to a user-specified mechanism.

Usage

make_Mixture(
  mechanism,
  directed,
  parameter,
  kind,
  size,
  niches,
  retcon = FALSE,
  link_DD = 0,
  link_DM = 0,
  force_connected = FALSE
)

Arguments

mechanism

A vector of mechanism names corresponding to the mechanisms each node acts in accordance with. Note that the first two mechanisms are irrelevant because the first two nodes default to connecting to each other. Currently supported mechanisms: "ER" (Erdos-Renyi random), "PA", (Preferential Attachment), "DD", (Duplication and Divergence), "DM" (Duplication and Mutation), "SW", (Small-World), and "NM" (Niche Model).

directed

A binary variable determining if the network is directed, resulting in off-diagonal asymmetry in the adjacency matrix. Either a single value or a vector of values the same length as the mechanism input vector.

parameter

Parameter of each node's mechanism. Either a single value or a vector of values the same length as the mechanism input vector.

kind

Either 'grow' or 'rewire', and determines if the nodes specified in the mechanism input vector are to be rewired or grown. Either a single value or a vector of values the same length as the mechanism input vector. The number of 'grow' nodes, excluding the first two which are always a pair of bidirectionally connected nodes, is the size of the final network.

size

Typically not specified. The size of the network depends on how many 'grow' events are part of the 'kind' input sequence. This should only be used when all four components of the network evolution ('mechanism', 'kind', 'parameter', and 'directed') are single name inputs instead of vectors.

niches

Used by the Niche Model to determine which nodes interact. Needs to be a vector of the same length as the number of nodes, and range between zero and one.

retcon

Binary variable determining if already existing nodes can attach to new nodes. Defaults to FALSE.

link_DD

Defaults to 0. A second parameter in the DD (Duplication & Divergence). Currently only one parameter per mechanism can be specified.

link_DM

Defaults to 0. A second parameter in the DM (Duplication & Mutation). Currently only one parameter per mechanism can be specified.

force_connected

Defaults to FALSE. Determines if nodes can be added to the growing network that are disconnected. If TRUE, this is prevented by re-determining the offending node's edges until the network is connected.

Details

This function grows, one node at a time, a mixture mechanism network. As each node is added to the growing network it can attach to existing nodes by its own node-specific mechanism. A sequence of mechanism names must be provided. Note: Currently each mechanism is assumed to have a single governing parameter.

Value

An unweighted mixture mechanism adjacency matrix.

References

Langendorf, R. E., & Burgess, M. G. (2020). Empirically Classifying Network Mechanisms. arXiv preprint arXiv:2012.15863.

Examples

# Import netcom
library(netcom)

# Start by creating a sequence of network evolutions. 
# There are four components to this sequence that can each be defined for every step 
# in the network's evolution. Or, you can also specify a component once which will 
# be used for every step in the newtwork's evolution.

mechanism <- c(
    rep("ER", 7),
    rep("PA", 2),
    rep("ER", 3)
)

kind <- c(
    rep("grow", 7),
    rep("rewire", 2),
    rep("grow", 3)
)

parameter <- c(
    rep(0.3, 7),
    rep(2, 2),
    rep(0.3, 3)
)
directed <- c(
    rep(TRUE, 7),
    rep(FALSE, 2),
    rep(TRUE, 3)
)

# Simulate a network according to the rules of this system evolution.
network <- make_Mixture(
     mechanism = mechanism, 
     kind = kind, 
     parameter = parameter, 
     directed = directed
)