| Title: | Complex Network Generation |
|---|---|
| Description: | Providing a set of functions to easily generate and iterate complex networks. The functions can be used to generate realistic networks with a wide range of different clustering, density, and average path length. For more information consult research articles by Amiyaal Ilany and Erol Akcay (2016) <doi:10.1093/icb/icw068> and Ilany and Erol Akcay (2016) <doi:10.1101/026120>, which have inspired many methods in this package. |
| Authors: | Marco Smolla [aut, cre] |
| Maintainer: | Marco Smolla <[email protected]> |
| License: | GPL-3 |
| Version: | 0.2.0 |
| Built: | 2024-10-26 05:41:47 UTC |
| Source: | https://github.com/marcosmolla/complexnet |
Calculates the expected average degree of a BNR network (single parent only) based on the approximation by Ilany and Akcay, 2016 (see details).
avg_degree_bnr(n, pb, pn, pr) ## S4 method for signature 'numeric,numeric,numeric,numeric' avg_degree_bnr(n, pb, pn, pr)avg_degree_bnr(n, pb, pn, pr) ## S4 method for signature 'numeric,numeric,numeric,numeric' avg_degree_bnr(n, pb, pn, pr)
n |
Number of nodes in the network |
pb |
Probability to connect to parent (default is 1) |
pn |
Probability to connect to neighbour of parent(s) |
pr |
Probability to connect to individuals that are not connected to |
The expected average degree is calculated as
Returns the expected average degree of a BNR network as a numeric value. This value is an analytic result and not a numeric approximation (compare examples below).
Ilany, A., and Akçay, E. (2016). Personality and Social Networks: A Generative Model Approach. Integrative and Comparative Biology, 56(6), 1197–1205. doi:10.1093/icb/icw068
# Expected degree avg_degree_bnr(n = 100, pb = 1, pn = .2, pr = .02) # Compare to simulated network with identical parameters adjm <- make_bnr(n = 100, np = c(0,0), pb = 1, pn = .2, pr = .02) mean(adjm) * 100# Expected degree avg_degree_bnr(n = 100, pb = 1, pn = .2, pr = .02) # Compare to simulated network with identical parameters adjm <- make_bnr(n = 100, np = c(0,0), pb = 1, pn = .2, pr = .02) mean(adjm) * 100
init_graph takes number of nodes (n) and average degree (deg) to generate a random graph.
init_graph(n, deg) ## S4 method for signature 'numeric,numeric' init_graph(n, deg)init_graph(n, deg) ## S4 method for signature 'numeric,numeric' init_graph(n, deg)
n |
Number of nodes in the network |
deg |
Average degree in the network |
Returns an unweighted (binary) adjacency matrix, where each cell represents the presence (1) or absence (0) of an interaction between the row and the column individual.
init_graph(n = 10, deg = 4)init_graph(n = 10, deg = 4)
Iterating a bnr network
iterate_bnr(adjm, np, pb, pn, pr) ## S4 method for signature 'matrix,numeric,numeric,numeric,numeric' iterate_bnr(adjm, np, pb, pn, pr)iterate_bnr(adjm, np, pb, pn, pr) ## S4 method for signature 'matrix,numeric,numeric,numeric,numeric' iterate_bnr(adjm, np, pb, pn, pr)
adjm |
Adjacency matrix |
np |
numeric vector setting ids for the newborn (i.e. which individual will be replaced with a new one) and a parent(s). Length 2 or 3. If you want to randomly select an id for the newborn (first value) and parents (second and third value), simply use c(0,0) or c(0,0,0). For one parent, the focal individual connects to this parent with probability pb. For two parent values, the individual connects to two parents each with probability pb. |
pb |
Probability to connect to parent. Default is 1. |
pn |
Probability to connect to neighbour of parent(s) |
pr |
Probability to connect to individuals that are not connected to the parent |
If you just want to iterate the graph you can use np=c(0,0) or np=c(0,0,0). However, the function does not return the ids of the newborn and the parent(s). If you want to keep track of the ids that are changed, you should provide these as an input to the function.
Returns an iterated version of the supplied adjacency matrix as a numeric matrix.
# Set up linking parameters: pb <- 1 pn <- 0.2 pr <- 0.01 # Generate a network based on these parameters adjm_t0 <- make_bnr(n = 100, np=c(0,0), pb = pb, pn = pn, pr = pr) # Iterate the network adjm_t1 <- iterate_bnr(adjm = adjm_t0, np=c(0,0), pb = pb, pn = pn, pr = pr)# Set up linking parameters: pb <- 1 pn <- 0.2 pr <- 0.01 # Generate a network based on these parameters adjm_t0 <- make_bnr(n = 100, np=c(0,0), pb = pb, pn = pn, pr = pr) # Iterate the network adjm_t1 <- iterate_bnr(adjm = adjm_t0, np=c(0,0), pb = pb, pn = pn, pr = pr)
Iterating a kp network
iterate_kp(adjm, np, pb, k, p) ## S4 method for signature 'matrix,numeric,numeric,numeric,numeric' iterate_kp(adjm, np, pb, k, p)iterate_kp(adjm, np, pb, k, p) ## S4 method for signature 'matrix,numeric,numeric,numeric,numeric' iterate_kp(adjm, np, pb, k, p)
adjm |
Adjacency matrix |
np |
numeric vector setting ids for the newborn (i.e. which individual will be replaced with a new one) and a parent(s). Length 2 or 3. If you want to randomly select an id for the newborn (first value) and parents (second and third value), simply use c(0,0) or c(0,0,0). For one parent, the focal individual connects to this parent with probability pb. For two parent values, the individual connects to two parents each with probability pb. |
pb |
Probability to connect to parent. Default is 1. |
k |
Degree (number of connections a new individual will form) |
p |
Maximum proportion of k that will be connections to neighbours of the parent. The complimentary k*(1-p) connections will be formed with random other individuals |
If you just want to iterate the graph you can use np=c(0,0) or np=c(0,0,0). However, the function does not return the ids of the newborn and the parent(s). If you want to keep track of the ids that are changed, you should provide these as an input to the function.
Returns an iterated version of the supplied adjacency matrix as a numeric matrix.
# Set up linking parameters: pb <- 1 k <- 4 p <- 0.2 # Generate a network based on these parameters adjm_t0 <- make_kp(n = 100, np=c(0,0), pb = pb, k = k, p = p) # Iterate the network adjm_t1 <- iterate_kp(adjm = adjm_t0, np=c(0,0), pb = pb, k = k, p = p)# Set up linking parameters: pb <- 1 k <- 4 p <- 0.2 # Generate a network based on these parameters adjm_t0 <- make_kp(n = 100, np=c(0,0), pb = pb, k = k, p = p) # Iterate the network adjm_t1 <- iterate_kp(adjm = adjm_t0, np=c(0,0), pb = pb, k = k, p = p)
This function takes adj.matrix (ADJM), probabilities to connect to parent(s), neighbours, and randoms (PB, PN, PR), the index of the parent (if NULL, default, NPARENT number of individuals are randomly chosen as parent), number of parents (NPARENT, default is 1).
make_bnr(n, np, pb, pn, pr) ## S4 method for signature 'numeric,numeric,numeric,numeric,numeric' make_bnr(n, np, pb, pn, pr) ## S4 method for signature 'numeric,numeric,missing,numeric,numeric' make_bnr(n, np, pb, pn, pr)make_bnr(n, np, pb, pn, pr) ## S4 method for signature 'numeric,numeric,numeric,numeric,numeric' make_bnr(n, np, pb, pn, pr) ## S4 method for signature 'numeric,numeric,missing,numeric,numeric' make_bnr(n, np, pb, pn, pr)
n |
Number of vertices (population size) |
np |
numeric vector setting ids for the newborn (i.e. which individual will be replaced with a new one) and a parent(s). Length 2 or 3. If you want to randomly select an id for the newborn (first value) and parents (second and third value), simply use c(0,0) or c(0,0,0). |
pb |
Probability to connect to parent (default is 1) |
pn |
Probability to connect to neighbour of parent(s) |
pr |
Probability to connect to individuals that are not connected to the parent |
It is important to note that, although all three parameters (PB, PN, PR) are probabilities, i.e. values between 0 and 1, the same value (say 0.2) means something different for each of them. This is because, PB is the probability to connect to the parent(s), i.e. 1 or two individuals. In contrast, PN and PR are the probabilities to connect to neighbours of the parent(s) or to random other individuals. In the case of a small social neighbourhood of the parent(s) a PR of 0.2 would mean to connect to a large amount of individuals in the remaining network. Therefore, it is important to keep in mind that the value of both (or all three) values is important and not the individual one in isolation.
Returns an unweighted (binary) adjacency matrix, where each cell represents the presence (1) or absence (0) of an interaction between the row and the column individual.
make_bnr(n = 10, np = c(0,0), pb = 1, pn = .2, pr = .01)make_bnr(n = 10, np = c(0,0), pb = 1, pn = .2, pr = .01)
This function ...
make_kp(n, np, pb, k, p) ## S4 method for signature 'numeric,numeric,numeric,numeric,numeric' make_kp(n, np, pb, k, p) ## S4 method for signature 'numeric,numeric,missing,numeric,numeric' make_kp(n, np, pb, k, p)make_kp(n, np, pb, k, p) ## S4 method for signature 'numeric,numeric,numeric,numeric,numeric' make_kp(n, np, pb, k, p) ## S4 method for signature 'numeric,numeric,missing,numeric,numeric' make_kp(n, np, pb, k, p)
n |
Number of vertices (population size) |
np |
numeric vector setting ids for the newborn (i.e. which individual will be replaced with a new one) and a parent(s). Length 2 or 3. If you want to randomly select an id for the newborn (first value) and parents (second and third value), simply use c(0,0) or c(0,0,0). |
pb |
Probability to connect to parent (default is 1) |
k |
Degree (number of connections a new individual will form) |
p |
Maximum proportion of k that will be connections to neighbours of the parent. The complimentary k*(1-p) connections will be formed with random other individuals |
It is important to note that ... P is a maximum value, say an individual wants to have 10 connections and P=0.5, i.e. it wants 5 connections to the neighbours of its parent but the parent only has 4 then it will only inherit those 4.
Returns an unweighed (binary) adjacency matrix, where each cell represents the presence (1) or absence (0) of an interaction between the row and the column individual.
make_kp(n = 10, np = c(0,0), pb = 1, k = 4, p = .5)make_kp(n = 10, np = c(0,0), pb = 1, k = 4, p = .5)