incidence.from.adjacency {incidentally}

Generates an incidence matrix from an adjacency matrix

Description

incidence.from.adjacency generates an incidence matrix from an adjacency matrix or network using a given generative model

Usage

incidence.from.adjacency(
  G,
  k = 1,
  p = 1,
  blau.param = c(2, 1, 10),
  maximal = TRUE,
  model = "team",
  class = NULL,
  narrative = TRUE
)

Arguments

G

A symmetric, binary adjacency matrix of class matrix or Matrix, or an undirected, unweighted unipartite graph of class igraph.

k

integer: Number of artifacts to generate

p

numeric: Tuning parameter for artifacts, 0 <= p <= 1

blau.param

vector: Vector of parameters that control blau space in the organizations model (see details)

maximal

boolean: Should teams/clubs models be seeded with maximal cliques?

model

string: Generative model, one of c("team", "club", "org") (see details)

class

string: Return object as matrix, Matrix, or igraph. If NULL, object is returned in the same class as G.

narrative

boolean: TRUE if suggested text & citations should be displayed.

Details

Given a unipartite network composed of i agents (i.e. nodes) that can be represented by an i x i adjacency matrix, incidence.from.adjacency generates a random i x k incidence matrix that indicates whether agent i is associated with artifact k. Generative models differ in how they conceptualize artifacts and how they associate agents with these artifacts.

The Team Model (model == "team") mirrors a team formation process, where each artifact represents a new team formed from the incumbants of a prior team (with probability p) and newcomers (with probability 1-p).

The Club Model (model == "club") mirrors a social club formation process, where each artifact represents a social club. Club members attempt to recruit non-member friends, who join the club if it would have a density of at least p.

The Organizations Model (model == "org") mirrors an organization (the artifact) recruiting members from social space, where those within the organization's niche join with probability p, and those outside the niche join with probability 1-p. blau.param is a vector containing three values that control the characteristics of the blau space. The first value is the space's dimensionality. The second two values are shape parameters of a Beta distribution that describes niche sizes. The default is a two-dimensional blau space, with organization niche sizes that are strongly positively skewed (i.e., many specialist organizations, few generalists).

Value

An incidence matrix of class matrix or Matrix, or a bipartite graph of class igraph.

References

Neal, Z. P. 2023. The duality of networks and groups: Models to generate two-mode networks from one-mode networks. Network Science.

Examples

G <- igraph::erdos.renyi.game(10, .4)
I <- incidence.from.adjacency(G, k = 1000, p = .95,
                              model = "team", narrative = TRUE)