graph.param.estimator {statGraph}

Graph Parameter Estimator

Description

graph.param.estimator estimates the parameter that best approximates the model to the observed graph according to the Graph Information Criterion (GIC).

Usage

graph.param.estimator(
  Graph,
  model,
  interval = NULL,
  eps = 0.01,
  search = "grid",
  ...
)

Arguments

Graph

the undirected graph (igraph object). If Graph has the attribute 'eigenvalues' containing the eigenvalues of Graph, such values will be used to compute spectral density of the graph.

model

either a string or a function:

A string that indicates one of the following models: 'ER' (Erdos-Renyi random graph), 'GRG' (geometric random graph), 'KR' (k regular random graph), 'WS' (Watts-Strogatz model), and 'BA' (Barabási-Albert model).

A function that returns a graph (represented by its adjacency matrix) generated by a graph model. It must contain two arguments: the first one corresponds to the graph size and the second to the parameter of the model.

interval

numeric vector containing the values that will be considered for the parameter estimation, or a list containing 'lo' and 'hi' that indicates the model's parameter search interval <lo,hi>. The graph.param.estimator will return the element of 'parameter' that minimizes the GIC. If the user does not provide the argument parameters, and model is a string, then default values are used for the predefined models ('ER', 'GRG', 'KR', 'WS', and 'BA'). The default parameter argument corresponds to a sequence from

0 to 1 with step eps for the 'ER' model (Erdos-Renyi random graph), in which the parameter corresponds to the probability to connect a pair of vertices;

0 to sqrt(2) with step eps for the 'GRG' model (geometric random graph), in which the parameter corresponds to the radius used to construct the geometric graph in a unit square;

0 to 'n' with step n*eps for the 'KR' model (k regular random graph), in which the parameter of the model corresponds to the degree k of a regular graph;

0 to 1 with step eps for the 'WS' model (Watts-Strogatz model), in which the parameter corresponds to the probability to reconnect a vertex;

and 0 to 3 with step eps for the 'BA' model (Barabási-Albert model), in which the parameter corresponds to the scaling exponent.

eps

precision of the grid and ternary search (default is 0.01).

search

string that indicates the search algorithm to find the parameter with the smallest GIC. If 'grid' (default) parameter is estimated using grid search, and only works when method is not 'fast'. If 'ternary' parameter is estimated using ternary search.

...

Other relevant parameters for GIC.

Value

A list with class 'statGraph' containing the following components:

method:

a string indicating the used method.

info:

a string showing details about the method.

data.name:

a string with the data's name(s).

param:

the parameter estimate. For the 'ER', 'GRG', 'KR', 'WS', and 'BA' models, the parameter corresponds to the probability to connect a pair of vertices, the radius used to construct the geometric graph in a unit square, the degree k of a regular graph, the probability to reconnect a vertex, and the scaling exponent, respectively.

dist:

the distance between the observed graph and the graph model with the estimated parameter.

References

Takahashi, D. Y., Sato, J. R., Ferreira, C. E. and Fujita A. (2012) Discriminating Different Classes of Biological Networks by Analyzing the Graph Spectra Distribution. _PLoS ONE_, *7*, e49949. doi:10.1371/journal.pone.0049949.

Silverman, B. W. (1986) _Density Estimation_. London: Chapman and Hall.

Sturges, H. A. The Choice of a Class Interval. _J. Am. Statist. Assoc._, *21*, 65-66.

Sheather, S. J. and Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. _Journal of the Royal Statistical Society series B_, 53, 683-690. http://www.jstor.org/stable/2345597.

Examples

set.seed(1)
G <- igraph::sample_gnp(n=50, p=0.5)

# Using a string to indicate the graph model
result1 <- graph.param.estimator(G, 'ER', eps=0.25)
result1


# Using a function to describe the graph model
# Erdos-Renyi graph
set.seed(1)
model <- function(n, p) {
  return(igraph::sample_gnp(n, p))
}
result2 <- graph.param.estimator(G, model,  seq(0.2, 0.8, 0.1))
result2