Predicts a graph from a time series of graphs.

This function predicts the graph at a future time step using a time series of graphs.

Usage

predict_graph(
  graphlist,
  formulation = 2,
  conf_level1 = NULL,
  conf_level2 = 90,
  dense_opt = 2,
  weights_opt = 6,
  weights_param = 0.001,
  h = 1
)

Arguments

graphlist: A list of graphs in igraph format.
formulation: Formulation 2 includes an additional condition constraining total edges by the predicted value. Formulation 1 does not have that constraint. Formulation 2 gives more realistic graphs due to that constraint. Default is set to 2.
conf_level1: A value between 50 and 100 denoting the confidence interval for the number of predicted nodes in the graph. If set to NULL the predicted graph has the mean number of predicted nodes. If set to 80 for example, there would be 3 predicted graphs. One with mean number of predicted nodes, and the other two with the number of nodes corresponding to lower and upper confidence bounds.
conf_level2: The upper confidence bound for the degree distribution. Default set to 90.
dense_opt: If set to 2 the dense option in R package lpSolve will be used.
weights_opt: Weights option ranging from 1 to 6 used for different edge weight schemes. Weights option 1 uses uniform weights for all edges. Option 2 uses binary weights. If the edge existed in a past graph, then weight is set to 1. Else set to 0. All possible new edges are assigned weight 1. Option 3 is a more selective version. Option 4 uses proportional weights according to the history. Option 5 uses proportional weights, but as the network is more in the past, it gives less weight. Option 5 uses linearly decaying proportional weights. Option 6 uses harmonically decaying weights. That is the network at T is given weight 1, T-1 is given weight 1/2 and so on. Default is set to 6.
weights_param: The weight given for possible edges from new vertices. Default set to 0.001.
h: The prediction time step. Default is h = 1.

Value

A list of predicted graphs. If conf_level1 is not NULL, then 3 graphs are returned one with the mean number of predicted nodes and the other 2 with the number of nodes equal to the lower and upper bound values of prediction. If If conf_level1 is NULL, only the mean predicted graph is returned.

Examples

set.seed(2024)
edge_increase_val <- new_nodes_val <- del_edge_val <- 0.1
graphlist <- list()
graphlist[[1]] <- gr <-  igraph::sample_pa(5, directed = FALSE)
for(i in 2:15){
  gr <-  generate_graph_exp(gr,
                        del_edge = del_edge_val,
                        new_nodes = new_nodes_val,
                        edge_increase = edge_increase_val )
  graphlist[[i]] <- gr
}
grpred <- predict_graph(graphlist[1:15], conf_level2 = 90, weights_opt = 6)
#> Registered S3 method overwritten by 'tsibble':
#>   method               from 
#>   as_tibble.grouped_df dplyr
#> Warning: 2 errors (1 unique) encountered for arima
#> [2] missing value where TRUE/FALSE needed
#> Registered S3 method overwritten by 'quantmod':
#>   method            from
#>   as.zoo.data.frame zoo 
grpred
#> $graph_mean
#> IGRAPH 185b249 U--- 34 23 -- 
#> + edges from 185b249:
#>  [1] 28--29 17--19 11--20 11--19 10--11  9--20  5--12  5--10  3--29  3--17
#> [11]  3-- 9  3-- 6  3-- 5  2--21  2--17  2-- 4  2-- 3  1--25  1--14  1-- 6
#> [21]  1-- 5  1-- 4  1-- 2
#> 
#> $graph_lower
#> NULL
#> 
#> $graph_upper
#> NULL
#>