Graph Prediction from a Graph Time Series.

netseer

The goal of netseer is to predict the graph structure including new nodes and edges from a time series of graphs. The methodology is explained in the preprint (Sevvandi Kandanaarachchi 2024). We will illustrate an example in this vignette.

Installation

You can install the development version of netseer from GitHub with:

# install.packages("devtools")
devtools::install_github("sevvandi/netseer")

An example

This is a basic example which shows you how to predict a graph at the next time point. First let us generate some graphs.

library(netseer)
library(igraph)
#> 
#> Attaching package: 'igraph'
#> The following objects are masked from 'package:stats':
#> 
#>     decompose, spectrum
#> The following object is masked from 'package:base':
#> 
#>     union

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
}

The graphlist contains the list of graphs we generated. Each graph is an igraph object. Let’s plot a couple of them.

Plotting a couple of graphs

plot(graphlist[[1]])

plot(graphlist[[8]])

plot(graphlist[[15]])

### Predicting the next graph

Let’s predict the next graph. The argument $h = 1$ specifies we want to predict the graph at the next time point.

grpred <- predict_graph(graphlist[1:15],h = 1)
#> 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 4ff4848 U--- 35 23 -- 
#> + edges from 4ff4848:
#>  [1] 17--19 11--19 10--11  9--20  5--12  5--10  3--17  3-- 9  3-- 6  2--21
#> [11]  2-- 4  2-- 3  1--25  1--14  1-- 6  1-- 5  1-- 4  1-- 2  7--31 10--32
#> [21] 20--33 14--34 20--35
#> 
#> $graph_lower
#> NULL
#> 
#> $graph_upper
#> NULL

plot(grpred$graph_mean)

ecount(grpred$graph_mean)
#> [1] 23
vcount(grpred$graph_mean)
#> [1] 35

Predicting the graph at 2 time steps ahead

Now let us predict the graph at 2 time steps ahead with $h=2$.

grpred2 <- predict_graph(graphlist[1:15], h = 2)
#> Warning: 2 errors (1 unique) encountered for arima
#> [2] missing value where TRUE/FALSE needed
grpred2
#> $graph_mean
#> IGRAPH a99ea21 U--- 38 26 -- 
#> + edges from a99ea21:
#>  [1] 10--11  9--20  5--12  5--10  3--17  3-- 9  2--21  2-- 4  2-- 3  1--14
#> [11]  1-- 6  1-- 5  1-- 4  1-- 2 19--31 17--31 17--32  7--32 11--33 28--33
#> [21] 16--34 10--34 16--35  6--36  3--37 12--38
#> 
#> $graph_lower
#> NULL
#> 
#> $graph_upper
#> NULL

plot(grpred2$graph_mean)

ecount(grpred2$graph_mean)
#> [1] 26
vcount(grpred2$graph_mean)
#> [1] 38

We see the predicted graph at $h=2$ has more vertices and edges than the graph at $h=1$.

Predicting the graph at 3 time steps ahead

Similarly, we can predict the graph at 3 time steps ahead. We don’t have a limit on $h$. But generally, as we get further into the future, the predictions are less accurate. This is with everything, not just graphs.

grpred3 <- predict_graph(graphlist[1:15], h = 3)
#> Warning: 2 errors (1 unique) encountered for arima
#> [2] missing value where TRUE/FALSE needed
grpred3
#> $graph_mean
#> IGRAPH dff11cd U--- 41 29 -- 
#> + edges from dff11cd:
#>  [1] 10--11  5--10  3--17  3-- 9  2-- 4  2-- 3  1--14  1-- 6  1-- 5  1-- 4
#> [11]  1-- 2 21--31 20--31 19--32  3--32 19--33  2--33  9--34 11--34 17--35
#> [21] 16--35 12--36  7--36  9--37 11--37 15--38 15--39 29--40 19--41
#> 
#> $graph_lower
#> NULL
#> 
#> $graph_upper
#> NULL

plot(grpred3$graph_mean)

ecount(grpred3$graph_mean)
#> [1] 29
vcount(grpred3$graph_mean)
#> [1] 41

References