Interactome-assisted graph re-seizing — resizeGraph • SEMgraph

An input directed graph is re-sized, removing edges or adding edges/nodes. This function takes three input graphs: the first is the input causal model (i.e., a directed graph), and the second can be either a directed or undirected graph, providing a set of connections to be checked against a directed reference network (i.e., the third input) and imported to the first graph.

Usage

resizeGraph(g = list(), gnet, d = 2, v = TRUE, verbose = FALSE, ...)

Arguments

g: A list of two graphs as igraph objects, g=list(graph1, graph2).
gnet: External directed network as an igraph object. The reference network should have weighted edges, corresponding to their interaction p-values, as an edge attribute E(gnet)$pv. Then, connections in graph2 will be checked by known connections from the reference network, intercepted by the minimum-weighted shortest path found among the equivalent ones by the Dijkstra algorithm, as implemented in the igraph function all_shortest_paths().
d: An integer value indicating the maximum geodesic distance between two nodes in the interactome to consider the inferred interaction between the same two nodes in graph2 as validated, otherwise the edges are removed. For instance, if d = 2, two interacting nodes must either share a direct interaction or being connected through at most one mediator in the reference interactome (in general, at most d - 1 mediators are allowed). Typical d values include 2 (at most one mediator), or mean_distance(gnet) (i.e., the average shortest path length for the reference network). Setting d = 0, is equivalent to gnet = NULL.
v: A logical value. If TRUE (default) new nodes and edges on the validated shortest path in the reference interactome will be added in the re-sized graph.
verbose: A logical value. If FALSE (default), the processed graphs will not be plotted to screen, saving execution time (for large graphs)
...: Currently ignored.

Value

"Ug", the re-sized graph, the graph union of the causal graph graph1 and the re-sized graph graph2

Details

Typically, the first graph is an estimated causal graph (DAG), and the second graph is the output of either SEMdag or SEMbap. Alternatively, the first graph is an empthy graph, and the second graph is a external covariance graph. In the former we use the new inferred causal structure stored in the dag.new object. In the latter, we use the new inferred covariance structure stored in the guu object. Both directed (causal) edges inferred by SEMdag() and covariances (i.e., bidirected edges) added by SEMbap(), highlight emergent hidden topological proprieties, absent in the input graph. Estimated directed edges between nodes X and Y are interpreted as either direct links or direct paths mediated by hidden connector nodes. Covariances between any two bow-free nodes X and Y may hide causal relationships, not explicitly represented in the current model. Conversely, directed edges could be redundant or artifact, specific to the observed data and could be deleted. Function resizeGraph() leverage on these concepts to extend/reduce a causal model, importing new connectors or deleting estimated edges, if they are present or absent in a given reference network. The whole process may lead to the discovery of new paths of information flow, and cut edges not corroborate by a validated network. Since added nodes can already be present in the causal graph, network resize may create cross-connections between old and new paths and their possible closure into circuits.

References

Grassi M, Palluzzi F, Tarantino B (2022). SEMgraph: An R Package for Causal Network Analysis of High-Throughput Data with Structural Equation Models. Bioinformatics, 38 (20), 4829–4830 <https://doi.org/10.1093/bioinformatics/btac567>

Author

Mario Grassi mario.grassi@unipv.it

Examples


# \donttest{

# Extract the "Protein processing in endoplasmic reticulum" pathway:

g <- kegg.pathways[["Protein processing in endoplasmic reticulum"]]
G <- properties(g)[[1]]; summary(G)
#> Frequency distribution of graph components
#> 
#>   n.nodes n.graphs
#> 1       7        1
#> 2      10        1
#> 3      12        1
#> 4      26        1
#> 
#> Percent of vertices in the giant component: 15.2 %
#> 
#>   is.simple      is.dag is.directed is.weighted 
#>        TRUE       FALSE        TRUE        TRUE 
#> 
#> which.mutual.FALSE 
#>                 34 
#> IGRAPH e8612d1 DNW- 26 34 -- 
#> + attr: name (v/c), weight (e/n)

# Reference network (KEGG interactome)
gnet <- kegg

# Extend a graph using new inferred DAG edges (dag+dag.new):

# Nonparanormal(npn) transformation
als.npn <- transformData(alsData$exprs)$data
#> Conducting the nonparanormal transformation via shrunkun ECDF...done.

dag <- SEMdag(graph = G, data = als.npn, beta = 0.1)
#> WARNING: input graph is not acyclic !
#>  Applying graph -> DAG conversion...
#> DAG conversion : TRUE 
#> Node Linear Ordering with TO setting
#> 
gplot(dag$dag)

ext <- resizeGraph(g=list(dag$dag, dag$dag.new), gnet = gnet, d = 2)
#> 
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#> 
#>  n. edges to be evaluated: 46 
#>  n. edges selected from interactome: 16 
#> 
gplot(ext) 


# Create a directed graph from correlation matrix, using
# i) an empty graph as causal graph,
# ii) a covariance graph,
# iii) KEGG as reference:

corr2graph<- function(R, n, alpha=5e-6, ...)
{
  Z <- qnorm(alpha/2, lower.tail=FALSE)
thr <- (exp(2*Z/sqrt(n-3))-1)/(exp(2*Z/sqrt(n-3))+1)
  A <- ifelse(abs(R) > thr, 1, 0)
  diag(A) <- 0
  return(graph_from_adjacency_matrix(A, mode="undirected"))
}

v <- which(colnames(als.npn) %in% V(G)$name)
selectedData <- als.npn[, v]
G0 <- make_empty_graph(n = ncol(selectedData))
V(G0)$name <- colnames(selectedData)
G1 <- corr2graph(R = cor(selectedData), n= nrow(selectedData))
ext <- resizeGraph(g=list(G0, G1), gnet = gnet, d = 2, v = TRUE)
#> 
 edge set= 1 of 130
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#> 
#>  n. edges to be evaluated: 130 
#>  n. edges selected from interactome: 72 
#> 

#Graphs
old.par <- par(no.readonly = TRUE)
par(mfrow=c(1,2), mar=rep(1,4))
plot(G1, layout = layout.circle)
plot(ext, layout = layout.circle)
#> Warning: vertex attribute color contains NAs. Replacing with default value 1

par(old.par)
# }