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.
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 ingraph2will 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 functionall_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
graph2as validated, otherwise the edges are removed. For instance, ifd = 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 mostd - 1mediators are allowed). Typicaldvalues include2(at most one mediator), ormean_distance(gnet)(i.e., the average shortest path length for the reference network). Setting d = 0, is equivalent tognet = 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>
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 23 1
#>
#> Percent of vertices in the giant component: 13.5 %
#>
#> is.simple is.dag is.directed is.weighted
#> TRUE FALSE TRUE TRUE
#>
#> which.mutual.FALSE
#> 28
#> IGRAPH 6ac77c5 DNW- 23 28 --
#> + attr: name (v/c), weight (e/n)
# 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 = kegg, d = 2)
#>
edge set= 1 of 39
edge set= 2 of 39
edge set= 3 of 39
edge set= 4 of 39
edge set= 5 of 39
edge set= 6 of 39
edge set= 7 of 39
edge set= 8 of 39
edge set= 9 of 39
edge set= 10 of 39
edge set= 11 of 39
edge set= 12 of 39
edge set= 13 of 39
edge set= 14 of 39
edge set= 15 of 39
edge set= 16 of 39
edge set= 17 of 39
edge set= 18 of 39
edge set= 19 of 39
edge set= 20 of 39
edge set= 21 of 39
edge set= 22 of 39
edge set= 23 of 39
edge set= 24 of 39
edge set= 25 of 39
edge set= 26 of 39
edge set= 27 of 39
edge set= 28 of 39
edge set= 29 of 39
edge set= 30 of 39
edge set= 31 of 39
edge set= 32 of 39
edge set= 33 of 39
edge set= 34 of 39
edge set= 35 of 39
edge set= 36 of 39
edge set= 37 of 39
edge set= 38 of 39
edge set= 39 of 39
#>
#> n. edges to be evaluated: 39
#> n. edges selected from interactome: 15
#>
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 = kegg, d = 2, v = TRUE)
#>
edge set= 1 of 104
edge set= 2 of 104
edge set= 3 of 104
edge set= 4 of 104
edge set= 5 of 104
edge set= 6 of 104
edge set= 7 of 104
edge set= 8 of 104
edge set= 9 of 104
edge set= 10 of 104
edge set= 11 of 104
edge set= 12 of 104
edge set= 13 of 104
edge set= 14 of 104
edge set= 15 of 104
edge set= 16 of 104
edge set= 17 of 104
edge set= 18 of 104
edge set= 19 of 104
edge set= 20 of 104
edge set= 21 of 104
edge set= 22 of 104
edge set= 23 of 104
edge set= 24 of 104
edge set= 25 of 104
edge set= 26 of 104
edge set= 27 of 104
edge set= 28 of 104
edge set= 29 of 104
edge set= 30 of 104
edge set= 31 of 104
edge set= 32 of 104
edge set= 33 of 104
edge set= 34 of 104
edge set= 35 of 104
edge set= 36 of 104
edge set= 37 of 104
edge set= 38 of 104
edge set= 39 of 104
edge set= 40 of 104
edge set= 41 of 104
edge set= 42 of 104
edge set= 43 of 104
edge set= 44 of 104
edge set= 45 of 104
edge set= 46 of 104
edge set= 47 of 104
edge set= 48 of 104
edge set= 49 of 104
edge set= 50 of 104
edge set= 51 of 104
edge set= 52 of 104
edge set= 53 of 104
edge set= 54 of 104
edge set= 55 of 104
edge set= 56 of 104
edge set= 57 of 104
edge set= 58 of 104
edge set= 59 of 104
edge set= 60 of 104
edge set= 61 of 104
edge set= 62 of 104
edge set= 63 of 104
edge set= 64 of 104
edge set= 65 of 104
edge set= 66 of 104
edge set= 67 of 104
edge set= 68 of 104
edge set= 69 of 104
edge set= 70 of 104
edge set= 71 of 104
edge set= 72 of 104
edge set= 73 of 104
edge set= 74 of 104
edge set= 75 of 104
edge set= 76 of 104
edge set= 77 of 104
edge set= 78 of 104
edge set= 79 of 104
edge set= 80 of 104
edge set= 81 of 104
edge set= 82 of 104
edge set= 83 of 104
edge set= 84 of 104
edge set= 85 of 104
edge set= 86 of 104
edge set= 87 of 104
edge set= 88 of 104
edge set= 89 of 104
edge set= 90 of 104
edge set= 91 of 104
edge set= 92 of 104
edge set= 93 of 104
edge set= 94 of 104
edge set= 95 of 104
edge set= 96 of 104
edge set= 97 of 104
edge set= 98 of 104
edge set= 99 of 104
edge set= 100 of 104
edge set= 101 of 104
edge set= 102 of 104
edge set= 103 of 104
edge set= 104 of 104
#>
#> n. edges to be evaluated: 104
#> n. edges selected from interactome: 64
#>
#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)
par(old.par)
# }