Nothing

```
# model averaging for bootstrapped network structures.
averaged.network.backend = function(strength, threshold) {
nodes = attr(strength, "nodes")
e = empty.graph(nodes)
# arcs with a strength of one should always be selected, regardless of
# the threshold.
significant = (strength$strength > threshold) | (strength$strength == 1)
# filter also the direction if present in the bn.strength object.
if ("direction" %in% names(strength))
significant = significant & (strength$direction >= 0.5)
# nothing to see, move along.
if (!any(significant))
return(e)
candidate.arcs = as.matrix(strength[significant, c("from", "to"), drop = FALSE])
if (all(which.undirected(candidate.arcs))) {
# update the arcs of the network, no cycles.
e$arcs = candidate.arcs
}#THEN
else {
# update the arcs of the network, minding cycles.
e$arcs = .Call(call_smart_network_averaging,
arcs = candidate.arcs,
nodes = nodes,
weights = strength$strength[significant])
}#ELSE
# update the network structure.
e$nodes = cache.structure(nodes, arcs = e$arcs)
# add back illegal arcs, so that cpdag() works correctly.
if ("illegal" %in% names(attributes(strength)))
e$learning$illegal = attr(strength, "illegal")
return(e)
}#AVERAGED.NETWORK.BACKEND
# compute the significance threshold for Friedman's confidence.
threshold = function(strength, method = "l1") {
# do not blow up with graphs with only 1 node.
if (nrow(strength) == 0)
return(0)
e = ecdf(strength$strength)
u = knots(e)
if (method == "l1") {
norm = function(p)
sum( diff(unique(c(0, u, 1))) * abs(e(unique(c(0, u[u < 1]))) - p))
}#THEN
p0 = optimize(f = norm, interval = c(0, 1))$minimum
# double-check the boundaries, they are legal solutions but optimize() does
# not check them.
if (norm(1) < norm(p0))
p0 = 1
if (norm(0) < norm(p0))
p0 = 0
quantile(strength$strength, p0, type = 1, names = FALSE)
}#THRESHOLD
```

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