Choosing Layouts for Real Data

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Two real-data workflows

For real graphs there is usually no single correct picture waiting to be recovered. The practical goal is to find a layout that is:

faithful to graph structure,
visually coherent,
and stable enough to trust.

In grip, that usually leads to one of two workflows:

a combinatorial workflow for unweighted or topology-first graphs, based on compare.layouts() and score.layout(),
a weighted workflow for graphs whose edge lengths carry real geometry, based on weighted.grip(), weighted scoring, and often 3D layouts.

This vignette shows both patterns. The bundled karate-club and Krackhardt-kite graphs illustrate the first one. The bundled coarsened HMP/U01 graph illustrates the second.

The same package-level decision rule still applies:

ordinary unweighted or topology-first graphs: start with grip(), compare.layouts(), and score.layout(),
weighted graphs with meaningful edge lengths: start with weighted.grip(), usually with 3D in the candidate set,
when a promising solve needs explanation rather than another run: add trace,
when a smaller weighted candidate set needs stronger metric-aware comparison: add GKK/LGKK as advanced public experimental tools.

library(grip)

The small helpers below keep the plotting code compact.

read.extdata.csv <- function(file.name) {
  candidates <- c(
    system.file("extdata", file.name, package = "grip"),
    file.path("inst", "extdata", file.name),
    file.path("..", "inst", "extdata", file.name)
  )
  path <- candidates[file.exists(candidates)][1L]
  if (!length(path) || is.na(path) || !nzchar(path)) {
    stop("could not locate ", file.name)
  }
  utils::read.csv(path, stringsAsFactors = FALSE)
}

read.edge.csv <- function(file.name) {
  as.matrix(read.extdata.csv(file.name))
}

read.karate.club <- function() {
  labels <- read.extdata.csv("karate-club-membership.csv")
  labels <- labels[order(labels$vertex), , drop = FALSE]
  labels$club
}

compact.summary <- function(x) {
  keep <- intersect(c(
    "candidate",
    "preset",
    "rounds",
    "final.rounds",
    "num.nbrs",
    "repulsion.factor",
    "sampled.stress.mean",
    "edge.length.cv.mean",
    "sampled.nonedge.sep.ratio.mean",
    "cluster.separation.mean",
    "stability.procrustes.mean",
    "score.composite"
  ), names(x))
  x[, keep, drop = FALSE]
}

plot.layout.triptych <- function(layouts,
                                 edges,
                                 titles,
                                 vertex.cols = NULL) {
  if (is.null(vertex.cols)) {
    vertex.cols <- rep(list("black"), length(layouts))
  }
  op <- par(mfrow = c(1, length(layouts)), mar = c(1.2, 1.2, 3.2, 1.2))
  on.exit(par(op), add = TRUE)
  for (i in seq_along(layouts)) {
    plot.layout(
      layouts[[i]],
      edges,
      projection = if (ncol(layouts[[i]]) == 3L) "ortho" else NULL,
      vertex.col = vertex.cols[[i]],
      edge.col = "gray82",
      main = titles[[i]]
    )
  }
}

edge.matrix.from.adj <- function(adj.list) {
  edges <- list()
  idx <- 0L
  for (u in seq_along(adj.list)) {
    nbrs <- adj.list[[u]]
    nbrs <- nbrs[nbrs > u]
    if (!length(nbrs)) next
    for (v in nbrs) {
      idx <- idx + 1L
      edges[[idx]] <- c(u, v)
    }
  }
  do.call(rbind, edges)
}

read.hmp.vignette.results <- function() {
  path <- system.file(
    "extdata", "hmp_u01_gc_coarse", "vignette_results.rds",
    package = "grip"
  )
  if (!nzchar(path)) {
    stop("could not locate bundled HMP/U01 vignette results")
  }
  readRDS(path)
}

Workflow 1: shortlist candidates on an unweighted real graph

The karate-club network is a good real-data starting point because it is small, interpretable, and comes with a known split between the Mr. Hi and Officer factions (Zachary 1977).

karate.edges <- read.edge.csv("karate-club-edges.csv")
karate.n <- max(karate.edges)
karate.club <- read.karate.club()
karate.cols <- ifelse(karate.club == "Mr. Hi", "#1b9e77", "#d95f02")

karate.cmp <- compare.layouts(
  edges = karate.edges,
  n = karate.n,
  dim = 3,
  candidates = c("default", "tree", "mesh"),
  clusters = karate.club,
  seeds = 1:3,
  sample.size.stress = 1000L,
  sample.size.nonedge = 2000L,
  edge.crossings = "never",
  return.layouts = TRUE
)

knitr::kable(compact.summary(karate.cmp$summary), digits = 3)

candidate	preset	rounds	final.rounds	num.nbrs	repulsion.factor	sampled.stress.mean	edge.length.cv.mean	sampled.nonedge.sep.ratio.mean	cluster.separation.mean	stability.procrustes.mean	score.composite
tree	tree	64	160	8	0.0	0.768	0.524	0.012	3.965	0.075	0.316
default	NA	20	25	10	1.0	11.411	0.207	0.206	1.134	0.427	0.579
mesh	mesh	128	128	20	1.5	10.483	0.224	0.000	2.029	0.215	0.605

plot.layout.triptych(
  layouts = list(
    karate.cmp$layouts$default[["1"]],
    karate.cmp$layouts$tree[["1"]],
    karate.cmp$layouts$mesh[["1"]]
  ),
  edges = karate.edges,
  titles = c("default", "tree", "mesh"),
  vertex.cols = rep(list(karate.cols), 3)
)

This is the main combinatorial real-data pattern:

compare a small number of plausible candidates,
use several seeds,
read the score table before picking a favorite picture,
and use metadata-aware metrics such as cluster.separation when they are genuinely meaningful.

A small local search around the strongest region

After the first shortlist, it is usually better to search locally than to launch a wide, blind parameter sweep.

karate.search <- compare.layouts(
  edges = karate.edges,
  n = karate.n,
  dim = 3,
  search = list(
    candidate.prefix = "karate.search",
    preset = c("tree"),
    rounds = c(96L, 128L),
    final_rounds = c(192L, 224L),
    repulsion_factor = c(1.25, 2.0)
  ),
  clusters = karate.club,
  seeds = 1:3,
  sample.size.stress = 1000L,
  sample.size.nonedge = 2000L,
  edge.crossings = "never",
  return.layouts = TRUE
)

knitr::kable(head(compact.summary(karate.search$summary), 6), digits = 3)

candidate	preset	rounds	final.rounds	num.nbrs	repulsion.factor	sampled.stress.mean	edge.length.cv.mean	cluster.separation.mean	stability.procrustes.mean	score.composite
karate.search.rounds.128.final_rounds.192.repulsion_factor.125	tree	128	192	8	1.25	9.634	0.191	1.775	0.336	0.316
karate.search.rounds.128.final_rounds.224.repulsion_factor.125	tree	128	224	8	1.25	9.923	0.190	1.716	0.321	0.406
karate.search.rounds.96.final_rounds.192.repulsion_factor.125	tree	96	192	8	1.25	9.387	0.198	1.815	0.283	0.429
karate.search.rounds.96.final_rounds.224.repulsion_factor.125	tree	96	224	8	1.25	9.683	0.196	1.764	0.280	0.459
karate.search.rounds.96.final_rounds.224.repulsion_factor.2	tree	96	224	8	2.00	10.876	0.196	1.766	0.315	0.526
karate.search.rounds.128.final_rounds.224.repulsion_factor.2	tree	128	224	8	2.00	11.380	0.191	1.718	0.276	0.594

op <- par(mfrow = c(1, 2), mar = c(4, 4, 2.2, 1))
on.exit(par(op), add = TRUE)

plot(
  karate.search$summary$repulsion.factor,
  karate.search$summary$sampled.stress.mean,
  pch = 19,
  col = "#1F3B73",
  xlab = "repulsion.factor",
  ylab = "sampled.stress.mean",
  main = "stress across local search"
)


plot(
  karate.search$summary$repulsion.factor,
  karate.search$summary$cluster.separation.mean,
  pch = 19,
  col = "#B24745",
  xlab = "repulsion.factor",
  ylab = "cluster.separation.mean",
  main = "cluster separation across search"
)

The point is not to overfit the graph. It is to identify a stable, sensible region of the parameter space.

A second small graph: direct scoring

Not every real-data task needs a comparison grid. On very small graphs it is often enough to realize one or two layouts and score them directly.

kite.edges <- read.edge.csv("krackhardt-kite-edges.csv")
kite.n <- max(kite.edges)

kite.coords <- grip(
  kite.edges,
  n = kite.n,
  dim = 2,
  preset = "tree",
  seed = 5
)

score.layout(kite.coords, edges = kite.edges, n = kite.n)
#>   n.vertices n.edges dim sampled.stress edge.length.cv median.edge.length
#> 1         10      18   2       1.262622      0.7467341           1.131498
#>   sampled.nonedge.sep.ratio edge.crossings cluster.separation
#> 1                 0.3247241              2                 NA

plot.layout(
  kite.coords,
  kite.edges,
  main = "Krackhardt kite",
  pch = 16,
  cex = 0.9,
  edge.col = "gray80"
)

score.layout() is especially useful when:

the layout was generated once and cached,
the layout came from another tool,
or you want to score a hand-curated final picture.

Workflow 2: when the real graph is weighted

Some real graphs are not just topological. Their edge lengths carry information that should influence the layout itself. The bundled hmp.u01.gc.coarse example is in that category: it is a weighted, coarsened real-world graph from the HMP+U01 16S amplicon analysis pipeline.

data(hmp.u01.gc.coarse)

hmp.graph.info <- data.frame(
  quantity = c(
    "coarse vertices",
    "weighted undirected edges",
    "selected k",
    "representation"
  ),
  value = c(
    hmp.u01.gc.coarse$graph_info$coarse_vertices,
    hmp.u01.gc.coarse$graph_info$edge_count,
    hmp.u01.gc.coarse$graph_info$selected_k,
    hmp.u01.gc.coarse$graph_info$representation
  ),
  stringsAsFactors = FALSE
)

hmp.weight.summary <- as.data.frame(t(summary(unlist(
  hmp.u01.gc.coarse$weight_list,
  use.names = FALSE
))))

knitr::kable(hmp.graph.info)

quantity	value
coarse vertices	1828
weighted undirected edges	4656
selected k	3
representation	>=1% relative abundance + PCA

knitr::kable(hmp.weight.summary, digits = 4)

Var1	Var2	Freq
A	Min.	0.0002
A	1st Qu.	0.0409
A	Median	0.0990
A	Mean	0.1370
A	3rd Qu.	0.1884
A	Max.	1.2078

A useful practical signal is that the edge-weight variation is large enough to matter.

hmp.weight.cv <- with(
  list(w = unlist(hmp.u01.gc.coarse$weight_list, use.names = FALSE)),
  stats::sd(w) / mean(w)
)

hmp.weight.cv
#> [1] 1.004854

For graphs like this, the weighted workflow differs from the combinatorial one:

start with weighted.grip() rather than grip(),
prefer 3D as the primary layout space,
and assess geometry with a weighted graph-metric criterion when possible.

A plain grip() solve can still be useful here as a topology-first baseline, but it should not be the default when the edge lengths themselves matter scientifically.

The direct weighted-candidate pattern looks like this:

weighted.candidates <- list(
  weighted_default = weighted.grip(
    adj_list = hmp.u01.gc.coarse$adj_list,
    weight_list = hmp.u01.gc.coarse$weight_list,
    n = length(hmp.u01.gc.coarse$adj_list),
    dim = 3,
    seed = 1
  ),
  weighted_irregular = weighted.grip(
    adj_list = hmp.u01.gc.coarse$adj_list,
    weight_list = hmp.u01.gc.coarse$weight_list,
    n = length(hmp.u01.gc.coarse$adj_list),
    dim = 3,
    preset = "irregular",
    seed = 1
  )
)

weighted.scores <- lapply(weighted.candidates, function(coords) {
  score.layout(
    coords,
    adj_list = hmp.u01.gc.coarse$adj_list,
    weight_list = hmp.u01.gc.coarse$weight_list,
    n = length(hmp.u01.gc.coarse$adj_list),
    clusters = hmp.u01.gc.coarse$vertex_data$cst,
    sample.size.stress = 2000L,
    sample.size.nonedge = 5000L,
    edge.crossings = "never"
  )
})

For smaller weighted real graphs, it is also worth comparing candidate layouts with:

prepare.geodesic.kk()
score.geodesic.kk()
prepare.landmark.geodesic.kk()
score.landmark.geodesic.kk()

because those make the weighted graph metric explicit rather than relying only on the general-purpose layout heuristics. These GKK/LGKK helpers are public, but they are best treated as advanced experimental tools layered on top of the main weighted workflow.

HMP/U01 as a large weighted case study

The package also ships a larger, more realistic weighted example: hmp.u01.gc.coarse. This graph is large enough that a full search is too heavy for a regular vignette build, so the package includes bundled precomputed results for a representative 3D search.

hmp.results <- read.hmp.vignette.results()
hmp.edges <- edge.matrix.from.adj(hmp.u01.gc.coarse$adj_list)
hmp.cst <- hmp.u01.gc.coarse$vertex_data$cst
hmp.cst.levels <- sort(unique(hmp.cst))
hmp.cst.cols <- setNames(grDevices::hcl.colors(length(hmp.cst.levels), "Dark 3"),
                         hmp.cst.levels)
hmp.cst.col <- hmp.cst.cols[hmp.cst]

hmp.case.info <- data.frame(
  quantity = c(
    "source dataset",
    "representation",
    "selected k",
    "original giant-component vertices",
    "coarsened vertices",
    "weighted undirected edges"
  ),
  value = c(
    hmp.u01.gc.coarse$graph_info$source_dataset,
    hmp.u01.gc.coarse$graph_info$representation,
    hmp.u01.gc.coarse$graph_info$selected_k,
    hmp.u01.gc.coarse$graph_info$original_vertices,
    hmp.u01.gc.coarse$graph_info$coarse_vertices,
    hmp.u01.gc.coarse$graph_info$edge_count
  ),
  stringsAsFactors = FALSE
)

knitr::kable(hmp.case.info)

quantity	value
source dataset	HMP+U01 16S amplicon
representation	>=1% relative abundance + PCA
selected k	3
original giant-component vertices	6474
coarsened vertices	1828
weighted undirected edges	4656

The bundled preset comparison used three 3D candidates:

default
tree
torus

hmp.preset.keep <- c(
  "candidate",
  "sampled.stress.mean",
  "edge.length.cv.mean",
  "sampled.nonedge.sep.ratio.mean",
  "cluster.separation.mean",
  "score.composite"
)

knitr::kable(hmp.results$preset_summary[, hmp.preset.keep], digits = 3)

candidate	sampled.stress.mean	edge.length.cv.mean	sampled.nonedge.sep.ratio.mean	cluster.separation.mean	score.composite
default	93.923	0.701	0.454	1.693	0.062
tree	96.322	1.073	0.290	3.400	0.594
torus	130.266	0.886	0.167	3.142	0.844

plot.layout.triptych(
  layouts = list(
    hmp.results$layouts$preset$default,
    hmp.results$layouts$preset$tree,
    hmp.results$layouts$preset$torus
  ),
  edges = hmp.edges,
  titles = c("default", "tree", "torus"),
  vertex.cols = rep(list(hmp.cst.col), 3)
)

For this graph, the useful next step was a small local search around the stronger region rather than a broad blind sweep.

hmp.local.keep <- c(
  "candidate",
  "rounds",
  "final.rounds",
  "repulsion.factor",
  "sampled.stress.mean",
  "cluster.separation.mean",
  "score.composite"
)

knitr::kable(
  head(hmp.results$local_search_summary[, hmp.local.keep], 4),
  digits = 3
)

candidate	rounds	final.rounds	repulsion.factor	sampled.stress.mean	cluster.separation.mean	score.composite
hmp.local.final_rounds.288.repulsion_factor.125	192	288	1.25	96.677	3.324	0.271
hmp.local.final_rounds.288.repulsion_factor.075	192	288	0.75	96.333	3.407	0.333
hmp.local.final_rounds.224.repulsion_factor.125	192	224	1.25	115.790	3.232	0.667
hmp.local.final_rounds.224.repulsion_factor.075	192	224	0.75	115.297	3.326	0.729

top.local <- hmp.results$top_local_candidates
plot.layout.triptych(
  layouts = lapply(top.local, function(nm) hmp.results$layouts$local[[nm]]),
  edges = hmp.edges,
  titles = top.local,
  vertex.cols = rep(list(hmp.cst.col), length(top.local))
)

This is the large-graph weighted pattern in practice:

keep the graph weighted,
prefer 3D,
use a short preset shortlist,
then search locally around the strongest region,
and interpret the final layouts together with domain labels such as CST.

For the HMP/U01-specific object structure, coarsening provenance, and bundled artifact paths, see the companion article HMP/U01 Weighted Graph Case Study.

Practical guidance

Use compare.layouts() for unweighted or topology-first real graphs.
Use a small candidate shortlist before any local search.
Keep 3D in the candidate set when the graph is structurally rich.
If edge lengths are scientifically meaningful, switch to weighted.grip().
Use trace.grip() or trace.weighted.grip() when a promising solve needs diagnosis rather than another broad sweep.
For weighted graphs, treat 3D as the primary evaluation space and use GKK/LGKK scoring only when the graph is small enough for those advanced experimental checks to be practical.

References

Zachary, Wayne W. 1977. “An Information Flow Model for Conflict and Fission in Small Groups.” Journal of Anthropological Research 33 (4): 452–73.

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