---
title: "Graph gallery: further examples"
output:
  rmarkdown::html_vignette:
    toc: true
vignette: >
  %\VignetteIndexEntry{Graph gallery: further examples}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

<style>
body { max-width: 1050px; }
body:has(nav.navbar) { max-width: none; }
.ivue-legend { max-width: 100%; }
.rglWebGL { max-width: 100%; }
th, td { vertical-align: top; }
pre { overflow-x: auto; }
</style>

For a new graph-distance embedding, start with SGD metric MDS and use
[sparse mode](sparse-metric-mds.html) when full fitting is too costly.
The weighted-GRIP and edge-KK examples here document alternatives or saved
comparisons; they are not an automatic large-graph pipeline.

```{r setup, include=FALSE}
library(grip)
knitr::opts_chunk$set(dev="jpeg", dev.args=list(quality=90), fig.retina=1, dpi=72, collapse=TRUE,comment='#>',fig.width=9,fig.height=5,out.width='100%')
source(system.file('scripts','vignette-views.R',package='grip'),local=TRUE)
```

Installed figures use static projections. To enable 3D rotation and layout
selection, render with `options(grip.vignette.interactive = TRUE)` and
**ivue** and **rgl** installed.


This companion contains the other nine graphs from the same saved gallery.
See the [main gallery](synthetic-graph-families.html) for the method, errors,
alignment, conversion rules, and complete reproduction recipe. All vertices
and edges remain in every display; the examples are split across pages to
reduce the number of simultaneous 3D views.

```{r gallery-data, include=FALSE}
source(system.file('scripts','graph-examples.R',package='grip'),local=TRUE)
bundle <- readRDS(system.file('extdata','graph-examples','layouts.rds',package='grip'))
have.ivue <- documentation.interactive()
```

```{r selected, include=FALSE}
gallery.ids <- c('dwt_307','494_bus','lesmis','dwt_66','karate','tree','saddle','paraboloid','torus')
```

```{r gallery-pages, results='asis', echo=FALSE}
cat(knitr::knit_child(system.file('scripts','graph-gallery.Rmd',package='grip'),
  envir=environment(),quiet=TRUE),sep='\n')
```


## Construction examples

These examples retain the distinctive irregular and recursive families from
the former website gallery. They compare generating coordinates with weighted
GRIP, separately from the saved metric-MDS/edge-KK collection above. These new
teaching fits use the stated seed and the current package; they do not extend
the saved MDS timing experiment. For these two teaching views only, each fit
is translated, rotated/reflected, and uniformly resized to match the generating
reference's root-mean-square radius. The caption reports the display multipliers.

### A folded irregular annulus

```{r annulus-recipe}
annulus <- irregular.annulus.surface.graph(rings=5,outer.count=36,
  inner.radius=.42,surface='folded',amplitude=.2)
annulus.fit <- grip(edges=annulus$edges,n=annulus$n,edge.weights=annulus$edge_weights,
  dim=3,metric='edge_length',preset='irregular',seed=4)
```

```{r annulus-view, echo=FALSE}
documentation.view(list('Weighted GRIP'=annulus.fit),annulus$edges,
  reference=annulus$coords_surface,common.size=TRUE,
  description='Folded annulus: gray generating reference and weighted GRIP. Aligned at a common overall size for display.')
```

The inner boundary forces routes around the hole. The gray generating surface
helps explain the graph construction; it is not an exact Euclidean realization
of every graph distance.

### A recursive cross pattern

```{r vicsek-recipe}
cross <- vicsek.surface.graph(level=3,surface='ripple',amplitude=.55)
cross.fit <- grip(edges=cross$edges,n=cross$n,edge.weights=cross$edge_weights,
  dim=3,metric='edge_length',preset='carpet',seed=3)
```

```{r vicsek-view, echo=FALSE}
documentation.view(list('Weighted GRIP'=cross.fit),cross$edges,
  reference=cross$coords_surface,common.size=TRUE,
  description='Recursive Vicsek pattern on a rippled surface. Aligned at a common overall size for display.')
```

Recursion introduces repeated branches and bottlenecks. For the recorded
stages of a related planar recursive construction, see
[Tracing and diagnosing layouts](grip-trace-and-diagnostics.html).