# Drawing Networks as Data Art: Literature on Placement, Bundling, Time, and Flow

- Author: Shuichiro Ogawa (Design Researcher / Design Consultant), https://jamjet-iqbal.com/
- Published: 2026-09-23; updated: 2026-09-24
- Canonical (HTML): https://jamjet-iqbal.com/en/notes/network-data-art-methods-literature/
- Japanese version: https://jamjet-iqbal.com/notes/network-data-art-methods-literature/ (Markdown: https://jamjet-iqbal.com/notes/network-data-art-methods-literature.md)
- Language: en
- Keywords: network-visualization, force-directed-layout, edge-bundling, arc-diagram, streamgraph, marbling, data-art, hive-plot, watercolor, ink-diffusion, literature

> A force-directed drawing of a network looks like the one true shape of that network, but it is only one of many arrangements. This note lays out the force equations of force-directed placement (Eades 1984, ForceAtlas2) and force-directed placement on a sphere (Kobourov and Wampler 2005), hive plots that set coordinates from attributes, edge bundling (Holten 2006), layouts along a single axis and along time (arc diagrams, ThemeRiver, streamgraphs, alluvial diagrams), mathematical marbling that makes patterns by dropping paint on water (Lu et al. 2012, Jaffer's drop mapping), prior works that treat data as art, and the curves and numerical methods used to draw the lines (centripetal Catmull–Rom curves, uniform B-splines, the midpoint method, Gaussian kernels, stream functions), and ways of rendering ink bleeding into paper (the watercolour model of Curtis et al. 1997, MoXi by Chu and Tai 2005, sumi painting by Guo and Kunii 1991), each with how far it was verified (full text, abstract, or bibliographic only). On this wiki's /network page, these methods were used to rearrange the same co-citation relations, which stay fixed while the arrangement changes with the method and the seed. The space each force-directed work is laid out in is fixed per work (marbling: a plane with the drawing area's aspect ratio; weave: an unbounded free plane; constellation: a sphere projected stereographically). The variation across seeds comes, for the weave, from initial-configuration families and ranges of force coefficients (including ForceAtlas2's LinLog and strong-gravity options), and for marbling and the constellation, from jitter in the initial placement and small ranges of coefficients.

A force-directed drawing of a network looks like the shape of the network itself.
Groups gather into islands, and a few edges bridge one island to the next.
Viewers want to read nearby things as similar and central things as important.

Building this wiki's [Citation Network](/en/network), we were drawn into the same reading.
Yet from the same references and the same co-citation pairs, changing only the random seed produces a picture with islands in different places and facing different directions.
Comparing the pictures does not settle which one is the true shape.

The literature treats this unease as a premise.
Gansner, Koren, and North (2005) name robustness against local minima as an advantage of layout by stress majorization, and compare results over 25 random initializations (verified in full text).
Framing the comparison this way already assumes that the outcome of a layout can depend on its initial placement.
Venturini, Jacomy, and Jensen (2021) discuss, as **relational ambiguity**, the point that nodes placed close together by a force-directed layout are not necessarily close in meaning.
Krzywinski et al. (2012) proposed hive plots, which avoid the problem on the placement side.
The publisher's abstract states that because axes and coordinates are set by node attributes, hive plots, unlike force-directed layouts, are reproducible and comparable (verified at abstract level).

A force-directed picture is one arrangement among many.
What other families of arrangement are there, and what does each hold fixed and what does it let move?

Each source below is tagged with how far it was read (full text, abstract, or bibliographic only).
For sources verified only bibliographically, nothing beyond the title is described.

## What force-directed placement balances

Force-directed placement defines forces between nodes and searches for positions where the forces balance.
What counts as a force changes the shape of the picture.

Eades's (1984) spring embedder treats vertices as rings and edges as springs (verified in full text).
The spring force is not proportional to distance; it acts with logarithmic strength, `c1 · log(d / c2)`.
Here d is the length of the spring (the distance between two vertices), and c1 and c2 are constants.

ForceAtlas2 (Jacomy et al., 2014) is a continuous layout algorithm designed for Gephi, and it defines its forces with the following equations (verified in full text).

- **Attraction**: `F_a = d` (Eq. 1). Proportional to distance d.
- **Repulsion**: `F_r = k_r (deg1 + 1)(deg2 + 1) / d` (Eq. 2). Proportional to the product of each node's degree plus one, and inversely proportional to distance.
- **LinLog attraction**: `F_a = log(1 + d)` (Eq. 3). An option that replaces attraction with the logarithm of distance.
- **Gravity**: `F_g = k_g (deg + 1)` (Eq. 4). With strong gravity, this is multiplied by distance d (Eq. 5).
- **Edge weight**: `F_a = w^δ · d` (Eq. 6). The edge weight w, raised to the power δ, multiplies the attraction.

Laid side by side, the equations show where degree enters.
deg + 1 appears as a coefficient of repulsion and of gravity, so higher-degree nodes push each other away harder and feel stronger gravity.
The word "mass", however, does not appear in the paper.
ForceAtlas2 uses degree as a coefficient on forces; it does not define mass.

The official d3-force documentation fixes mass explicitly.
The simulation uses velocity Verlet integration with a time step of Δt = 1, and every particle has mass m = 1.
Since the mass is 1, force equals acceleration.
alpha corresponds to the temperature in simulated annealing, and the simulation stops once alpha falls below alphaMin.
The many-body repulsion (forceManyBody) is computed with a quadtree and the Barnes–Hut approximation (theta 0.9).
The default random source is a linear congruential generator with a fixed seed.

Fixing the random numbers lets the same picture be reproduced any number of times.
But reproducing one arrangement is not the same as the arrangement being uniquely determined.

The Barnes–Hut approximation originates in Barnes and Hut's (1986) hierarchical O(N log N) force-calculation algorithm.
The design of D3 itself is described by Bostock, Ogievetsky, and Heer (2011).
Classics of graph drawing also include Fruchterman and Reingold's (1991) force-directed placement and Kamada and Kawai's (1989) algorithm for drawing general undirected graphs.
Noack (2009) states in its title the proposition that modularity clustering is force-directed layout.
The five sources in this paragraph were verified bibliographically only.

## Setting coordinates from attributes instead of forces

In force-directed placement, positions follow from the balance of forces.
Krzywinski et al.'s (2012) hive plots set positions from attributes.
According to the abstract, node attributes determine which axis a node goes on and where it sits along that axis.
The abstract's claim is that the same data yields the same figure, so figures of different networks can be placed side by side and compared (verified at abstract level).

In 2009, Krzywinski and co-authors published Circos.
Its title calls Circos "an information aesthetic for comparative genomics".
It is an example of a visualization methods paper naming aesthetics in its title.
The abstract was checked, but its description of the layout method was not, so it is not described here.

## Bundling edges

Even once node positions are set, many edges turn the picture into a mass of lines.
Holten's (2006) hierarchical edge bundles is a method for visualizing adjacency relations in hierarchical data.
A single bundling strength, β, controls the drawing continuously from straight lines (the raw connections) to bundles (the implicit adjacency between parents in the hierarchy) (verified in full text).
From the same data, β alone moves the picture between one that shows individual connections and one that shows relations between groups.

According to the abstract, Holten and van Wijk's (2009) force-directed edge bundling bundles edges by treating them as springs that attract one another (verified at abstract level).

## Arranging along a single axis and along time

Another approach skips choosing positions in two dimensions and lines elements up along a single axis.
According to the abstract, Wattenberg's (2002) arc diagram connects pairs of identical substrings in a string with arcs, showing the structure of repetition (verified at abstract level).
What the arc height encodes was not checked, because the full text was not reached.

Taking time as the axis leads to a family that draws changing quantities as the thickness of bands.
According to the abstract, Havre et al.'s (2002) ThemeRiver represents the strength of themes in a document collection as the width of bands in a river flowing along time (verified at abstract level).
Byron and Wattenberg (2008) showed that stacked graphs, ThemeRiver, and Streamgraph each minimize a different energy function (verified in full text).
The same paper also proposes how to color and order the layers.
Differences in the shape of the baseline can therefore be explained as differences in the quantity being minimized, not as matters of taste.

Some figures show the network itself reorganizing over time.
Rosvall and Bergstrom (2010) presented the alluvial diagram as a figure for mapping change in large networks (verified in full text).

## Drawing as patterns on water

Marbling is a technique that drops paint or ink on water and makes patterns with the flow of the water.
It is not a network method.
Still, if the order and places of the drops are set from data, a network's history can be drawn as a pattern on water (how this wiki does so is described below).

Lu, Jaffer, Jin, Zhao, and Mao (2012) published a mathematical way of simulating marbling in *IEEE Computer Graphics and Applications*.
According to the abstract, simulating marbling with closed-form expressions improves control, ease of implementation, parallelism, and speed, allowing real-time visual feedback and flowing animations (verified at abstract level; the full text was not obtained).
The abstract also says designs can start from a blank sheet, raster images, or videos.

The drop formula itself is written by the co-author Jaffer on his explanatory page *Dropping Paint* (verified in full text).
When a drop of radius r is placed with center C, a point P on the water moves radially away from the center to C + (P − C) · √(1 + r² / |P − C|²).
If a drop of area a is placed and then a drop of area b is placed at the same center, the covered area becomes a + b.
By comparing the areas of annuli, the page shows that this mapping preserves the area of every neighbourhood that does not contain C.
An annulus pushed outward keeps its area and becomes thinner than before.
The earlier a drop, the more later drops distort its outline; only the last drop keeps a round outline.

## Building the curves

Once the points are placed, how a curve joins them still changes how the lines read.
A curve that overshoots, or loops within a span, runs through places unrelated to the relation it draws and invites misreading.

A **Catmull–Rom curve** is a cubic interpolating curve that passes through every control point.
Catmull and Rom (1974) is given as the standard source (bibliographic only).
Yuksel, Schaefer, and Keyser (2009) treat the family whose knot sequence is t_{i+1} = |P_{i+1} − P_i|^α + t_i (equation (1), verified in full text).
α = 0 is the uniform, α = 1/2 the centripetal, and α = 1 the chordal parameterization.
They prove that for cubic Catmull–Rom curves only the centripetal parameterization produces no cusps and no self-intersections within a span (Section 3, Theorems 1 to 3).
Their Figure 3 illustrates, as a pyramid, the algorithm of Barry and Goldman that evaluates a span by stacking linear interpolations.
The original, Barry and Goldman (1988), is given as the standard source (bibliographic only).
The journal version by the same authors (Yuksel, Schaefer, and Keyser, 2011) was checked up to the bibliographic record and abstract.

For the basis of the **uniform cubic B-spline**, de Boor (1978) and Bartels, Beatty, and Barsky (1987) are given as the standard sources (both bibliographic only).
Holten's (2006) hierarchical edge bundles draw an edge as a curve whose control points are the path in the hierarchy, and set the bundling strength by pulling the control points toward the straight line between the end points: P'_i = β P_i + (1 − β)(P_0 + i/(N − 1)(P_{N−1} − P_0)) (Section 3.2, equation (1), verified in full text).

The flow on the water in marbling and the bands of the river figure build their curves numerically.
For the **midpoint method** (second-order Runge–Kutta) that carries points on the water along the flow step by step, Press et al. (1992); for **density estimation** with a Gaussian kernel, Silverman (1986); and for building a velocity field v = (∂ψ/∂y, −∂ψ/∂x) from a **stream function** ψ, Batchelor (1967/2000) are given as the standard sources.
All three were checked bibliographically only; for Press et al., the table of contents confirms that Section 16.1 covers Runge–Kutta methods.
A velocity field built from a stream function has zero divergence, because the order of partial derivatives does not matter (∂²ψ/∂x∂y = ∂²ψ/∂y∂x).
A flow with no sources and no sinks preserves area, so carrying the pattern on the water along it changes the pattern's area only by numerical error.
Jaffer's drop mapping also preserves area away from C.
Both drops and flow move the water continuously without tearing it, so even when they alternate, the ink rings never cross; each push only makes them thinner and longer.

## Modelling ink bleeding into paper

The methods so far decide where points and lines go.
How a line, once placed, looks on paper is the subject of another line of research.
The light look of /network (sumi on washi) borrows its ideas from it.

Curtis et al. (1997) produce the look of watercolour by computing layers of paper, water, and pigment (full text checked).
Paper is represented by a height field and a fluid capacity field (§4.1).
**Edge darkening**, where pigment gathers at the rim of a wet area, is written as a step that removes water near the boundary of the wet area and carries pigment outward (§4.3.3, eq. (3)).
**Granulation**, where pigment settles into the valleys of the paper and looks grainy, is expressed by a coefficient γ through which the paper height governs the adsorption and desorption of pigment (§2.1, §4.5).

How ink spreads through absorbent paper is the subject of MoXi by Chu and Tai (2005).
According to the abstract, it computes percolation in a non-uniform porous medium in real time with the lattice Boltzmann method and reproduces ink dispersing in absorbent paper (abstract checked).
Whether the ink spreads along the fibres of the paper cannot be confirmed from the abstract.

Attempts to compute the bleed of sumi painting go back to Guo and Kunii (1991).
Their model reproduces the bleed from the structure of the paper, the flow of the liquid, and the adsorption of particles; this topic was checked through an index abstract and the related-work section of Curtis et al. (1997) (abstract-equivalent).

No peer-reviewed graphics study that models the fibre structure of washi was found.
The search covered English-language literature; Japanese-language databases were not searched.

## Prior works that treat data as art

For the lineage of works made with data, this note has only confirmed where the works are and their bibliographic details.
Nothing is described about their content or methods beyond the pages that were checked.

Viégas and Wattenberg (2007) discussed artistic data visualization (verified at abstract level).
How to read their definition is covered in [What Data Visualization and Data Art Share, and Where They Differ](https://jamjet-iqbal.com/en/notes/data-viz-vs-data-art-literature/).
Kosara's (2007) title calls visualization criticism "the missing link" between information visualization and art (bibliographic only).
Lima's (2011) *Visual Complexity: Mapping Patterns of Information* is cited here as the source of the term "Networkism".
The passage where the term is defined was not checked.

The existence of Lupi and Posavec's (2016) *Dear Data* was confirmed on the publisher's page, Posavec's *Writing Without Words* on the artist's official page, and Lombardi's *Narrative Structures* on the Whitney Museum's artist page.
For Viégas and Wattenberg's *Wind Map* (2012), the 2012 launch and the authors were confirmed on the artists' official page (hint.fm). Independent sources agree that MoMA holds it.

## How this wiki's /network page uses them

[The Citation Network of This Wiki: Analysis and Artworks Treating Each Note as a Hyperedge](https://jamjet-iqbal.com/en/notes/citation-weave-of-this-wiki/) analyzed the references of this wiki's public notes as a citation network.
References cited by two or more notes are knots, and pairs of knots listed in the same note are linked as co-citations.
**Co-citation** is the relation in which two documents are cited by the same third document (Small, 1973); **bibliographic coupling** is the relation in which two documents cite the same third document (Kessler, 1963).

The works on the [Citation Network](/en/network) page hold these relations fixed and change only the arrangement.
Which knot is linked to which by co-citation is the same in every work.
What changes is where on the plane, and along which axis, those relations are placed.

In the force-directed works (marbling, the weave, and the constellation), knot positions are computed in the browser on every view by forces whose forms are borrowed from ForceAtlas2.
Each knot's mass was set to the number of notes that cite that reference, and acceleration was taken as force divided by mass.
How hard a knot pushes (its charge) is the square root of its mass (in marbling and the constellation, multiplied by a per-knot jitter).
This is this wiki's own design, taken neither from ForceAtlas2 nor from the d3-force defaults.
ForceAtlas2 does not define mass, and d3-force fixes mass at 1.
The pull to the center differs by work.
In the weave, the pull to the center carries no mass, so heavier references are drawn in less.
In marbling and the constellation, the pull to the center is multiplied by mass, so its acceleration does not depend on mass.
What the design supports is only that the same force accelerates a reference cited by more notes less.
In measurements on the weave's layout, a reference cited by more notes also has co-citation springs whose total weight grows roughly in proportion to its mass, and its distance moved per tick was not smaller (the numbers are in "Formulas of the works" in [The Citation Network of This Wiki: Analysis and Artworks Treating Each Note as a Hyperedge](https://jamjet-iqbal.com/en/notes/citation-weave-of-this-wiki/)).
The seed changes on every view; it is not shown on screen and is kept only in the URL hash.
The same seed yields the same picture.
Changing the seed with "Generate again" changes where the groups sit and the details, but the co-citation pairs and their weights do not change.

The space each work is laid out in is fixed per work.
Marbling fills a rectangle with the drawing area's aspect ratio from edge to edge as one sheet of cloth (dense within groups, sparse between them).
The constellation places knots on the unit sphere and maps them to the drawing area by stereographic projection (Snyder, 1987).
According to the abstract, Kobourov and Wampler (2005) generalized force-directed layout from Euclidean geometry to spherical and hyperbolic geometries by extending distance, angle, and force interactions through projections to and from suitably chosen tangent spaces (verified at abstract level).
The constellation on /network does not use that computation; it takes the simpler route of moving stars by forces in three-dimensional space, then pulling their positions back to length 1 and dropping their velocities onto the tangent plane.
In marbling and the constellation, repulsion between references in different groups reaches further and pushes harder than between references in the same group, so the groups can be read from the density of points alone.
ForceAtlas2's repulsion (equation 2) reaches every pair.
Cutting off its reach and separating reach and strength inside and across groups is not in ForceAtlas2; it is this wiki's own design.
The marbling sheet also carries a weak spring that assigns the order in which references joined the network to the horizontal axis (older on the left).
This spring is much weaker than the co-citation attraction, though, and the order of arrival can hardly be read from the horizontal positions of the settled layout (rank correlation −0.20 to +0.34 over five seeds at two aspect ratios, 1.605 and 1.638).
In marbling, time is shown not by where the points sit but by the overlap and stretching of the ink rings and by their bleed, described in the marbling item below.
Only the weave spreads the network on a free plane with no frame and, when drawing, maps it to the drawing area with the seed's rotation and reflection.

The way the picture varies with the seed comes not from the co-citation relations but from the initial configuration and from the force coefficients.
As seen at the start, the comparison by Gansner, Koren, and North (2005) presupposes that the result of a force-directed layout can depend on its initial configuration.
/network uses this dependence on the initial configuration so that no single arrangement is shown as the answer.
In marbling and the constellation, each seed draws the jitter of positions on arrival and the per-knot jitter of charge.
Marbling also draws small ranges of coefficients (0.85 to 1.15 times and so on), and the constellation draws the viewpoint on the celestial sphere.
In the weave, each seed draws a drawing orientation (rotation and reflection), an initial-configuration family (disc, spiral, ring, two lobes, line, or scattered clusters), and multipliers for the force coefficients.
For every family but the disc, each knot's pull to the center is aimed at a template position decided only by the groups and the order in which knots arrived.
In addition, with probability 0.3 the attraction becomes ForceAtlas2's LinLog type (equation 3), and with probability 0.2 the gravity becomes strong gravity (equation 5).
These two forms are options that ForceAtlas2 itself presents, and their equations were verified in the full text.
The families and template positions, the coefficient ranges, and choosing the forms by chance are not in ForceAtlas2; they are this wiki's own design.
Averaged over five seeds (7, 11, 23, 101, 202), the rank correlation between co-citation weight and distance was −0.448 for the weave, −0.426 for the constellation, and −0.468 for marbling.
The silhouette, which measures how clearly groups separate, was 0.464 for the constellation and 0.623 for marbling, against 0.377 for the weave.
In every work, references cited together more often still tend to sit closer, and groups separate most clearly in marbling.
How this was measured, and the full numbers, are under "Why no single arrangement is shown as the answer" in [The Citation Network of This Wiki: Analysis and Artworks Treating Each Note as a Hyperedge](https://jamjet-iqbal.com/en/notes/citation-weave-of-this-wiki/).

The other works each borrow their arrangement from different literature.
The tabs run through the live works, marbling (the default, leftmost), the rings, the weave, and the constellation, and then the stills, the bundle, the arcs, and the river.
Every work places the sources cited by only one note as small faint dots around where that note sits.

- **Marbling**: In the order the notes were written, each note drops one drop of ink and then, at once, a drop of water at the same center (its radius 0.8 times the ink's). The water pushes the ink into a thin ring. Each drop falls at the centroid of the knots the note cites, as they sit in the plane layout, and the area of the ink drop is proportional to the number of references the note cites. The drop mapping is Jaffer's formula; later drops push earlier rings outward, so the rings of earlier notes are stretched thin further out. The flow on the water is built from a divergence-free stream function (alternating, meandering bands, a uniform strain that stretches along the flow, a flow toward the four corners, and small vortices placed downstream of the large drops) and carried with the midpoint method. The flow is handed out little by little while the drops fall, so the earlier a ring falls, the longer it is carried. The knot points stay where the layout put them and appear when the drop of the first note citing that reference falls. In a variant that also carried the points by the drops and the flow, the measures of group separation dropped far below those of the layout.
- **Weave**: Each note becomes one thread that runs through the force-placed knots nearest first, drawn as a centripetal Catmull–Rom curve through its control points. The threads are fine lines that do not bleed, and both ends taper to the same minimum width.
- **Constellation**: Knots become stars on a sphere, mapped to the drawing area by stereographic projection. Only co-cited pairs within 0.08 times the short side of the drawing area are candidates for lines; in order of how often they are cited together, a pair is joined only if its line crosses no other line and its constellation stays at 10 stars or fewer (a maximum spanning forest by Kruskal's method). Many small constellations are scattered across the sky. Sources cited by only one note are scattered as small faint stars near that note's stars.
- **Rings**: The period of interest sets a band of radii, and the group sets an angular sector. Like a hive plot, this sets the frame of the coordinates from attributes. Only the position inside the cell where band and sector meet is decided by forces: a strong pull to the cell center, pushing within the cell, and weak springs across cells. A wedge-shaped crack opens between the start and the end of the order of sectors; its direction turns with the seed, but the mapping of radius to period and angle to group order does not change.
- **Bundle**: Knots are placed on a circle, and co-citations are bundled with Holten's (2006) method. The hierarchy runs root, group, period, knot, and β is set to 0.85. The straightened control points are joined by a uniform cubic B-spline with tripled end points.
- **Arcs**: Notes are placed along a single baseline in the order they were written, and notes that cite the same reference (bibliographic coupling) are joined by semicircular arcs. The form is borrowed from the arc diagram, but what repeats is not a substring but a cited reference. Because the arcs are true semicircles, arc height reads as the distance in writing order (how many notes were written in between).
- **River**: A streamgraph that stacks, per group, the number of times notes pass through knots, spread with a Gaussian kernel along the dates the notes were written. The baseline minimizes the slope of the layers weighted by their thickness, and groups that start early sit in the middle while later ones are added on the outside. Both are chosen from the baselines and layer orderings discussed by Byron and Wattenberg (2008). The layer boundaries are smoothed with centripetal Catmull–Rom curves. In the light theme the layers are filled as pale ink laid on the washi and the boundaries are thin ink lines, with no cut-outs and no drop shadows. In the dark theme bands growing slightly brighter towards each layer's midline are added only in the finishing, and no bright core line is drawn on the midline.

The look splits in two with the site theme.
In the light theme, every work is finished as if printed in sumi ink on washi.
The spread of ink and water on the paper is not computed.
The flow on the water in marbling, too, only carries points along a flow given by formulas; no fluid equations are solved.
Bleed is not a post-process applied to the finished picture; it is kept as the width and edge of each single line, in five levels.
Around the core of a bleeding line spreads a wet body built from outlines that grow fainter outward.
The body is laid on the paper blurred, so its edge fades smoothly into the paper without steps.
No feathering (capillary strands) runs out along the fibres beyond the edge.
Just inside the outer edge of the body, ink gathers in a thin band.
This band draws on the edge darkening of Curtis et al. (1997), but it is kept faint and weakened where lines are crowded, so the edge never gets as dark as in watercolour.
Where lines are packed densely their bands overlap, and without that weakening the overlaps would read as ragged stripes.
The fine grains, darker in the valleys of the paper tooth, placed in the body of the oldest lines draw on the granulation in the same paper.
From MoXi no computation is borrowed, only the look of paper absorbing differently from place to place, so that the edge wavers; only the outer edge of the band wavers slightly with the direction of the washi fibres and the paper tooth.
Keeping bleed per line, letting the outer edge of the band waver along the washi fibres, weakening the edge by how crowded the lines are, and the way the washi fibres are drawn are not in the studies above; they are this wiki's own design.
The amount of bleed is mapped to the age of the link a line stands for (the older the line, the more it bleeds).
Which date the age is measured from differs by work and is listed under "The two looks" in [The Citation Network of This Wiki: Analysis and Artworks Treating Each Note as a Hyperedge](https://jamjet-iqbal.com/en/notes/citation-weave-of-this-wiki/).
In the dark theme, lines add up over a dark field and glow, and the same amount of bleed becomes the spread of the glow.
Red lines never bleed in either theme.
Every work is drawn in thin lines without bleed while it is being drawn; once drawing ends, a "Finishing" label appears and the picture moves over about 10 seconds to the same drawing redrawn with wash lines.
Its progress is proportional to elapsed time.
Because the weave's threads do not bleed, in the light theme the finishing leaves its lines unchanged, and in the dark theme only the overall glow is added.
This shows the finished state as a clearly marked last move rather than a continuation of the drawing.
Groups are shown in order of paper share, and both themes fix a single hue.
The light theme uses the shade of one ink (fewer papers are lighter, more papers darker), and the dark theme the brightness of a slightly warm white light (fewer papers are dimmer, more papers brighter).
The shape of a source's mark is the same in both themes: academic sources (papers and preprints) are filled discs, and practice sources (companies, public bodies, and the web, such as news and blogs) are rings.
This is the same split as the paper share.

The island shape seen at the start was one arrangement, decided by the seed and the design of the forces.
The bundle, the arcs, and the river rearrange the same co-citation pairs along other axes: hierarchy and time.
Marbling lays the order in which notes were written over the same layout as overlapping drops.
Which arrangement best reflects how this wiki's interests move cannot be decided by laying the pictures side by side.

## What remains unchecked

- Fruchterman and Reingold (1991), Kamada and Kawai (1989), Barnes and Hut (1986), Bostock et al. (2011), and Noack (2009) were verified bibliographically only, and their content is not used as evidence in this note.
- The arc-height encoding in Wattenberg (2002) and the full text of Kosara (2007) were not reached.
- Catmull and Rom (1974), Barry and Goldman (1988), de Boor (1978), Bartels et al. (1987), Press et al. (1992), Silverman (1986), and Batchelor (1967/2000) were checked bibliographically only and are cited only as the standard sources for their formulas. Snyder (1987) was also checked bibliographically only and is cited as the standard source for the stereographic projection. Yuksel et al. (2011) was checked up to the abstract.
- Lu et al. (2012) was checked up to the abstract; the full text was not obtained. The drop formula was checked on the co-author Jaffer's explanatory page, and whether it matches the formula in the paper was not checked. Kobourov and Wampler (2005) were also checked only up to the abstract; the tangent-space computation was not read.
- Circos (Krzywinski et al., 2009) and Viégas and Wattenberg (2007) were checked up to the abstract, but this note describes nothing beyond their titles.
- Chu and Tai (2005) were checked up to the abstract, and Guo and Kunii (1991) only through an index abstract and the related-work section of Curtis et al. (1997). How MoXi treats the fibres of the paper was not checked, nor whether Japanese-language literature models the fibres of washi.
- For the prior works (Dear Data, Writing Without Words, Narrative Structures, Wind Map), only their existence was confirmed; their methods and their relation to network drawing were not examined.

## References

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## Related notes

- [The Citation Network of This Wiki](https://jamjet-iqbal.com/en/notes/citation-weave-of-this-wiki/): the citation network analysis drawn with the literature in this note. Knots, co-citation, groups, and periods are defined there.
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