Add Egocentric layout

[emfeltham]

Adds Egocentric, a stress-majorization layout centred on a single focal vertex, following Brandes and Pich (2011).

Brandes, Ulrik, and Christian Pich. "More flexible radial layout." Journal of Graph Algorithms and Applications 15.1 (2011): 157-173.

pos = egocentric(g; focus=v)
pos = egocentric(g; focus=v, maxdist=4)             # bound the extent
pos = egocentric(g; focus=v, maxdist=4, compress=1) # one outer ring for "d > 4"

Layout

The layout interpolates between two objectives:

• the plain stress objective, which matches all pairwise euclidean distances to graph distances (this is Stress), and
• a focus objective, which only weights the pairs involving the focal vertex.

Minimizing the focus objective alone places every vertex at a radius equal to its graph distance from the focus. The result reads as concentric rings of constant geodesic distance, while the angles still come from the unconstrained stress solution, so vertices that are close in the network stay close on their ring. Optimization walks a schedule tseq of mixing parameters from 0 to 1, majorizing each stage to convergence: pure stress picks sensible angles first, then the radii are gradually enforced.

Notes

• Implemented as an IterativeLayout, so LayoutIterator animates the schedule. The final layout is emitted twice, because layout returns the second to last item of the iterator.
• The majorization sweep updates positions in place (Gauss-Seidel). The simultaneous (Jacobi) variant of the same update oscillates rather than converging — on a two-vertex graph it alternates around the ideal distance indefinitely. With the in-place sweep the radii land within ~1e-15 of the graph distances.
• The focal vertex is never moved and stays at the origin. Stress is translation invariant, so holding one vertex fixed only fixes the gauge. It also means initialpos, pin and the returned positions all live in the same focus-centred frame, which is what makes pin usable here.
• Initial positions come from classical (Torgerson) MDS of the graph distances plus a small jitter, computed inline from LinearAlgebra so there is no new dependency. This makes the result largely independent of seed.
• Unconnected vertices reuse the existing uncon_dist treatment from Stress rather than being dropped, so the layout keeps the adjacency matrix -> one position per vertex contract.
• maxdist optionally compresses vertices beyond a given ring onto a narrow outer band, keeping their angles. Without it a handful of remote vertices can dominate the frame, since radius equals graph distance. compress controls the falloff and accepts a function (default log1p), a number (collapse onto a single outer ring), or nothing (clamp onto the maxdist ring).

Supports dim/Ptype, initialpos, pin, seed/rng, weighted adjacency matrices, and composes with Align.

Specific changes

• src/egocentric.jl (new), included from src/NetworkLayout.jl
• test/runtests.jl: a Testing Egocentric Layout testset covering construction and argument validation, the focus sitting at the origin, radii matching graph distances (2d and 3d), weighted adjacency matrices, the maxdist/compress variants and that compression leaves angles untouched, unconnected vertices, determinism, initialpos/pin, the iterator, and monotone stress decrease along a stage
• docs/src/index.md: an Egocentric Layout section with examples and an iterator animation, plus Egocentric added to the list of layouts that support pin

[codecov]

Codecov Report

❌ Patch coverage is 97.50000% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 97.28%. Comparing base (6ad1e2f) to head (7264d87).
⚠️ Report is 4 commits behind head on master.

Files with missing lines	Patch %	Lines
src/egocentric.jl	97.50%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #104      +/-   ##
==========================================
- Coverage   97.41%   97.28%   -0.14%     
==========================================
  Files          10       11       +1     
  Lines         580      736     +156     
==========================================
+ Hits          565      716     +151     
- Misses         15       20       +5     

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[hexaeder]

thanks for the contribution! Can you rebase on master and get rid of the double ejecting of final layout? That was an actual bug i fixed in #105

[emfeltham]

Okay, great. Take a look and let me know!