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CURRENT: 80 RANDOM GRAPH GIANT COMPONENT OBSERVATORY

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Random Graph Giant Component Observatory

Observe the emergence of a giant connected component in an Erdős–Rényi random graph as the mean degree c crosses the finite-size threshold near 1.

structure / random graph Observation Model

ROUTE 80 / STRUCTURE / RANDOM GRAPH

G(n,p) / p = c/n

Fragments become a giant component

Draw a simple Erdős–Rényi graph by sampling every possible edge in lexicographic order. Increase the mean degree c and watch components merge near c ≈ 1.

READY

GRAPH shows vertices and sampled edges. COMPONENTS highlights one connected component. DISTRIBUTION, SUSCEPTIBILITY, and GIANT PROBABILITY become aggregate views after an ensemble or c sweep.

Initial deterministic graph loaded. All calculations stay local in this browser.

Nodes n: —
Edges m: —
p = c/n: —
Mean degree c: —
Smax / n: —
Smax ratio: —
Components: —
Giant?: —

OBSERVATORY CONTROLS

Set the ensemble

GRAPH

MODEL STATUS

MODEL: G(n,p)
EDGE ORDER: LEX
THRESHOLD: c ≈ 1

PARAMETERS

SEEDED

SEED

NODES n

MEAN DEGREE c

RUNS

Each run uses seed + run index. For n=256, runs are limited to 16 for a bounded local workload.

OPERATIONS

LOCAL ONLY

CANCEL stops before the next chunk. Hidden tabs pause without advancing the LCG.

VIEW

D cycles

KEYBOARD

Focus the canvas: R RESET · G GENERATE · E ENSEMBLE · D VIEW · +/− change c · arrows select node · Enter highlight · Escape cancel.

COMPONENT READOUT

Connected components

HISTORY 0

Smax: —
Smax / n: —
Smax − n: —
Finite χf: —
Component count: —
Selected node: —
Mean degree: —
Giant Smax/n ≥ .5: —

χf = Σs²nₛ / Σsnₛ after removing one largest component. A giant flag uses the finite-size rule Smax/n ≥ 0.5.

SIZE s	COUNT nₛ	NODE SHARE

ENSEMBLE READOUT

Finite-size transition

No ensemble yet

Runs: —
Giant probability: —
Mean Smax/n: —
Mean finite χf: —
Mean components: —
c: —

The critical mean degree is c = np ≈ 1. Repeated seeded graphs show a broad finite-size crossover, not a single sharp sample result.

c	GIANT	PROBABILITY	MEAN Smax/n	MEAN χf

DETERMINISTIC ACCEPTANCE

Exact fixtures

READY

seed 801, n 16 checks four c values. Then seeds 801–832, n 64, 32 runs check the ensemble at four c values.

CHECK	ACTUAL	EXPECTED	RESULT

Observation report

MODEL CONTRACT

Every pair has one chance

G(n,p) is a simple undirected graph. For each lexicographic pair (i,j), p=c/n decides one edge. The LCG is x′ = (1664525x + 1013904223) mod 2³², with u=x/2³². Union-find then labels connected components.

WHAT TO WATCH

Near c ≈ 1

At c below 1, many small components dominate.
Near 1, Smax/n and χf broaden across seeded runs.
Above 1, giant probability rises while the residual finite mass shrinks.

SCOPE

Structure, not motion

This chamber observes random graph connectivity and finite-size statistics. It has no spatial geometry, path search, field diffusion, or physical network measurement.

No upload, registration, or external random source is used.

OBSERVATION POLICY

This observatory runs a deterministic G(n,p) model in your browser. Graphs, calculations, reports, and images stay local. It does not measure visitors, devices, social networks, or physical systems.

Route

This chamber belongs to Structures & Symmetries.

STRUCTURE Back to Structures & Symmetries Route.