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File:Planted clique 15,32.svg

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Original file (SVG file, nominally 768 × 768 pixels, file size: 9 KB)

Summary

Description
English: A 15-vertex planted clique (blue vertices and upper edges) in a 32-vertex random graph (all vertices and lower edges). Every pair of blue vertices is adjacent; the remaining pairs are adjacent randomly with probability 1/2.
Date
Source Own work
Author David Eppstein

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

Source code

from PADS import SVG
import sys
import random
n = 32
k = 15
r = 6
w = 4*n*r

def vertex(i):
    return 4*i*r + 2*r + (w//2)*1j

def radius(i,j):
    return 2*abs(i-j)*r

planted = set()
while len(planted) < k:
    planted.add(random.randrange(n))

svg = SVG.SVG(w+w*1j,sys.stdout)

svg.group(stroke=SVG.colors.black)

svg.group(fill=SVG.colors.none)
for i in range(n):
    for j in range(i):
        if i in planted and j in planted:
            svg.arc(vertex(i),vertex(j),radius(i,j))
        elif random.randrange(2):
            svg.arc(vertex(j),vertex(i),radius(i,j))
svg.ungroup()

svg.group(fill=SVG.colors.blue)
for i in range(n):
    if i in planted:
        svg.circle(vertex(i),r)
svg.ungroup()

svg.group(fill=SVG.colors.yellow)
for i in range(n):
    if i not in planted:
        svg.circle(vertex(i),r)
svg.ungroup()

svg.ungroup()
svg.close()

Captions

A 15-vertex planted clique in a 32-vertex random graph

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depicts

16 November 2023

File history

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Date/TimeThumbnailDimensionsUserComment
current08:14, 17 November 2023Thumbnail for version as of 08:14, 17 November 2023768 × 768 (9 KB)David EppsteinUploaded own work with UploadWizard

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