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Info:

Efficient C code to list k-cliques such as described in:
"Listing k-cliques in Sparse Real-World Graphs. M. Danisch, O. D. Balalau, M. Sozio. WWW2018".
https://papers-gamma.link/paper/32

Arboricity.c is an implementation of the algorithm to list all k-cliques described in:
"Arboricity and subgraph listing algorithms. Chiba, N., & Nishizeki, T. SIAM Journal on Computing, 14(1), 210-223, 1985".

Arboricity.c

This program iterates over all k-cliques. This is an implementation of the 1985 paper of Chiba And Nishizeki "Arboricity and subgraph listing".

To compile

"gcc Arboricity.c -O9 -o Arboricity".

To execute

"./Arboricity edgelist.txt k".

  • "edgelist.txt" should contain the graph: one edge on each line separated by a space.
  • Will print the number of k-cliques.

kClist.c

This program iterates over all k-cliques. This is an improvement of the 1985 algorithm of Chiba And Nishizeki detailed in "Arboricity and subgraph listing".

To compile

"gcc kClist.c -O9 -o kClist".

To execute

"./kClist k edgelist.txt".

  • "edgelist.txt" should contain the graph: one edge on each line separated by a space.
  • Will print the number of k-cliques.

kClistCore.c

This program enumerates all k-cliques, computes the k-clique core decomposition and computes a k approximation of a k-cliques densest subgraph.

To compile

"gcc kClistCore.c -O9 -o kClistCore".

To execute

"./kClistCore k edgelist.txt ckdeg.txt ckcore.txt ckdens.txt".

  • k of k-clique to enumerate.
  • "edgelist.txt" should contain the graph: one edge on each line separated by a space.
  • Will print the total number of k-cliques.
  • Will print the k-clique core number of the graph
  • Will print the k-clique density, the edge density and the size of the found 1/k-approximation densest subgraph
  • Will write in ckdeg.txt the ID of each node followed by its k-clique degree
  • Will write in ckcore.txt the ID of each node followed by its k-clique core number in a k-clique core ordering
  • Will write in ckdens.txt the the k-clique density, the edge density and the size of the densest subgraph followed by the ID of each node in it

kClistDens.c

This program iterates over all k-cliques. It find a k(1+eps) approximation of the kclique densest. It is highly scallable.

To compile:

"gcc kClistDens.c -O9 -o kClistDens -fopenmp".

To execute:

"./kClistDens p k eps edgelist.txt".

  • "edgelist.txt" should contain the graph: one edge on each line separated by a space.
  • k is the size of the k-cliques
  • p is the number of threads
  • eps is the precision
  • Will print the number of k-cliques and the density of the found kclique densest.

kClistEdgeParallel.c

This program iterates over all k-cliques. This is an improvement of the 1985 algorithm of Chiba And Nishizeki detailed in "Arboricity and subgraph listing". It processes edges in parallel.

To compile:

"gcc kClistEdgeParallel.c -O9 -o kClistEdgeParallel -fopenmp".

To execute:

"./kClistEdgeParallel p k edgelist.txt".

  • "edgelist.txt" should contain the graph: one edge on each line separated by a space.
  • k is the size of the k-cliques
  • p is the number of threads
  • Will print the number of k-cliques.

kClistNodeParallel.c

This program iterates over all k-cliques. This is an improvement of the 1985 algorithm of Chiba And Nishizeki detailed in "Arboricity and subgraph listing". It processes nodes in parallel.

To compile:

"gcc kClistNodeParallel.c -O9 -o kClistNodeParallel -fopenmp".

To execute:

"./kClistNodeParallel p k edgelist.txt".

  • "edgelist.txt" should contain the graph: one edge on each line separated by a space.
  • k is the size of the k-cliques
  • p is the number of threads
  • Will print the number of k-cliques.

Initial contributors

Maximilien Danisch
Technical consultants: Qinna Wang, Oana Balalau and Mauro Sozio
2015 - 2018
http://bit.ly/danisch
maximilien.danisch@gmail.com

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Algorithms to list k-cliques in real-world graphs

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