CORE
🇺🇦Â
 make metadata, not war
Services
Services overview
Explore all CORE services
Access to raw data
API
Dataset
FastSync
Content discovery
Recommender
Discovery
OAI identifiers
OAI Resolver
Managing content
Dashboard
Bespoke contracts
Consultancy services
Support us
Support us
Membership
Sponsorship
Community governance
Advisory Board
Board of supporters
Research network
About
About us
Our mission
Team
Blog
FAQs
Contact us
Simple and efficient four-cycle counting on sparse graphs
Authors
Paul Burkhardt
David G. Harris
Publication date
26 April 2023
Publisher
View
on
arXiv
Abstract
We consider the problem of counting 4-cycles (
C
4
C_4
C
4
​
) in a general undirected graph
G
G
G
of
n
n
n
vertices and
m
m
m
edges (in bipartite graphs, 4-cycles are also often referred to as
butterflies
\textit{butterflies}
butterflies
). There have been a number of previous algorithms for this problem; some of these are based on fast matrix multiplication, which is attractive theoretically but not practical, and some of these are based on randomized hash tables. We develop a new simpler algorithm for counting
C
4
C_4
C
4
​
requiring
O
(
m
δ
ˉ
(
G
)
)
O(m\bar\delta(G))
O
(
m
δ
ˉ
(
G
))
time and
O
(
n
)
O(n)
O
(
n
)
space, where
δ
ˉ
(
G
)
≤
O
(
m
)
\bar \delta(G) \leq O(\sqrt{m})
δ
ˉ
(
G
)
≤
O
(
m
​
)
is the
average
Â
degeneracy
\textit{average degeneracy}
average degeneracy
parameter introduced by Burkhardt, Faber & Harris (2020). It has several practical improvements over previous algorithms; for example, it is fully deterministic, does not require any sorting of the adjacency list of the input graph, and avoids any expensive arithmetic in its inner loops. To the best of our knowledge, all previous efficient algorithms for
C
4
C_4
C
4
​
counting have required
Ω
(
m
)
\Omega(m)
Ω
(
m
)
space. The algorithm can also be adapted to count 4-cycles incident to each vertex and edge
Similar works
Full text
Available Versions
arXiv.org e-Print Archive
See this paper in CORE
Go to the repository landing page
Download from data provider
oai:arXiv.org:2303.06090
Last time updated on 24/03/2023