#### Computational Science Technical Note CSTN-003

#
Circuits as a Classifier for Small-World Network Models

##
A. Leist and K. A. Hawick

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Archived March 2004, Revised February 2009

**Abstract**

The number and length distribution of circuits or loops in a graph or network give important insights into its key characteristics.
We discuss the circuit properties of various small-world or scale-free network models generated with different small-world
probability parameter values. The small-world properties usually manifest themselves in terms of reduced path-length properties or
the set of inter-node distances present in a graph. We show how the number of circuits present can increase or decrease with a
larger probability of small-world shortcut links applied, depending upon which model is used. Circuit properties are
computationally expensive and we consider counting only a partial circuit distribution and thus being able to use circuits as a
classifier for these models in practical cases.

**Keywords:**
circuits; graphs; small-world; scale-free networks

**Full Document Text:**
PDF version.

**Citation Information:** BiBTeX database for CSTN Notes.

**BiBTeX reference:**

@INPROCEEDINGS{CSTN-003,
author = {A. Leist and K. A. Hawick},
title = {Circuits as a Classifier for Small-World Network Models},
booktitle = {Proc. WORLDCOMP 2009 International Conference on Foundations of Computer
Science (FSC 09) Las Vegas, USA.},
year = {2009},
number = {CSTN-003},
month = {13-16 July},
institution = {Massey University},
url = {http://www.massey.ac.nz/~kahawick/cstn/003/cstn-003.html}
}

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