The University of Southampton
University of Southampton Institutional Repository

Neural complexity: a graph theoretic interpretation

Barnett, Lionel, Buckley, Christopher L. and Bullock, Seth (2011) Neural complexity: a graph theoretic interpretation Physical Review E, 83, (4), 041906-[8pp]. (doi:10.1103/PhysRevE.83.041906).

Record type: Article


One of the central challenges facing modern neuroscience is to explain the ability of the nervous system to coherently integrate information across distinct functional modules in the absence of a central executive. To this end Tononi et al. [Proc. Nat. Acad. Sci. USA 91, 5033 (1994)] proposed a measure of neural complexity that purports to capture this property based on mutual information between complementary subsets of a system. Neural complexity, so defined, is one of a family of information theoretic metrics developed to measure the balance between the segregation and integration of a system's dynamics. One key question arising for such measures involves understanding how they are influenced by network topology. Sporns et al. [Cereb. Cortex 10, 127 (2000)] employed numerical models in order to determine the dependence of neural complexity on the topological features of a network. However, a complete picture has yet to be established. While De Lucia et al. [Phys. Rev. E 71, 016114 (2005)] made the first attempts at an analytical account of this relationship, their work utilized a formulation of neural complexity that, we argue, did not reflect the intuitions of the original work. In this paper we start by describing weighted connection matrices formed by applying a random continuous weight distribution to binary adjacency matrices. This allows us to derive an approximation for neural complexity in terms of the moments of the weight distribution and elementary graph motifs. In particular we explicitly establish a dependency of neural complexity on cyclic graph motifs.

PDF BarnettNcomp.pdf - Accepted Manuscript
Download (251kB)

More information

Published date: 8 April 2011
Organisations: Agents, Interactions & Complexity


Local EPrints ID: 271969
ISSN: 1539-3755
PURE UUID: f0fa1671-4b26-4efc-bad6-40c2b3172c0f

Catalogue record

Date deposited: 31 Jan 2011 17:34
Last modified: 18 Jul 2017 06:36

Export record



Author: Lionel Barnett
Author: Christopher L. Buckley
Author: Seth Bullock

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton:

ePrints Soton supports OAI 2.0 with a base URL of

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.