Volume 94, Number 1, April 2011
|Number of page(s)||6|
|Published online||28 March 2011|
A Hebbian approach to complex-network generation
Dipartimento di Fisica, Università degli Studi di Parma - viale Usberti 7/A, 43100 Parma, Italy, EU
2 Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Parma - Parma, Italy, EU
3 Dipartimento di Fisica, Sapienza Università di Roma - P.le A. Moro 5, 00182, Rome, Italy, EU
4 Gruppo Nazionale di Fisica Matematica, Sezione di Roma1 - Rome, Italy, EU
Accepted: 28 February 2011
Through a redefinition of patterns in a Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach highlights the intrinsic connection between the kind of interactions among components and the emergent topology describing the system itself; also, it allows to effectively address the statistical mechanics on the resulting networks. Indeed, a wide class of analytically treatable, weighted random graphs with a tunable level of correlation can be recovered and controlled. We especially focus on the case of imitative couplings among components endowed with similar patterns (i.e. attributes), which naturally gives rise to small-world effects. We also solve the thermodynamics (at a replica symmetric level) by extending the double stochastic stability technique: free energy, self-consistency relations and fluctuation analysis for a picture of criticality are obtained. Finally, applications are considered, with particular attention to the agreement among the non-trivial features predicted by the theory and the experimental findings.
PACS: 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 02.10.Ox – Combinatorics; graph theory / 05.70.Fh – Phase transitions: general studies
© EPLA, 2011
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.