6533b7d6fe1ef96bd1266f80
RESEARCH PRODUCT
A Hebbian approach to complex-network generation
Adriano BarraElena AgliariElena Agliarisubject
Random graphStatistical Mechanics (cond-mat.stat-mech)Computer scienceReplicaDegrees of freedom (statistics)General Physics and AstronomyFOS: Physical sciencesStatistical mechanicsComplex networkPhysics and Astronomy (all)Hebbian theoryStatistical physicsFocus (optics)Condensed Matter - Statistical MechanicsTopology (chemistry)description
Through a redefinition of patterns in an 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 clarifies 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, as we show, naturally and without any a-priori assumption, 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-01-01 |