Random walks on deterministic scale-free networks: exact results.
Phys Rev E Stat Nonlin Soft Matter Phys
; 80(3 Pt 1): 031125, 2009 Sep.
Article
in En
| MEDLINE
| ID: mdl-19905080
We study the random walk problem on a class of deterministic scale-free networks displaying a degree sequence for hubs scaling as a power law with an exponent gamma=log 3/log 2. We find exact results concerning different first-passage phenomena and, in particular, we calculate the probability of first return to the main hub. These results allow to derive the exact analytic expression for the mean time to first reach the main hub, whose leading behavior is given by tau approximately V1-1/gamma, where V denotes the size of the structure, and the mean is over a set of starting points distributed uniformly over all the other sites of the graph. Interestingly, the process turns out to be particularly efficient. We also discuss the thermodynamic limit of the structure and some local topological properties.
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Collection:
01-internacional
Database:
MEDLINE
Type of study:
Clinical_trials
Language:
En
Journal:
Phys Rev E Stat Nonlin Soft Matter Phys
Journal subject:
BIOFISICA
/
FISIOLOGIA
Year:
2009
Document type:
Article
Affiliation country:
Italia
Country of publication:
Estados Unidos