Role of dimensionality in complex networks.
Deep connections are known to exist between scale-free networks and non-Gibbsian statistics. For example, typical degree distributions at the thermodynamical limit are of the form , where the q-exponential form optimizes the nonadditive entropy Sq (which, for q → 1, recovers the Boltzmann-Gibbs entropy). We introduce and study here d-dimensional geographically-located networks which grow with preferential attachment involving Euclidean distances through . Revealing the connection with q-statistics, we numerically verify (for d = 1, 2, 3 and 4) that the q-exponential degree distributions exhibit, for both q and k, universal dependences on the ratio αA/d. Moreover, the q = 1 limit is rapidly achieved by increasing αA/d to infinity.
Universidade Federal do Rio Grande do Norte, Departamento de Física Teórica e Experimental, Natal-RN, 59078-900, Brazil.
Samuraí
S
Brito
Universidade Federal do Rio Grande do Norte, Departamento de Física Teórica e Experimental, Natal-RN, 59078-900, Brazil.|National Institute of Science and Technology of Complex Systems, Brazil.
L R
LR
da Silva
National Institute of Science and Technology of Complex Systems, Brazil.|Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil, and Santa Fe Institute, 1399 Hyde Park Road, New Mexico 87501, USA.
Constantino
C
Tsallis