Role of dimensionality in complex networks.
Role of dimensionality in complex networks.
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DOI：
10.1038/srep27992
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发表时间：
2016-06-20
影响因子：
4.6
通讯作者：
Tsallis C
中科院分区：
文献类型：
--
作者：
Brito S;da Silva LR;Tsallis C
无标度网络和非吉布斯统计之间存在深层联系。例如，典型的度分布在临界极限是这样的形式，其中q指数形式优化了非加性熵Sq（当q → 1时，它恢复了玻尔兹曼-吉布斯熵）。我们在这里介绍和研究d维的地理位置的网络，通过涉及欧几里德距离的优先附件增长。揭示与q-统计量的联系，我们数值验证（d = 1，2，3和4），q-指数度分布表现出，对于q和k，普遍依赖于比率αA/d。此外，通过将αA/d增加到无穷大，可以快速达到q = 1的极限。
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.