中文摘要：

在这糊，在限制下面平均距离和平均的度 仍然保持近似不变，我们学习了随机的规模 -- 免费网络模型。如果网络维持它的度分发和最大的度 k_c 的形式，我们发现了那 isN 依赖的截止功能 k_c (N)< N，度分发将是近似 power-lawwith 在 2 和 3 之间的一个代表。分发代表与平均的度有小关系，由 表示了。直径限制能作为一个环境选择压力被解释，它能解释网络的没有规模的性质。数字结果显示在直径限制下面，优先的附件能生产截止功能 k_c (N)< N 和幂定律度分发。

英文摘要：

In this paper, under the constraint that the average distance and the average degree （k） remain approximately constant, we studied a random scale-free network model. We found that, if the network maintains the form of its degree distribution and the maximal degree kc is N-dependent cutoff function kc（N）〈 N, the degree distribution would be approximately power-law with an exponent between 2 and 3. The distribution exponent has little relationship with the average degree, denoted by （k）. The diameter constraint can be interpreted as an environmental selection pressure, which could explain the scale-free nature of networks. The numerical results indicate that, under the diameter constraint, the preferential attachment can produce the cutoff function kc（N）〈 N and power-law degree distribution.