摘 要：随机演化网络中的BFW 渗流模型具有的强不连续相变以及多重巨型分支稳定共存的特性引起了统计物理学家的广泛关注。本文基于混合连边机制，提出了修改的BFW 模型。大量模拟实验表明存在一个调控参数的临界点。当偏好连边概率大于该临界点时，生成网络的度分布呈现幂律分布；而小于临界点时，生成网络的度分布呈现泊松分布。进一步对该模型渗流特性的分析结果表明，当偏好概率大于临界点时，模型具有多级相变；而小于临界点时，只有一次相变发生。更有趣的是，当偏好概率小于临界点时，序参量在热力学极限下是自平均的。相反，序参量会出现随机震荡现象，且在热力学极限下不具有自平均性质。
关键词：随机网络；渗流；多级相变；自平均
中图分类号：N94；O357.3 文献标识码：A 文章编号：2096-4706（2018）02-0085-05
Research on Network Evolution and Seepage Transformation Based on Hybrid Connection Mechanism
WANG Ruijie
（ABA Teachers University，Aba 623002，China）
Abstract：The characteristics of the discontinuous percolation at the transition point and multiple giant components coexist in the supercritical region of the BFW model on random network has attracted much attention from physicists and statisticians. A modified BFW percolation model is proposed by changing the way of selecting the candidate edge. Through large numbers of numerical simulations， we find that there exists a critical point，which separates the type of the network structure. If the probability of the preferential attachment excesses the critical point，the network degree exhibits a power-law distribution. Otherwise，the network degree is poisson distribution. Additionally，the percolation process of the modified BFW model is researched. Simulation results indicate that the percolation undergoes multi-transition when the probability of the preferential attachment excesses the critical point. More interestingly，order parameter has random fluctuations when the probability of the preferential attachment excesses the critical point.
Keywords：random network；percolation；multiple-transition；self-averaging
参考文献：
[1] AHARONY A，STAUFFER D.Introduction to percolation theory [M].S.l.：Taylor and Francis，2003.
[2] Klaus Dietz.Infectious diseases of humans：dynamics and control [J].Trends Parasitol，1992，8（5）：179.
[ 3 ] D a v i d S t r a n g，S O U L E s a r a h a . D i f f u s i o n i n organizations and social movements：from hybrid corn to poison pills [J].Annu Rev Sociol，1998，24.
[4] SAHINI M，SAHIMI M.Applications of percolation theory [M].S.l.：Taylor and Francis，2014.
[5] ROZENFELD HD，SONG C，MAKSE HA.Smallw o r l d t o f r a c t a l t r a n s i t i o n i n c o m p l e x n e t w o r k s：a renormalization group approach [J].Phys Rev Lett，2010，104（2）.
[6] ERDőS P，RÉNYI A. On the evolution of random graphs [J].Bull.Inst.Internat. Statist.，1961.
[7] D.ACHLIOPTAS，R M.D'SOUZA，J.SPENCER. Explosive percolation in random networks [J].Science，2009，323（3)：1453-1455.
[8] ZIFF RM. Explosive growth in biased dynamic percolation on two-dimensional regular lattice networks [J]. Phys Rev Lett，2009，103（4）.
[9] CHO YS，KAHNG B，KIM D.Cluster aggregation model for discontinuous percolation transitions [J].Physical Review E，2010，81（3）.
[10] Oliver RiordanLutz Warnke.Achlioptas processes are not always self-averaging [J].Phys. Rev.E，2012.
[11] Chen，Wei，D'SOUZA R M.Explosive percolation with multiple giant components [J] Phys Rev Lett，2011，106（11）.
[12] PRICE D D S. Networks of scientific papers [J].Science，1965，149（3683）：510-515.
[13] Noga Alon，Joel H. Spencer.Random graphs [M].Hoboken，NJ，USA：John Wiley & Sons，Inc.，2000：155-181.
作者简介：王睿婕（1989-），女，汉，四川新津人，研究实习员，硕士研究生，研究方向：复杂网络。