Shi Haijia, Shi Lei
State Key Joint-Laboratory of Environmental Simulation and Pollution Control, School of Environment, Tsinghua University, Beijing, China.
PLoS One. 2014 Jun 17;9(6):e99634. doi: 10.1371/journal.pone.0099634. eCollection 2014.
As function units, network motifs have been detected to reveal evolutionary mechanisms of complex systems, such as biological networks, food webs, engineering networks and social networks. However, emergence of motifs in growing networks may be problematic due to large fluctuation of subgraph frequency in the initial stage. This paper contributes to present a method which can identify the emergence of motif in growing networks. Based on the Erdös-Rényi(E-R) random null model, the variation rate of expected frequency of subgraph at adjacent time points was used to define the suitable detection range for motif identification. Upper and lower boundaries of the range were obtained in analytical form according to a chosen risk level. Then, the statistical metric Z-score was extended to a new one, Z(continuous), which effectively reveals the statistical significance of subgraph in a continuous period of time. In this paper, a novel research framework of motif identification was proposed, defining critical boundaries for the evolutionary process of networks and a significance metric of time scale. Finally, an industrial ecosystem at Kalundborg was adopted as a case study to illustrate the effectiveness and convenience of the proposed methodology.
作为功能单元，网络基序已被检测出来以揭示复杂系统的进化机制，如生物网络、食物网、工程网络和社会网络。然而，由于初始阶段子图频率的大幅波动，增长网络中基序的出现可能存在问题。本文提出了一种能够识别增长网络中基序出现的方法。基于厄多斯 - 雷尼（E-R）随机零模型，利用相邻时间点子图预期频率的变化率来定义基序识别的合适检测范围。根据选定的风险水平，以解析形式获得该范围的上下边界。然后，将统计指标Z分数扩展为一个新的指标Z(连续)，它能有效揭示子图在连续时间段内的统计显著性。本文提出了一个新颖的基序识别研究框架，定义了网络进化过程的临界边界和时间尺度的显著性度量。最后，以卡伦堡的一个工业生态系统为例进行研究，以说明所提方法的有效性和便利性。
