title: Identifying emerging motif in growing networks.
abstract: 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.
authors.affiliation: State Key Joint-Laboratory of Environmental Simulation and Pollution Control, School of Environment, Tsinghua University, Beijing, China.
authors.forename: Haijia
authors.initials: H
authors.lastname: Shi
authors.affiliation: State Key Joint-Laboratory of Environmental Simulation and Pollution Control, School of Environment, Tsinghua University, Beijing, China.
authors.forename: Lei
authors.initials: L
authors.lastname: Shi
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D007221:Industry