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Identifying emerging motif in growing networks.

Shi H, Shi L - PLoS ONE (2014)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: State Key Joint-Laboratory of Environmental Simulation and Pollution Control, School of Environment, Tsinghua University, Beijing, China.

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 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.

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Results of motifs identification in a random experiment.(A) The variation of the significance metric Z-score in the whole evolutionary process. (B) Identification results of motifs when n is equal to 1, 2……10, separately. The accuracy of each n is compared with the ideal result in the first row.
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pone-0099634-g004: Results of motifs identification in a random experiment.(A) The variation of the significance metric Z-score in the whole evolutionary process. (B) Identification results of motifs when n is equal to 1, 2……10, separately. The accuracy of each n is compared with the ideal result in the first row.

Mentions: In order to simulate the temporal variation of the metric Z-score of subgraphs in real networks, 100 random numbers around the statistical threshold (let ) are generated by the function (7) as below, which is designed to be of both the time continuity and randomness, shown in Figure 4(A):


Identifying emerging motif in growing networks.

Shi H, Shi L - PLoS ONE (2014)

Results of motifs identification in a random experiment.(A) The variation of the significance metric Z-score in the whole evolutionary process. (B) Identification results of motifs when n is equal to 1, 2……10, separately. The accuracy of each n is compared with the ideal result in the first row.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4061033&req=5

pone-0099634-g004: Results of motifs identification in a random experiment.(A) The variation of the significance metric Z-score in the whole evolutionary process. (B) Identification results of motifs when n is equal to 1, 2……10, separately. The accuracy of each n is compared with the ideal result in the first row.
Mentions: In order to simulate the temporal variation of the metric Z-score of subgraphs in real networks, 100 random numbers around the statistical threshold (let ) are generated by the function (7) as below, which is designed to be of both the time continuity and randomness, shown in Figure 4(A):

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: State Key Joint-Laboratory of Environmental Simulation and Pollution Control, School of Environment, Tsinghua University, Beijing, China.

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 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.

Show MeSH
Related in: MedlinePlus