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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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The structure and degree distribution of the industrial network at Kalundborg.(A) Red vertices represent enterprises and links represent material and energy flow. The chronological order of these directed edges are marked with the serial number 1, 2…, 35. (B) The in-degree and out-degree distribution in 2011.
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pone-0099634-g005: The structure and degree distribution of the industrial network at Kalundborg.(A) Red vertices represent enterprises and links represent material and energy flow. The chronological order of these directed edges are marked with the serial number 1, 2…, 35. (B) The in-degree and out-degree distribution in 2011.

Mentions: In this industrial network, enterprises were abstracted into vertices and material and energy flows between each pair of them were abstracted into directed edges. By now, there have been 20 vertices and 35 directed edges. Its growth process is shown in Figure 5 (A), in which the chronological order of these directed edges are marked with the serial number 1, 2…, 35. Multiple edges were conserved in the description of networks, but simplified in the process of motif detection. All the information about our case was obtained from the official website of Kalundborg symbiosis: http://www.symbiosis.dk/en/system.


Identifying emerging motif in growing networks.

Shi H, Shi L - PLoS ONE (2014)

The structure and degree distribution of the industrial network at Kalundborg.(A) Red vertices represent enterprises and links represent material and energy flow. The chronological order of these directed edges are marked with the serial number 1, 2…, 35. (B) The in-degree and out-degree distribution in 2011.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0099634-g005: The structure and degree distribution of the industrial network at Kalundborg.(A) Red vertices represent enterprises and links represent material and energy flow. The chronological order of these directed edges are marked with the serial number 1, 2…, 35. (B) The in-degree and out-degree distribution in 2011.
Mentions: In this industrial network, enterprises were abstracted into vertices and material and energy flows between each pair of them were abstracted into directed edges. By now, there have been 20 vertices and 35 directed edges. Its growth process is shown in Figure 5 (A), in which the chronological order of these directed edges are marked with the serial number 1, 2…, 35. Multiple edges were conserved in the description of networks, but simplified in the process of motif detection. All the information about our case was obtained from the official website of Kalundborg symbiosis: http://www.symbiosis.dk/en/system.

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