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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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Defining suitable detection range for different subgraph templates based on E-R random  model.(A) The rate of frequency change of subgraph template 1  in growing networks with fixed number of vertices N, which varies from 4 to 20. The range between 1±α is fielded in gray. α = 0.1. (B) The detection range of subgraph template 1 for networks of different size and connectivity. (C) The detection range for different subgraph templates (T1–T6). α = 0.1. (D) Networks from multidiscipline are compared with the suitable detection range for subgraph template 1.
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pone-0099634-g003: Defining suitable detection range for different subgraph templates based on E-R random model.(A) The rate of frequency change of subgraph template 1 in growing networks with fixed number of vertices N, which varies from 4 to 20. The range between 1±α is fielded in gray. α = 0.1. (B) The detection range of subgraph template 1 for networks of different size and connectivity. (C) The detection range for different subgraph templates (T1–T6). α = 0.1. (D) Networks from multidiscipline are compared with the suitable detection range for subgraph template 1.

Mentions: The variation of of template 1 in networks of different size which are generated by random model is shown in Figure 3(A). Each curve records a growing process of a network composed by a set of vertices in the range of 4–20. Let 1±α (α = 0.10) be the acceptable variable range of for motif identification, which is fielded in gray. Then the upper and lower boundaries of this range are given in the forms of analytical solutions. It is evident that the larger N of a network is, the wider this range is. Meanwhile, when α is equal to 0.05 or 0.01, the corresponding functions of upper and lower boundaries are also given, shown in Figure 3(B). It is indicated that with the growth of α, this range becomes wider and wider.


Identifying emerging motif in growing networks.

Shi H, Shi L - PLoS ONE (2014)

Defining suitable detection range for different subgraph templates based on E-R random  model.(A) The rate of frequency change of subgraph template 1  in growing networks with fixed number of vertices N, which varies from 4 to 20. The range between 1±α is fielded in gray. α = 0.1. (B) The detection range of subgraph template 1 for networks of different size and connectivity. (C) The detection range for different subgraph templates (T1–T6). α = 0.1. (D) Networks from multidiscipline are compared with the suitable detection range for subgraph template 1.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0099634-g003: Defining suitable detection range for different subgraph templates based on E-R random model.(A) The rate of frequency change of subgraph template 1 in growing networks with fixed number of vertices N, which varies from 4 to 20. The range between 1±α is fielded in gray. α = 0.1. (B) The detection range of subgraph template 1 for networks of different size and connectivity. (C) The detection range for different subgraph templates (T1–T6). α = 0.1. (D) Networks from multidiscipline are compared with the suitable detection range for subgraph template 1.
Mentions: The variation of of template 1 in networks of different size which are generated by random model is shown in Figure 3(A). Each curve records a growing process of a network composed by a set of vertices in the range of 4–20. Let 1±α (α = 0.10) be the acceptable variable range of for motif identification, which is fielded in gray. Then the upper and lower boundaries of this range are given in the forms of analytical solutions. It is evident that the larger N of a network is, the wider this range is. Meanwhile, when α is equal to 0.05 or 0.01, the corresponding functions of upper and lower boundaries are also given, shown in Figure 3(B). It is indicated that with the growth of α, this range becomes wider and wider.

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