7,129
个编辑
更改
无编辑摘要
:<math>Z(G^\prime) = \frac{F_G(G^\prime) - \mu_R(G^\prime)}{\sigma_R(G^\prime)}</math>
:<math>Z(G^\prime) = \frac{F_G(G^\prime) - \mu_R(G^\prime)}{\sigma_R(G^\prime)}</math>
式中，{{math|μ<sub>R</sub>(G′)}} 和 {{math|σ<sub>R</sub>(G′)}}分别代表集合{{math|R(G)}}中的平均和标准偏差频率。<ref name="mil1">{{cite journal |vauthors=Milo R, Shen-Orr SS, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |volume=298 |year=2002|journal=Science|issue=5594|pages=824–827 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="alb1">{{cite journal |vauthors=Albert R, Barabási AL |title=Statistical mechanics of complex networks |journal=Reviews of Modern Physics |volume=74 |issue=1 |year=2002 |pages=47–49 |doi=10.1103/RevModPhys.74.47 |bibcode=2002RvMP...74...47A|arxiv=cond-mat/0106096 |citeseerx=10.1.1.242.4753 }}</ref><ref name="mil2">{{cite journal |vauthors=Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheffer M, Alon U |title=Superfamilies of designed and evolved networks |journal=Science |volume=303 |issue=5663 |year=2004 |pages=1538–1542 |pmid=15001784 |doi=10.1126/science.1089167 |bibcode=2004Sci...303.1538M |url=https://semanticscholar.org/paper/87ad24efd5329046d37cd704f970323e878710ca }}</ref><ref name="sch1">{{cite encyclopedia|last=Schwöbbermeyer |first=H |title=Network Motifs |encyclopedia=Analysis of Biological Networks |editor=Junker BH, Schreiber F |publisher=Hoboken, New Jersey: John Wiley & Sons |year=2008 |pages=85–108}}</ref><ref name="bor1">{{cite encyclopedia |last1=Bornholdt |first1=S |last2=Schuster |first2=HG |title=Handbook of graphs and networks : from the genome to the Internet |journal=Handbook of Graphs and Networks: From the Genome to the Internet |pages=417 |year=2003|bibcode=2003hgnf.book.....B }}</ref><ref name="cir1">{{cite journal |vauthors=Ciriello G, Guerra C |title=A review on models and algorithms for motif discovery in protein-protein interaction networks |journal=Briefings in Functional Genomics and Proteomics |year=2008 |volume=7 |issue=2 |pages=147–156 |doi=10.1093/bfgp/eln015|pmid=18443014 |doi-access=free }}</ref> {{math|Z(G′)}}越大，子图{{math|G′}}作为模体的意义也就越大。
式中，{{math|μ<sub>R</sub>(G′)}} 和 {{math|σ<sub>R</sub>(G′)}}分别代表集合{{math|R(G)}}中的平均和标准偏差频率。<ref name="mil1">{{cite journal |vauthors=Milo R, Shen-Orr SS, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |volume=298 |year=2002|journal=Science|issue=5594|pages=824–827 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="alb1">{{cite journal |vauthors=Albert R, Barabási AL |title=Statistical mechanics of complex networks |journal=Reviews of Modern Physics |volume=74 |issue=1 |year=2002 |pages=47–49 |doi=10.1103/RevModPhys.74.47 |bibcode=2002RvMP...74...47A|arxiv=cond-mat/0106096 |citeseerx=10.1.1.242.4753 }}</ref><ref name="mil2">{{cite journal |vauthors=Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheffer M, Alon U |title=Superfamilies of designed and evolved networks |journal=Science |volume=303 |issue=5663 |year=2004 |pages=1538–1542 |pmid=15001784 |doi=10.1126/science.1089167 |bibcode=2004Sci...303.1538M |url=https://semanticscholar.org/paper/87ad24efd5329046d37cd704f970323e878710ca }}</ref><ref name="sch1">{{cite encyclopedia|last=Schwöbbermeyer |first=H |title=Network Motifs |encyclopedia=Analysis of Biological Networks |editor=Junker BH, Schreiber F |publisher=Hoboken, New Jersey: John Wiley & Sons |year=2008 |pages=85–108}}</ref><ref name="bor1">{{cite encyclopedia |last1=Bornholdt |first1=S |last2=Schuster |first2=HG |title=Handbook of graphs and networks : from the genome to the Internet |journal=Handbook of Graphs and Networks: From the Genome to the Internet |pages=417 |year=2003|bibcode=2003hgnf.book.....B }}</ref><ref name="cir1">{{cite journal |vauthors=Ciriello G, Guerra C |title=A review on models and algorithms for motif discovery in protein-protein interaction networks |journal=Briefings in Functional Genomics and Proteomics |year=2008 |volume=7 |issue=2 |pages=147–156 |doi=10.1093/bfgp/eln015|pmid=18443014 |doi-access=free }}</ref> {{math|Z(G′)}}越大，子图{{math|G′}}作为模体的意义也就越大。
[[File:Different occurrences of a sub-graph in a graph.jpg|thumb|图1 ''图中子图的不同出现''. (M1 – M4) 是图（a）中子图（b）的不同出现。对于频率概念{{math|F<sub>1</sub>}},集合M1，M2，M3，M4表示所有匹配项，因此{{math|F<sub>1</sub> {{=}} 4}}。对于{{math|F<sub>2</sub>}}，两个集合M1，M4或M2，M3之一是可能的匹配，{{math|F<sub>2</sub> {{=}} 2}}。最后，对于频率概念{{math|F<sub>3</sub>}}仅允许匹配项之一（M1至M4），因此{{math|F<sub>3</sub> {{=}} 1}}。随着网元的使用受到限制，这三个频率概念的频率降低。]]
[[File:Different occurrences of a sub-graph in a graph.jpg|thumb|图1 ''图中子图的不同出现''. (M1 – M4) 是图（a）中子图（b）的不同出现。对于频率概念{{math|F<sub>1</sub>}},集合M1，M2，M3，M4表示所有匹配项，因此{{math|F<sub>1</sub> {{=}} 4}}。对于{{math|F<sub>2</sub>}}，两个集合M1，M4或M2，M3之一是可能的匹配，{{math|F<sub>2</sub> {{=}} 2}}。最后，对于频率概念{{math|F<sub>3</sub>}}仅允许匹配项之一（M1至M4），因此{{math|F<sub>3</sub> {{=}} 1}}。随着网元的使用受到限制，这三个频率概念的频率降低。]]
其中{{math|N}}表示随机网络的数目，{{math|i}}定义在随机网络的集合上，若条件{{math|c(i)}}成立，则Kroneckerδ函数{{math|δ(c(i))}}是1。在网络{{math|G}}中，一个特定的n维子图{{math|N′}}的集中度<ref name="kas1">{{cite journal |vauthors=Kashtan N, Itzkovitz S, Milo R, Alon U |title=Efficient sampling algorithm for estimating sub-graph concentrations and detecting network motifs |journal=Bioinformatics |year=2004 |volume=20 |issue=11 |pages=1746–1758 |doi=10.1093/bioinformatics/bth163|pmid=15001476 |doi-access=free }}</ref><ref name="wer1">{{cite journal |author=Wernicke S |title=Efficient detection of network motifs |journal=IEEE/ACM Transactions on Computational Biology and Bioinformatics |year=2006 |volume=3 |issue=4 |pages=347–359 |doi=10.1109/tcbb.2006.51|pmid=17085844 |citeseerx=10.1.1.304.2576 }}</ref>是指子图在网络中出现频率与n维非同构子图的总频率之比，其计算公式如下：
其中{{math|N}}表示随机网络的数目，{{math|i}}定义在随机网络的集合上，若条件{{math|c(i)}}成立，则Kroneckerδ函数{{math|δ(c(i))}}是1。在网络{{math|G}}中，一个特定的n维子图{{math|N′}}的集中度<ref name="kas1">{{cite journal |vauthors=Kashtan N, Itzkovitz S, Milo R, Alon U |title=Efficient sampling algorithm for estimating sub-graph concentrations and detecting network motifs |journal=Bioinformatics |year=2004 |volume=20 |issue=11 |pages=1746–1758 |doi=10.1093/bioinformatics/bth163|pmid=15001476 |doi-access=free }}</ref><ref name="wer1">{{cite journal |author=Wernicke S |title=Efficient detection of network motifs |journal=IEEE/ACM Transactions on Computational Biology and Bioinformatics |year=2006 |volume=3 |issue=4 |pages=347–359 |doi=10.1109/tcbb.2006.51|pmid=17085844 |citeseerx=10.1.1.304.2576 }}</ref>是指子图在网络中出现频率与n维非同构子图的总频率之比，其计算公式如下：