From d63061a8eff64272e0da03f2d738c62dac736e6e Mon Sep 17 00:00:00 2001 From: microLizzy <32970198+microLizzy@users.noreply.github.com> Date: Thu, 17 Oct 2019 22:03:03 -0700 Subject: [PATCH] Update motifs-and-structral-roles_lecture.md --- .../motifs-and-structral-roles_lecture.md | 15 +++++++++++++-- 1 file changed, 13 insertions(+), 2 deletions(-) diff --git a/preliminaries/motifs-and-structral-roles_lecture.md b/preliminaries/motifs-and-structral-roles_lecture.md index 67caa24..fd435de 100755 --- a/preliminaries/motifs-and-structral-roles_lecture.md +++ b/preliminaries/motifs-and-structral-roles_lecture.md @@ -18,10 +18,21 @@ Network motifs are recurring, significant patterns of interconnections in the ne Recurrence of motif represents it occurs with high frequency. We allow overlapping of motifs. -Significance of a motif means it is more frequent than expected. The key idea here is we say subgraphs that occur in a real network much more often than in a random network have functional significance. Significance can be measured using Z-score which is defined as: \begin{equation} Z_{i} = \frac{N_{i}^{real} - \overline N_{i}^{rand}}{std(N_{i}^{rand})} \end{equation}
+Significance of a motif means it is more frequent than expected. The key idea here is we say subgraphs that occur in a real network much more often than in a random network have functional significance. Significance can be measured using Z-score which is defined as: + +$$ +Z_{i} = \frac{N_{i}^{real} - \overline N_{i}^{rand}}{std(N_{i}^{rand})} +$$ + where $$N_{i}^{real}$$ is #(subgraphs of type i) in network $$G^{real}$$ and $$N_{i}^{rand}$$ is #(subgraphs of type i) in randomized network $$G^{rand}$$. -Network significance profile (SP) is defined as: \begin{equation} SP_{i} = \frac{Z_{i}}{\sqrt{\sum_{j} {Z_j^{2}}}} \end{equation} where SP is a vector of normalized Z-scores. +Network significance profile (SP) is defined as: + +$$ +SP_{i} = \frac{Z_{i}}{\sqrt{\sum_{j} {Z_j^{2}}}} +$$ + +where SP is a vector of normalized Z-scores. ### Configuration Model