Update motifs-and-structral-roles_lecture.md

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} <br>
+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