Network Motif

Definition

Network motifs are recurrent and significant interconnected subgraphs of a larger Graph. To be considered a motif, a sub graph must occur more frequently than expected by chance in randomized graphs with same statistics (e.g. number of nodes, edges, degree sequence).

Z-Score

The significance of a network motif can be measured by the Z-score. $Z=\frac{N_{\text{real}}-{\bar{N}}_{\text{rand}}}{{\sigma }_{\text{rand}}}$ where $N_{\text{real}}$ is occurrence of the subgraph in $G_{\text{real}}$, ${\bar{N}}_{\text{real}}$ is the average of occurrence of the subgraph in $G_{\text{rand}}$, and ${\sigma }_{\text{rand}}$ is the standard deviation of occurrence of the subgraph in $G_{\text{rand}}$.

The occurrences are measured by Graph-Level Subgraph Frequency or Node-Level Subgraph Frequency.

A high Z-score indicates that the Subgraph appears significantly more often in the real network than expected by chance, suggesting it may be a functionally important motif.

Network Significance Profile

Motifs performs specific functions within a graph, contributing to the overall behavior of it. Different types of graphs (e.g. gene regulation networks, neural networks, social networks, and word connectivity) often have characteristic motifs.