# Motif-Based Centrality

#### Definition

The motif-based centrality c

It is defined as:

Two extensions of this centrality exist: motif-based centrality with roles and motif-based centrality with classes.

Such different functions of vertices within motifs are called roles and three roles can be assigned to the vertices of the FFL motif. The motif-based centrality with roles C

By assigning the same role to similar vertices of a group of similar motifs we can establish a centrality based on a class (or group) of motifs. The motif-based centrality with classes C

see [KOSCHÜTZKI, D., 2007] for more details.

_{mc}:V↦R assigns to every vertex v∈V(G) the number of matches the vertex v occurs in.It is defined as:

c

_{mc}(v)≔|{G_{M}|G_{M}∈G_{M}∧v∈V(G_{M})}|Two extensions of this centrality exist: motif-based centrality with roles and motif-based centrality with classes.

Such different functions of vertices within motifs are called roles and three roles can be assigned to the vertices of the FFL motif. The motif-based centrality with roles C

_{mbr}restricts the number of counted matches to those matches where the vertex occurs in the match with the role under consideration;By assigning the same role to similar vertices of a group of similar motifs we can establish a centrality based on a class (or group) of motifs. The motif-based centrality with classes C

_{mbc}is the sum of motif-based centralities with roles C_{mbr}for the same role in similar or related motifs.see [KOSCHÜTZKI, D., 2007] for more details.

#### Software

#### References

- KOSCHÜTZKI, D., SCHWÖBBERMEYER, H. & SCHREIBER, F. 2007. Ranking of network elements based on functional substructures. Journal of Theoretical Biology, 248, 471-479.
- KOSCHÜTZKI, D. & SCHREIBER, F. 2008. Centrality analysis methods for biological networks and their application to gene regulatory networks. Gene regulation and systems biology, 2, 193.