Multi-layer graph

up:: 041 MOC Graph Theory

Multi-layer graphs are basically a collection of different graphs which are also related to each other.

Given a collection of graphs with Adjacency Matrix $\{A_{ij}^{\alpha }{\}}_{\alpha }$, we have that the multi-layer graph composed by them has adjacency matrix

$$A=\underset{\alpha }{⨁}{A}_{ij}^{\alpha }+C$$

where the $A_{ij}^{\alpha }$ matrices compose the main blocks of $A$ (i.e. intra-layer relations) and $C$ takes care of off-diagonal blocks (i.e. inter-layer interactions).

---

References

• Casas, Alberto Aleta. “Networks, epidemics and collective behavior: from physics to data science”. PhD Thesis, Universidad de Zaragoza, 2019. https://dialnet.unirioja.es/servlet/tesis?codigo=300533.