Hypergraph

A hypergraph is defined as:

• $\mathcal{G}=(\mathcal{V},\mathcal{E},\mathit{W})$
• vertex set $\mathcal{V}$
• hyperedge set $\mathcal{E}$
• weight matrix $\mathit{W}$, each hyperedge is assigned with a weight
• incidence matrix $\mathit{H}$ defines $\mathcal{G}$, dimensions $|\mathcal{V}|\times |\mathcal{E}|$

• weight function for vertex $v$ is $d(v)=\sum _{e\in \mathcal{E}}w(e)h(v,e)$
• weight function for edge $e$ is $d(e)=\sum _{v\in \mathcal{V}}h(v,e)$
• $D_e$ and $D_v$ diagonal matrices of edge and vertex degrees