# Table 4 Statistics of network configurations of bipartite networks

Network configurations

Network statistics

Interpretation

Edges: L

$$\mathop \sum \nolimits_{R = 1}^{R} \mathop \sum \nolimits_{P = 1}^{P} M_{RP}$$

Number of edges in the bipartite network

Two stars:$$S_{R2}$$

$$\mathop \sum \nolimits_{R = 1}^{R} \mathop \sum \nolimits_{{P^{\prime } > P}}^{P} M_{RP} M_{{RP^{\prime } }}$$

Correspondent to an edge between node set P in the 1-mode network

Two stars:$$S_{P2}$$

$$\mathop \sum \nolimits_{P = 1}^{P} \mathop \sum \nolimits_{{R^{\prime } > R}}^{R} M_{PR} M_{{PR^{\prime } }}$$

Correspondent to an edge between node set R in the 1-mode network

Three stars:$$S_{R3}$$

$$\mathop \sum \nolimits_{R = 1}^{R} \mathop \sum \nolimits_{{P^{\prime \prime } > P^{\prime } > P}}^{P} M_{RP} M_{{RP^{\prime } }} M_{{RP^{\prime \prime } }}$$

Correspondent to a triangle between node set P in the 1-mode network

Three stars:$$S_{P3}$$

$$\mathop \sum \nolimits_{P = 1}^{P} \mathop \sum \nolimits_{{R^{\prime \prime } > R^{\prime } > R}}^{R} M_{PR} M_{{PR^{\prime } }} M_{{PR^{\prime \prime } }}$$

Correspondent to a triangle between node set R in the 1-mode network

Three trails:$$L_{3}$$

$$\mathop \sum \nolimits_{{P^{\prime } > P}}^{P} \mathop \sum \nolimits_{{R^{\prime } > R}}^{R} M_{PR} M_{{PR^{\prime } }} M_{{P^{\prime } R}} \left( {1 - M_{{P^{\prime } R^{\prime } }} } \right)$$

Reflect global connectivity in bipartite networks

Cycle:$$C_{4}$$

$$\mathop \sum \nolimits_{{P^{\prime } > P}}^{P} \mathop \sum \nolimits_{{R^{\prime } > R}}^{R} M_{PR} M_{{PR^{\prime } }} M_{{P^{\prime } R}} M_{{P^{\prime } R^{\prime } }}$$

Local closures in bipartite networks

1. $${M}_{RP}$$ represents the value of the elements in the bi-adjacent matrix of the bipartite network. If node R and P are linked, $${M}_{RP}=1$$. Otherwise $${M}_{RP}=0$$