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 |