Cycles and clustering in bipartite networks

Area of Science:

• Network science
• Graph theory
• Sociology

Background:

• Standard clustering coefficient is undefined in networks lacking three-node cycles (e.g., bipartite networks).
• Existing methods for analyzing clustering in such networks are limited.
• Understanding network structure is crucial in fields like epidemiology and social science.

Purpose of the Study:

• To introduce and validate an alternative clustering coefficient for networks without three-node cycles.
• To compare this new coefficient with the standard one in bipartite and monopartite networks.
• To develop an improved method for estimating cycles of larger sizes in complex networks.

Main Methods:

• Defined a novel clustering coefficient based on the fraction of four-node cycles.
• Computed this coefficient for bipartite and monopartite sexual contact networks.
• Compared the results with traditional clustering coefficient calculations.
• Derived a new analytical expression for estimating larger cycles.

Main Results:

• The new four-node cycle-based coefficient demonstrated similar clustering properties to the standard coefficient where applicable.
• Clustering coefficients were comparable between the bipartite and monopartite sexual contact networks.
• The derived expression for estimating larger cycles showed improved accuracy and broader applicability.

Conclusions:

• The proposed clustering coefficient is a viable alternative for networks lacking three-node cycles.
• Network clustering is consistent across different network structures (bipartite vs. monopartite) in sexual contact data.
• The new analytical estimation method enhances the understanding of complex network structures.