Modeling and analysis of affiliation networks with preferential attachment and subsumption

Area of Science:

• Network Science
• Complex Systems
• Data Mining

Background:

• Preferential attachment models network growth based on node degree.
• Affiliation networks represent groups of nodes, often lacking power-law degree distributions in graph views.
• Existing models do not fully capture the structure of affiliation networks.

Purpose of the Study:

• To propose a preferential attachment mechanism tailored for affiliation networks.
• To demonstrate the emergence of power-law characteristics in hypergraph and simplicial complex representations of these networks.
• To provide a framework for synthetic generation of diverse affiliation network structures.

Main Methods:

• Developed a preferential attachment model for affiliation networks.
• Utilized hypergraph and simplicial complex representations to analyze network properties.
• Investigated algorithmic and analytic features including implicit preferential attachment and subsumption.

Main Results:

• The proposed model exhibits power-law degree distributions in hypergraph and simplicial complex views.
• The model demonstrates implicit preferential attachment and a locality property.
• Subsumption in simplicial complexes allows for implicit deletion of affiliations and control over size distribution.

Conclusions:

• The new preferential attachment model effectively captures affiliation network characteristics.
• Hypergraph and simplicial complex representations are crucial for observing power-law behavior.
• The framework serves as a versatile tool for simulating and studying affiliation networks.