Features and heterogeneities in growing network models.

Area of Science:

• Network Science
• Complex Systems
• Statistical Physics

Background:

• Complex networks often exhibit node heterogeneity, with features ranging from discrete categories (e.g., website types, gene functions) to continuous variables (e.g., embedding space positions).
• Existing growing network models, such as preferential attachment, often simplify or overlook these intrinsic node properties.

Purpose of the Study:

• To generalize existing growing network models with preferential attachment to incorporate heterogeneous node features.
• To analyze the impact of node heterogeneity on network growth dynamics, degree distribution, and other topological properties.

Main Methods:

• Development of a generalized growing network model that accounts for discrete and continuous node features.
• Mathematical analysis of the emergent "effective fitness" for different node classes.
• Evaluation of network properties including degree distribution, clustering coefficient, and degree correlations.

Main Results:

• Node heterogeneity leads to an "effective fitness" for node classes, governing their link acquisition rates.
• The generalized model exhibits multiscaling degree distributions, similar to established fitness models.
• The model demonstrates robust preferential attachment, resulting in small clustering coefficients and negative degree correlations (disassortative mixing) at large network sizes.

Conclusions:

• Preferential attachment in growing networks with heterogeneous nodes generally leads to small clustering coefficients and disassortative mixing.
• The concept of "effective fitness" provides a unified framework for understanding link dynamics in heterogeneous complex networks.
• The findings offer insights into the structural properties of real-world networks like the World Wide Web and biological systems.