Dimensionality of social networks using motifs and eigenvalues

Area of Science:

• Network science
• Computational social science
• Complex systems

Background:

• Understanding the intrinsic dimensionality of social networks is crucial for modeling their structure and evolution.
• Previous models often assume simplified network topologies, potentially missing key organizational principles.

Purpose of the Study:

• To investigate and quantify the dimensionality of social networks.
• To propose and validate a hypothesis regarding the relationship between network dimension and network size.

Main Methods:

• Developing experimental methods to predict network dimensionality.
• Utilizing a social network model based on an m-dimensional metric space with power-law influence regions.
• Analyzing real-world social network data from Facebook and LinkedIn.

Main Results:

• The optimal model fit occurs when the dimension (m) scales logarithmically with the number of nodes.
• This supports the 'logarithmic dimension hypothesis' for social networks.
• Validation through analysis of motif count distributions and eigenvalue distributions.

Conclusions:

• Social networks possess a dimension that grows logarithmically with their size.
• This finding provides a new perspective on the fundamental structure of large-scale social systems.
• The proposed model and hypothesis offer a more accurate representation of real-world network properties.