Comparing brain networks of different size and connectivity density using graph theory.

Area of Science:

• Neuroscience
• Network Science
• Computational Biology

Background:

• Graph theory is crucial for analyzing brain connectivity (functional and anatomical).
• Comparing network topologies is complicated by variations in the number of nodes (N) and average degree (k).
• These variations can lead to spurious results when comparing empirical brain networks.

Purpose of the Study:

• To review and assess methods for overcoming biases in graph-theoretic comparisons of brain networks.
• To identify the benefits and pitfalls of different approaches for network analysis.
• To guide researchers in selecting appropriate methods for comparing network topologies.

Main Methods:

• Evaluation of graph definition strategies (unweighted/weighted graphs, fixed thresholds, average degrees, edge densities).
• Analysis of normalization techniques using random surrogates and their impact on graph measures.
• Exploration of methods estimating N,k-dependence for size effect correction.
• Inclusion of social science methods like exponential random graph models and motif counting.

Main Results:

• No single method provides a fully unbiased comparison of network topologies.
• Fixing N and k can alter network properties by including/excluding non-significant connections.
• Normalization via random surrogates can amplify N and k sensitivity for certain measures (e.g., clustering coefficient, small-world index).
• Estimating N,k-dependence shows promise for correcting size effects.

Conclusions:

• Comparing brain network topologies requires careful consideration of network size and density.
• Existing methods have limitations, and researchers must choose approaches based on their specific data and research questions.
• Further development of methods to account for N,k-dependence is needed for robust network analysis.