Structural and information-theoretic complexity measures of brain networks: Evolutionary aspects and implications

Area of Science:

• Neuroscience
• Network Science
• Evolutionary Biology

Background:

• Understanding the evolution of neuronal phenotypes across species is complex.
• Complex network theory offers tools to analyze connectomic data using parameters like clustering coefficient, centrality, von Neumann entropy, and multifractality.
• These parameters may correlate with phylogenetic markers such as genome size.

Purpose of the Study:

• To investigate interspecific variations in network complexity measures across four mammalian connectomes (Felis catus, Mus musculus, Macaca mulatta, Homo sapiens).
• To identify potential evolutionary signatures within mammalian brain networks using structural and information-theoretic measures.
• To explore the relationship between network properties and genome size as a phylogenetic marker.

Main Methods:

• Analysis of structural complexity (clustering coefficient, centrality) and information-theoretic measures (von Neumann entropy, multifractality) in four mammalian connectomes.
• Comparison of these measures against genome size as a phylogenetic marker.
• Investigation of allometric scaling behavior of von Neumann entropy with community structure and its correlation with genome size.

Main Results:

• Network complexity measures partially corroborated the phylogenetic order but showed violations, notably with Mus musculus data.
• Von Neumann entropy exhibited significant allometric scaling with community structure across all connectomes (p<0.0001, R²>0.95).
• The scaling exponent of von Neumann entropy demonstrated monotonicity with genome size, suggesting a conserved evolutionary relationship.

Conclusions:

• While some network complexity measures offer partial evolutionary insights, von Neumann entropy's consistent allometric scaling with community structure and its monotonic relationship with genome size present a more robust evolutionary signature.
• This finding highlights the potential of information-theoretic measures in understanding the evolution of brain networks.
• Further analysis using synthetic network models provided insights into the singularities of real connectomes.