Clustering under the line graph transformation: application to reaction network

Area of Science:

• Network science
• Systems biology
• Biochemistry

Background:

• Real-world networks often consist of two complementary networks, such as metabolic networks with compounds and reactions as nodes.
• Line graph transformation is a technique to relate these networks, where edges become nodes.
• Metabolic compound networks are classified as hierarchical, but reaction networks lack detailed topological study.

Purpose of the Study:

• To investigate the topological properties of metabolic reaction networks.
• To apply line graph transformation to hierarchical networks and analyze the resulting network's clustering coefficient.
• To determine the classification of metabolic reaction networks based on their topological characteristics.

Main Methods:

• Applied line graph transformation to a hierarchical network model.
• Calculated the degree-dependent clustering coefficient (C(k)) for the transformed network.
• Compared theoretical predictions with experimental data from the KEGG database for chemical reactions.

Main Results:

• The initial hierarchical network showed C(k) scaling as approximately k(-1.1).
• The transformed network exhibited weak scaling, with C(k) approximately k(0.08).
• Theoretical predictions showed good agreement with experimental KEGG database data.

Conclusions:

• The weak scaling of the transformed network suggests it is a degree-independent clustering network.
• This finding allows for a discussion on the hierarchical classification of metabolic reaction networks.
• The study provides new insights into the network structure of metabolic reactions.