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    Area of Science:

    • Computational Biology
    • Systems Biology
    • Network Analysis

    Background:

    • Graphlet Degree Distribution Agreement (GDDA) is a metric for comparing graphlets.
    • GDDA has known stability issues in low-density graphs.
    • Graphlets are now used for comparing Petri net models of biological systems.

    Purpose of the Study:

    • To investigate GDDA stability issues in modified graphlets for Petri net models.
    • To quantify the impact of instability on GDDA values.
    • To determine if this is a common problem for Petri net biological models.

    Main Methods:

    • Analysis of GDDA metric performance on modified graphlets.
    • Evaluation across a spectrum of graph densities for Petri net models.
    • Comparison of instability characteristics with undirected Protein-Protein Interaction (PPI) models.

    Main Results:

    • GDDA remains unstable for modified graphlets within certain density ranges.
    • Instability affects some biological networks represented by Petri nets.
    • The scale of instability impact is reduced by approximately half compared to original graphlets.
    • Vulnerable density areas differ from PPI models, with a stable area observed for very sparse models.

    Conclusions:

    • GDDA instability persists in modified graphlets for Petri net biological models.
    • The characteristics and impact of instability are altered in the Petri net context.
    • Specific density ranges require careful consideration when using GDDA for these models.