Reorderability of node-filtered order complexes.

Area of Science:

• Complex Systems
• Network Science
• Applied Topology

Background:

• Growing graphs model diverse developmental processes, from biological systems to social networks.
• These systems often follow specific proliferation rules for node and connection emergence.
• Deviations from these rules, like altered node order, can impact system development.

Purpose of the Study:

• To investigate the topological changes in growing graph trajectories when node emergence order is perturbed.
• To quantify the robustness of different growing graph models to node order permutations.
• To establish theoretical links between local and global reorderability in complex networks.

Main Methods:

• Applied topological methods were used to analyze graph structures.
• Six different growing graph models were evaluated.
• Metrics for global reorderability (robustness to random node order) and local reorderability (robustness to local node swaps) were developed and applied.

Main Results:

• The six graph models exhibit a spectrum of both local and global reorderability.
• Theoretical connections were established between robustness to pairwise node ordering and arbitrary node orderings.
• The study identifies specific models that are more resilient to perturbations in node emergence sequence.

Conclusions:

• The reorderability of growing graphs is a key topological property that varies across different models.
• Understanding reorderability has implications for designing more robust and adaptable complex systems.
• Future work can explore practical applications in network design and analysis.