Flagser

Flagser computes persistent homology of directed flag complexes constructed from finite directed graphs to analyze topological features of large-scale network data.

Key Features:

• Directed Flag Complex Construction: Constructs directed flag complexes from finite directed graphs.
• Persistent Homology Computation: Computes persistent homology for flexible filtrations on the graph and its flag complex, building upon Ripser with optimizations for large computations.
• Flexibility with Graph Types: Supports both directed and undirected input graphs.
• Approximate Homology Computations: Provides an "Approximate" option that reduces computation time for homology while maintaining high precision.
• Parallelization and Performance Recording: Enables parallelization across multiple CPU cores during complex construction and records hardware usage, memory consumption, and computation times.

Scientific Applications:

• Neuroscience (Blue Brain Project): Construction of directed flag complexes from digital reconstructions of brain microcircuitry produced by the Blue Brain Project.
• Large-scale network analysis: Application to various other large-scale datasets for topological analysis of complex networks.

Methodology:

Constructs directed flag complexes from finite directed graphs and computes persistent homology for filtrations on the graph and complex using algorithms derived from Ripser; supports an "Approximate" computation mode, enables parallelization across cores, and records hardware usage, memory consumption, and computation times.