Graph-based dependency management

When managing module dependencies in a system, treat the dependencies as a directed graph and apply appropriate graph algorithms to ensure proper initialization order and prevent errors.

Key considerations:

1. Implement topological sorting for dependencies to ensure modules are initialized in the correct order (modules should be initialized after their dependencies)
2. Handle circular dependencies explicitly - they can cause infinite recursion in graph traversal algorithms
3. Calculate proper distance metrics when modules have multiple import paths

Example of calculating proper distance in a module graph:

// When adding a related module, calculate the correct distance 
// by considering all possible paths
public addRelatedModule(module: Module) {
  this._imports.add(module);
  // Take the maximum distance to ensure all dependencies are resolved
  module.distance = this._distance + 1 > module._distance 
    ? this._distance + 1 
    : module._distance;
}

For circular dependencies, consider implementing cycle detection as part of your topological sort or applying algorithms like Tarjan’s strongly connected components algorithm to identify and manage cycles appropriately.

Failing to use proper graph algorithms for dependency management can lead to subtle runtime errors where modules are initialized in an incorrect order, resulting in undefined references or incomplete configurations.