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September 10, 2026

Graph theory can be abstract, but translating it into Python using standard data structures makes the mechanics much clearer.

The Core Implementation

Here is a snippet of how the main traversal logic works. We keep track of visited nodes to avoid infinite loops and build our component groups recursively:

def dfs(node, visited, matrix, current_component):
    visited.add(node)
    current_component.append(node)
    
    # Check all possible neighbors in the matrix
    for neighbor in range(len(matrix[node])):
        if matrix[node][neighbor] == 1 and neighbor not in visited:
            dfs(neighbor, visited, matrix, current_component)

Reflections

This approach worked flawlessly for the dataset provided. Moving forward, I might optimize this for sparse graphs by using adjacency lists instead of matrices to save memory.