This project implements a Markov Chain scaling analysis in Python, focusing on the computation of path probabilities and their scaling behaviors. The analysis includes polynomial and exponential scaling methods. This was implemented as a course project for the courese PH5490 at IIT Madras. Link to the refered paper is: https://www.nature.com/articles/ncomms6121

Path Checking: Utilizes breadth-first search (BFS) to identify paths from the start state to the target state.

Node Filtering: Removes nodes that are not involved in the identified paths.

Graph Analysis: Identifies strongly connected components and classifies them as acyclic, monocyclic, or multicyclic.

Polynomial Scaling: This method computes the growth of paths in polynomial terms.

Exponential Scaling: This method analyzes the growth of paths in exponential terms.

NumPy: For numerical operations and handling arrays.

SciPy: For sparse matrix operations and linear algebra.

NetworkX: For graph-based computations and pathfinding.

Matplotlib: For visualizing results through plots.

To use this implementation, you can define a transition matrix for a simple Markov chain and specify start and target states. The scaling analysis can then be computed based on these parameters.