Graph Created:
Vertices: ['Alice', 'Bob', 'Charlie', 'Elise']
Edges (with valence): A-B(1), B-C(1), C-E(1), A-E(2), A-C(1)
Valences: A=4, B=2, C=3, E=3
====================
--- Initial State ---
Alice=2, Bob=-3, Charlie=4, Elise=-1
Total Degree: 2
---
Applying sequence of set_fire operations...

Applying set_fire({'Alice', 'Charlie', 'Elise'})...
--- State after fire 1 ---
Alice=1, Bob=-1, Charlie=3, Elise=-1
Total Degree: 2
---

Applying set_fire({'Alice', 'Charlie', 'Elise'})...
--- State after fire 2 ---
Alice=0, Bob=1, Charlie=2, Elise=-1
Total Degree: 2
---

Applying set_fire({'Bob', 'Charlie'})...
--- Final State after Sequence ---
Alice=2, Bob=0, Charlie=0, Elise=0
Total Degree: 2
---
====================
Equivalent Net Firing Script:
{'Alice': 0, 'Bob': -1, 'Charlie': 1, 'Elise': 0}
====================
Laplacian Created.
====================
Applying Laplacian with the net firing script...
--- Final State via Laplacian ---
Alice=2, Bob=0, Charlie=0, Elise=0
Total Degree: 2
---
====================
Comparing final states...
Sequence Final State: {'Alice': 2, 'Bob': 0, 'Charlie': 0, 'Elise': 0}
Laplacian Final State:{'Alice': 2, 'Bob': 0, 'Charlie': 0, 'Elise': 0}

Success! The final states from both methods are identical.
