trophic.py

import numpy as np

def compute_trophic_influence(edges, num_nodes, decay=0.9, tol=1e-6, max_iter=100):
    S = np.zeros((num_nodes, num_nodes))

    # Step 1: Weighted influence
    for consumer, prey in edges:
        S[consumer - 1][prey - 1] = 1 / (prey + 1)  # Uneven weights

    # Step 2: Normalize rows
    for i in range(num_nodes):
        row_sum = np.sum(S[i])
        if row_sum > 0:
            S[i] /= row_sum

    # Step 3: Power iteration with teleportation
    T = np.ones(num_nodes) / num_nodes  # uniform init
    for _ in range(max_iter):
        new_T = (1 - decay) / num_nodes + decay * (S @ T)
        if np.linalg.norm(new_T - T, ord=1) < tol:
            break
        T = new_T

    apex_node = np.argmax(T) + 1
    return apex_node, T

# Your edges
edges = [
    (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
    (2, 1), (2, 3), (2, 4), (2, 5), (2, 7),
    (3, 1), (3, 2), (3, 4), (3, 5), (3, 6),
    (4, 1), (4, 2), (4, 3),
    (5, 1), (5, 2), (5, 3), (5, 6),
    (6, 1), (6, 3), (6, 4), (6, 9),
    (7, 2), (7, 8), (7, 9),
    (8, 5), (8, 7),
    (9, 6), (9, 7)
]

num_nodes = 9
apex_node, trophic_levels = compute_trophic_influence(edges, num_nodes)

# Output
print(f"Highest value node (apex node): {apex_node}")
print("Trophic influence values for all nodes:")
for node, value in enumerate(trophic_levels, 1):
    print(f"Node {node}: {value:.6f}")