import json

# Sample data structure based on your JSON
data = {
    "primes": [
        {"value": 2, "category": "prime"},
        {"value": 3, "category": "prime"},
        {"value": 5, "category": "prime"},
        # add other nodes as needed
    ],
    "perfect_numbers": [
        {"value": 6, "category": "perfect_number"},
        {"value": 28, "category": "perfect_number"},
        # add other nodes as needed
    ],
    "relationships": [
        {"source": 2, "target": 3, "relationship": "generates_Mersenne_prime"},
        # add other predefined relationships
    ]
}

# Inferred relationship function
def infer_relationships(nodes):
    inferred_relationships = []
    node_values = {node['value']: node for node in nodes}
    
    # Iterate over node pairs to find possible relationships
    for source in nodes:
        for target in nodes:
            if source == target:
                continue
            
            source_value = source['value']
            target_value = target['value']
            
            # Check for multiplication relationship
            if target_value % source_value == 0:
                factor = target_value // source_value
                inferred_relationships.append({
                    "source": source_value,
                    "target": target_value,
                    "relationship": f"multiplied_by_{factor}"
                })
                
            # Check for addition relationship
            if target_value - source_value > 0:
                addend = target_value - source_value
                inferred_relationships.append({
                    "source": source_value,
                    "target": target_value,
                    "relationship": f"add_{addend}"
                })
                
    return inferred_relationships

# Infer relationships
nodes = data["primes"] + data["perfect_numbers"]
new_relationships = infer_relationships(nodes)

# Append new relationships to the original data
data["relationships"].extend(new_relationships)

# Output the updated JSON
with open("updated_graph_data.json", "w") as file:
    json.dump(data, file, indent=4)