Create app.py

app.py

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+import gradio as gr
+import numpy as np
+import matplotlib.pyplot as plt
+import networkx as nx
+
+# Helper Functions
+def parse_graph_input(graph_input):
+    """Parse user input to create an adjacency list."""
+    try:
+        graph = eval(graph_input)
+        if isinstance(graph, dict):
+            return graph
+    except:
+        pass
+
+    try:
+        edges = eval(graph_input)
+        if not isinstance(edges, list):
+            raise ValueError("Invalid graph input. Please use an adjacency list or edge list.")
+        
+        graph = {}
+        for u, v in edges:
+            graph.setdefault(u, []).append(v)
+            graph.setdefault(v, []).append(u)
+        return graph
+    except:
+        raise ValueError("Invalid graph input. Please use a valid adjacency list or edge list.")
+
+def visualize_graph(graph):
+    """Generate a visualization of the graph using a circular layout."""
+    plt.figure()
+    nodes = list(graph.keys())
+    edges = [(u, v) for u in graph for v in graph[u]]
+    
+    pos = nx.circular_layout(nx.Graph(edges))
+    nx.draw(
+        nx.Graph(edges),
+        pos,
+        with_labels=True,
+        node_color='lightblue',
+        edge_color='gray',
+        node_size=500,
+        font_size=10
+    )
+    return plt.gcf()
+
+def spectral_isomorphism_test(graph1, graph2):
+    """Perform spectral isomorphism test with step-by-step explanation."""
+    adj_spectrum1 = sorted(np.linalg.eigvals(nx.adjacency_matrix(nx.Graph(graph1)).todense()).real)
+    adj_spectrum2 = sorted(np.linalg.eigvals(nx.adjacency_matrix(nx.Graph(graph2)).todense()).real)
+    lap_spectrum1 = sorted(np.linalg.eigvals(nx.laplacian_matrix(nx.Graph(graph1)).todense()).real)
+    lap_spectrum2 = sorted(np.linalg.eigvals(nx.laplacian_matrix(nx.Graph(graph2)).todense()).real)
+
+    adj_spectrum1 = [round(float(x), 2) for x in adj_spectrum1]
+    adj_spectrum2 = [round(float(x), 2) for x in adj_spectrum2]
+    lap_spectrum1 = [round(float(x), 2) for x in lap_spectrum1]
+    lap_spectrum2 = [round(float(x), 2) for x in lap_spectrum2]
+
+    output = (
+        f"### **Spectral Isomorphism Test Results**\n\n"
+        f"#### **Step 1: Node and Edge Counts**\n"
+        f"- **Graph 1**: Nodes: {len(graph1)}, Edges: {sum(len(neighbors) for neighbors in graph1.values()) // 2}\n"
+        f"- **Graph 2**: Nodes: {len(graph2)}, Edges: {sum(len(neighbors) for neighbors in graph2.values()) // 2}\n\n"
+        f"#### **Step 2: Adjacency Spectra**\n"
+        f"- Graph 1: {adj_spectrum1}\n"
+        f"- Graph 2: {adj_spectrum2}\n"
+        f"- Are the adjacency spectra approximately equal? {'✅ Yes' if np.allclose(adj_spectrum1, adj_spectrum2) else '❌ No'}\n\n"
+        f"#### **Step 3: Laplacian Spectra**\n"
+        f"- Graph 1: {lap_spectrum1}\n"
+        f"- Graph 2: {lap_spectrum2}\n"
+        f"- Are the Laplacian spectra approximately equal? {'✅ Yes' if np.allclose(lap_spectrum1, lap_spectrum2) else '❌ No'}\n\n"
+        f"#### **Final Result**\n"
+        f"- Outcome: {'✅ PASS' if np.allclose(adj_spectrum1, adj_spectrum2) and np.allclose(lap_spectrum1, lap_spectrum2) else '❌ FAIL'}\n"
+        f"- Conclusion: The graphs are {'isomorphic' if np.allclose(adj_spectrum1, adj_spectrum2) and np.allclose(lap_spectrum1, lap_spectrum2) else 'NOT isomorphic'}.\n"
+    )
+    return output
+
+def process_inputs(graph1_input, graph2_input):
+    """Process user inputs and perform the spectral isomorphism test."""
+    graph1 = parse_graph_input(graph1_input)
+    graph2 = parse_graph_input(graph2_input)
+
+    result = spectral_isomorphism_test(graph1, graph2)
+
+    graph1_plot = visualize_graph(graph1)
+    graph2_plot = visualize_graph(graph2)
+
+    return graph1_plot, graph2_plot, result
+
+# Gradio Interface
+with gr.Blocks(title="Graph Theory Project") as demo:
+    gr.Markdown("# Graph Theory Project")
+    gr.Markdown("Analyze two graphs using spectral isomorphism tests!")
+
+    with gr.Row():
+        graph1_input = gr.Textbox(label="Graph 1 Input (e.g., '{0: [1], 1: [0, 2], 2: [1]}' or edge list)")
+        graph2_input = gr.Textbox(label="Graph 2 Input (e.g., '{0: [1], 1: [0, 2], 2: [1]}' or edge list)")
+
+    with gr.Row():
+        graph1_output = gr.Plot(label="Graph 1 Visualization")
+        graph2_output = gr.Plot(label="Graph 2 Visualization")
+
+    result_output = gr.Textbox(label="Results", lines=20)
+
+    submit_button = gr.Button("Run")
+    submit_button.click(process_inputs, inputs=[graph1_input, graph2_input], outputs=[graph1_output, graph2_output, result_output])
+
+# Launch the app
+demo.launch()