---
title: Opinion Dynamics
description: A complete example simulating how agents converge on a shared opinion through repeated neighbor interactions.
---

## Overview

This example models **opinion dynamics** — a classic ABM scenario where each agent holds a real-valued opinion and gradually shifts toward the average opinion of its neighbors. Over time, agents converge toward consensus.

It demonstrates:
- Setting up parameters and a custom graph
- Writing initial data and timestep functions
- Running to convergence
- Reading final state

## The simulation

```python
import random
import networkx as nx
from emergent import AgentModel

# ── 1. Define agent behavior ──────────────────────────────────────────────────

def initial_data(model):
    """Each agent starts with a random opinion in [0, 1]."""
    return {"opinion": random.uniform(0, 1)}


def timestep(model):
    """
    Each agent moves its opinion halfway toward the average
    opinion of its immediate neighbors.
    """
    graph = model.get_graph()
    updates = {}

    for node in graph.nodes():
        neighbors = list(graph.neighbors(node))
        if not neighbors:
            continue
        neighbor_avg = sum(graph.nodes[n]["opinion"] for n in neighbors) / len(neighbors)
        current = graph.nodes[node]["opinion"]
        updates[node] = (current + neighbor_avg) / 2

    # Apply updates after the full graph has been read (synchronous update)
    for node, new_opinion in updates.items():
        graph.nodes[node]["opinion"] = new_opinion


# ── 2. Configure the model ────────────────────────────────────────────────────

model = AgentModel()
model.update_parameters({
    "num_nodes": 30,
    "graph_type": "cycle",
    "convergence_data_key": "opinion",
    "convergence_std_dev": 0.005,
})
model.set_initial_data_function(initial_data)
model.set_timestep_function(timestep)

# ── 3. Run ────────────────────────────────────────────────────────────────────

model.initialize_graph()
steps = model.run_to_convergence()
print(f"Converged after {steps} timesteps")

# ── 4. Inspect results ────────────────────────────────────────────────────────

graph = model.get_graph()
opinions = [graph.nodes[n]["opinion"] for n in graph.nodes()]
print(f"Final opinion range: {min(opinions):.4f} – {max(opinions):.4f}")
print(f"Std dev: {sum((o - sum(opinions)/len(opinions))**2 for o in opinions) / len(opinions) ** 0.5:.6f}")
```

## What to expect

On a **cycle graph**, information only travels between immediate neighbors, so convergence is slower than on a complete graph. With 30 nodes and a convergence threshold of `0.005`, you should see the simulation settle in a few hundred timesteps with all agents very close to a shared mean opinion.

## Variations to try

<AccordionGroup>
  <Accordion title="Switch to a complete graph">
    Change `graph_type` to `"complete"` to see how convergence speed changes when every agent can directly influence every other agent.

    ```python
    model.update_parameters({"graph_type": "complete"})
    ```
  </Accordion>

  <Accordion title="Use a scale-free network">
    Replace the built-in graph with a Barabási–Albert graph to model opinion dynamics on a social network with hubs.

    ```python
    G = nx.barabasi_albert_graph(n=30, m=2)
    model.set_graph(G)
    ```
  </Accordion>

  <Accordion title="Add noise to each update">
    Introduce a small random perturbation at each step to prevent perfect convergence and model real-world uncertainty.

    ```python
    model.update_parameters({"noise": 0.02})

    def timestep_with_noise(model):
        graph = model.get_graph()
        updates = {}
        for node in graph.nodes():
            neighbors = list(graph.neighbors(node))
            if not neighbors:
                continue
            avg = sum(graph.nodes[n]["opinion"] for n in neighbors) / len(neighbors)
            current = graph.nodes[node]["opinion"]
            noise = random.uniform(-model["noise"], model["noise"])
            updates[node] = max(0, min(1, (current + avg) / 2 + noise))
        for node, val in updates.items():
            graph.nodes[node]["opinion"] = val

    model.set_timestep_function(timestep_with_noise)
    ```
  </Accordion>
</AccordionGroup>
