Knowledge graphs

How connected are you?

In the curriculum:Knowledge graphsSee the map →

🎓 School maths · Years 8–9Networks & problem solving — Count steps along connections to find the shortest path.Maths by year →

The Case. They say everyone is only a few friends away from anyone on Earth. A knowledge graph — dots for people, lines for friendships — lets a computer prove it.

Your tools. Plain Python explores the graph friend-by-friend to find the shortest chain; matplotlib draws it.

Investigate. Press Run. The orange path is the shortest chain of friends from You to Star.

This ‘spread out and search’ idea is how maps find routes and how search engines connect facts.
Add a new friendship to the list and watch the shortest path change.

your_code.py

Starting Python…

import matplotlib.pyplot as plt
import numpy as np
from collections import deque

# A knowledge graph: who knows who.
friends = {
    "You":  ["Sam", "Mia"],
    "Sam":  ["You", "Leo"],
    "Mia":  ["You", "Zoe"],
    "Leo":  ["Sam", "Star"],
    "Zoe":  ["Mia", "Star"],
    "Star": ["Leo", "Zoe"],   # the famous person!
}

def shortest_path(start, goal):
    q = deque([[start]])
    seen = {start}
    while q:
        path = q.popleft()
        if path[-1] == goal:
            return path
        for f in friends[path[-1]]:
            if f not in seen:
                seen.add(f); q.append(path + [f])
    return None

path = shortest_path("You", "Star")
print("You are", len(path) - 1, "hops from Star:", " -> ".join(path))

# Draw the graph in a circle.
names = list(friends)
pos = {n: (np.cos(t), np.sin(t))
       for n, t in zip(names, np.linspace(0, 2 * np.pi, len(names), endpoint=False))}
for n, nbrs in friends.items():
    for m in nbrs:
        plt.plot([pos[n][0], pos[m][0]], [pos[n][1], pos[m][1]], color="#cdd7e6", zorder=1)
for n, (x, y) in pos.items():
    on = n in path
    plt.scatter([x], [y], s=900, color="#ff7a59" if on else "#2f6df6", zorder=2)
    plt.text(x, y, n, ha="center", va="center", color="white", fontsize=9, zorder=3)
plt.title("How are you connected to Star?")
plt.axis("off")
plt.show()

The Reveal

Starting Python… (first time only — a few seconds)

🗒️ Detective's notes

Bundles your findings, chart and code into one PDF you can keep, print or hand in.

🧩 How this code works

The tools it uses

Matplotlib — your crayon box — it turns numbers into charts and pictures.
NumPy — a row of boxes that holds numbers, so you can do maths to all of them at once.
collections — handy containers, like a queue for exploring step by step.

What this one does

• It draws a line chart — great for change over time.
• It draws a scatter graph — great for one thing vs another.

How to read it, top to bottom

1. Import — bring in the tools (listed above).
2. The data — the lists and numbers near the top. These are the bits you change.
3. The work — a little maths, or a loop that repeats a step.
4. Show it — print(...) writes words; plt.show() draws the picture.

Use it for your own problems

Change the numbers at the top and press Run — nothing breaks, so experiment!
Ask your own version of the question — swap in your family, your scores, your week.
The same tools work on any numbers — that's the superpower you're learning.

Need a hint?

The computer checks all friends 1 hop away, then 2 hops, then 3 — the first time it reaches Star is the shortest path.