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How many steps apart are any two people? Why can a rumour reach everyone so fast?
Graph Networks lab · Last updated: 16 October 2026
How many steps apart are any two people? In this 3D lab, you build a network of friends, measure the paths between them and watch a rumour race through it. It introduces graph theory, the maths behind social networks, maps, the internet and how diseases spread.
What you'll discover
- A graph is a set of dots, called nodes, joined by lines, called edges.
- Because friends-of-friends multiply so quickly, most people in a network are only a few steps apart.
- A few long-range links and well-connected hubs make a message spread through a network much faster.
The science in plain words
In maths, a graph is not a chart but a network: a set of points called nodes joined by lines called edges. Nodes can be people, cities, web pages or airports, and edges can be friendships, roads, links or flights. Graph theory began in 1736, when Leonhard Euler proved that nobody could walk across all seven bridges of the city of Königsberg exactly once each.
One useful measure is the path length between two nodes: the smallest number of edges you must travel to get from one to the other. In social networks these paths are surprisingly short. If each person knows 100 others, then within two steps you can reach up to 10,000 people, and within three steps up to a million, ignoring overlaps. Numbers grow so quickly that a handful of steps can, in principle, connect huge populations. This is the idea behind the phrase six degrees of separation.
Networks like this are called small-world networks. Most links are local, between people who share friends, but a few long-range links act as shortcuts across the whole network, and some hubs have far more connections than average. That is why a rumour, a viral video or an infection can reach almost everyone in a few rounds of passing on, and why removing a few key hubs can slow it down.
Where it fits
- India, NCERT: A maths topic beyond the NCERT science syllabus for classes 6 to 10.
- United States: Grades 6 to 12
Common questions
What is graph theory?
Graph theory is the branch of maths that studies networks made of points, called nodes, joined by lines, called edges. It is used to plan routes, design computer networks, run social media, schedule tasks and understand how diseases spread through communities.
What does six degrees of separation mean?
It is the idea that any two people on Earth are linked by a short chain of acquaintances, about six steps long. Because each person knows many others, the number of people you can reach grows extremely fast with each step, so long chains are rarely needed.
Why do rumours spread so quickly?
Each person who hears a rumour can pass it to several others, so the number who know it multiplies with every round. Social networks also contain well-connected people and links between separate groups, which act as shortcuts and carry the rumour into new circles very fast.
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Try it yourself
The Graph Networks lab is one of the interactive 3D science labs inside Taz. Change one thing, predict what will happen, then run it and watch. Labs open after you sign in.