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# Graph Theory

Any connected group of things can be represented as a graph: cities and roads, people and friendships, and more. Learn why an even number of people have an odd number of friends.

**entire** figure:

1) without picking up your writing/tracing tool and

2) without ever doubling back along a line already traced?

The project of building 20 roads connecting 9 cities is under way, as outlined above. So far, only some of the 20 roads are constructed, and the digit on each city indicates the number of constructed roads to other cities.

How many complete roads are there among these cities?

In the following graph, is there a path that visits each node exactly once?

You may start at any node.

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