@Applied Course Please edit the question. Diagram is missing.

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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 _____?

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Let $V$ be the degree of each node and $E$ be the number of edges in the graph. As such, each digit on each city is $V$, and the number of roads will be $E$. The sum of all degrees will equal twice number of edges:

$\Sigma V=2E$

Therefore $2E=1+1+1+2+2+3+3+4+5 = 11$

There are $11$ complete roads among these cities.

The road map with red complete tracks can be illustrated as seen below:

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