The number of possible graphs with n nodes is:

  • A: n
  • B: n2
  • C: n3
  • D: 2n
  • E: 2n2

    Answer: E

    Whoa! This is huge. There are 65,536 possible graphs with 4 nodes, and 33,554,432 possible graphs with 5 nodes.

    If we think about the adjacency matrix representation of a graph, there is an n × n matrix with a 0 or 1 in position [i][j] iff there is an arc from i to j. Since there are n2 bits, the number of values of all possible matrices of bits is 2n2

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