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Three Properties of Real-World Graphs

From Graph Theory in the Information Age by Fan Chung:

Empirically, most real-world graphs have the following properties:

  • sparsity — The number of edges is within a constant multiple of the number of vertices.
  • small world phenomenon — Any two vertices are connected by a short path. Two vertices having a common neighbor are more likely to be neighbors.
  • power law degree distribution — The degree of a vertex is the number of its neighbors. The number of vertices with degree j (or having j neighbors) is proportional to j
    for some fixed constant β.

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