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    Degree Sequence

    Definition

    Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees (valencies) of its graph vertices. The number of degree sequences for a graph of a given order is closely related to graphical partitions. The sum of the elements of a degree sequence of a graph is always even due to fact that each edge connects two vertices and is thus counted twice.

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    RandomGraph

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