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The [[degree (graph theory)|degree]] of a node in a network (sometimes referred to incorrectly as the [[Connectivity (graph theory)|connectivity]]) is the number of connections or [[Edge (graph theory)#Graph|edges]] the node has to other nodes. If a network is [[directed graph|directed]], meaning that edges point in one direction from one node to another node, then nodes have two different degrees, the in-degree, which is the number of incoming edges, and the out-degree, which is the number of outgoing edges.
The degree distribution ''P''(''k'') of a network is then defined to be the fraction of nodes in the network with degree ''k''. Thus if there are ''n'' nodes in total in a network and ''n''<sub>''k''</sub> of them have degree ''k'', we have
The same information is also sometimes presented in the form of a ''cumulative degree distribution'', the fraction of nodes with degree smaller than ''k'', or even the ''complementary cumulative degree distribution'', the fraction of nodes with degree greater than or equal to ''k'' (1 - ''C'') if one considers ''C'' as the ''cumulative degree distribution''; i.e. the complement of ''C''.
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