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In the study of graphs and networks, the degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability distribution of these degrees over the whole network.The degree of a node in a network sometimes referred to incorrectly as the connectivity is the number of connections or edges the node has to other nodes. If a network is directed, meaning that edges point in one direction from one node to another node, then nodes have two different degrees, the indegree, which is the number of incoming edges, and the outdegree, which is the number of outgoing edges.The degree distribution Pk 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 nk of them have degree k, we have Pk = nkn.The same information is also sometimes presented in the form of a cumulative degree distribution, the fraction of nodes with degree greater than or equal to k.The degree distribution assumes considerable importance in the empirical study of networks such as the Internet and social networks, as well as in theoretical studies of mathematical network models. The simplest of network models, for example, the Bernoulli random graph, in which each of n nodes is connected or not with independent probability p or − p, has a binomial distribution of degreesor Poisson in the limit of large n. Most networks in the real world, however, have degree distributions very different from this. Most are highly rightskewed, meaning that a large majority of nodes have low degree but a small number, known as "hubs", have high degree. Some networks, notably the Internet, the world wide web, and some social networks are found to have degree distributions that approximately follow a power law Pk ~ k−ã, where ã is a constant. Such networks are called scalefree networks and have attracted particular attention for their structural and dynamical properties.