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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 in-degree, which is the number of incoming edges, and the out-degree, which is the number of ...
The degree distribution P(k) of a network is defined to be the fraction of nodes in the network with degree k. The simplest network model, for example, the (Erdős–Rényi model) random graph, in which each of n nodes is independently connected (or not) with probability p (or 1 − p), has a binomial distribution of degrees k (or Poisson in ...
The degrees of the vertices are represented as half-links or stubs. The sum of stubs must be even in order to be able to construct a graph (=). The degree sequence can be drawn from a theoretical distribution or it can represent a real network (determined from the adjacency matrix of the network).
The highest-degree nodes are often called "hubs", and are thought to serve specific purposes in their networks, although this depends greatly on the domain. In a random network the maximum degree, or the expected largest hub, scales as k max ~ log N, where N is the network size, a very slow dependence.
The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely indegree and outdegree. Accordingly, indegree is a ...
A network is called scale-free [6] [14] if its degree distribution, i.e., the probability that a node selected uniformly at random has a certain number of links (degree), follows a mathematical function called a power law. The power law implies that the degree distribution of these networks has no characteristic scale.
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In network science, the network entropy is a disorder measure derived from information theory to describe the level of randomness and the amount of information encoded in a graph. [1] It is a relevant metric to quantitatively characterize real complex networks and can also be used to quantify network complexity [ 1 ] [ 2 ]
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