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24 is then the minimum eccentricity across all vertices, and the diameter is the maximum eccentricity across all vertices. Thus, the radius represents the maximal distance from the most “central” node in the graph to all other nodes, and the diameter represents the maximal distance from the least “central” node in the graph to all other nodes. Due to the computational complexity associated with determining the actual ra- dius and diameter, the radius and diameter of a graph is often estimated by calculating the eccentricity of a large random sample of nodes in the network. In such cases, the diameter should be viewed as a lower bound of the true diameter, and the radius as an upper bound of the true radius. 2.3.3 Degree distribution The degree distribution of a graph is a function P(k) which describes the fraction of the network’s nodes which have degree k. The degree distribution describes how the links in the graph are distributed among the nodes. For example, the degree distribution of a graph with randomly placed edges among n nodes follows a binomial distribution of P (k) = n − 1pk (1 − p)n−1−k (2.1) k where p represents the probability that any two nodes are connected. Most real-world networks have been shown to deviate from random graphs, and instead, have a bias whereby a few high-degree nodes hold a large fraction of the links.PDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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