Definition
Given a (di)graph G = (V, E) (strongly) connected, where n = |V | and m = |E| (note that, since the graph is connected, we have m ≥ n − 1), the distance between two vertices u, v ∈ V is the number of edges along the shortest path from u to v and is denoted as d(u, v). The number of nodes separating u and v, i.e., d(u, v) − 1, is also called degree of separation.
The eccentricity of a node u is ecc(u) =max v ∈ V d(u, v), which measures in how many hops u can reach any other node in the graph. Hence, the diameter D (resp. the radius R) of G is defined as the maximum (resp. minimum) eccentricity among all the nodes, i.e., D =max u ∈ V ecc(u) (resp. R =min u ∈ V ecc(u)).
Given a node u ∈ V and an h ∈ [D] (where, for any positive integer x, [x] denotes the set {1, 2, …, x}), we call B h (u) the set {v : v ∈ V, d(u, v) ≤ h} and, similarly, N...
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Crescenzi, P., Marino, A. (2018). Degrees of Separation and Diameter in Large Graphs. In: Sakr, S., Zomaya, A. (eds) Encyclopedia of Big Data Technologies. Springer, Cham. https://doi.org/10.1007/978-3-319-63962-8_59-1
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Degrees of Separation and Diameter in Large Graphs- Published:
- 15 June 2022
DOI: https://doi.org/10.1007/978-3-319-63962-8_59-2
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Degrees of Separation and Diameter in Large Graphs- Published:
- 14 February 2018
DOI: https://doi.org/10.1007/978-3-319-63962-8_59-1