The diameter of random graphs
نویسندگان
چکیده
منابع مشابه
The Diameter of Random Graphs
Extending some recent theorems of Klee and Larman, we prove rather sharp results about the diameter of a random graph. Among others we show that if d = d(n) > 3 and m = m(n) satisfy (log n)/d 3 log log n -> oo, 2rf_Imd'/'nd+x log n -» oo and dd~2md~l/nd — log n -» -oo then almost every graph with n labelled vertices and m edges has diameter d. About twenty years ago Erdös [7], [8] used random g...
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We show that the diameter D(Gn) of a random labelled connected planar graph with n vertices is asymptotically almost surely of order n1/4, in the sense that there exists a constant c > 0 such that P (D(Gn) ∈ (n1/4− , n )) ≥ 1− exp(−n ) for small enough and n large enough (n ≥ n0( )). We prove similar statements for rooted 2-connected and 3-connected maps and planar graphs.
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We consider the diameter of a random graph G(n, p) for various ranges of p close to the phase transition point for connectivity. For a disconnected graph G, we use the convention that the diameter of G is the maximum diameter of its connected components. We show that almost surely the diameter of random graph G(n, p) is close to log n log(np) if np → ∞. Moreover if np log n = c > 8, then the di...
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Large real-world networks are typically scale-free. Recent research has shown that such graphs are described best in a geometric space. More precisely, the internet can be mapped to a hyperbolic space such that geometric greedy routing performs close to optimal (Boguná, Papadopoulos, and Krioukov. Nature Communications, 1:62, 2010). This observation pushed the interest in hyperbolic networks as...
متن کاملThe Diameter of Random Sparse Graphs
Abstract We consider the diameter of a random graph G(n, p) for various ranges of p close to the phase transition point for connectivity. For a disconnected graph G, we use the convention that the diameter of G is the maximum diameter of its connected components. We show that almost surely the diameter of random graph G(n, p) equals (1 + o(1)) log n log(np) if np → ∞. Moreover if np log n = c >...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1981
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1981-0621971-7