The Largest Eigenvalue of Sparse Random Graphs
نویسندگان
چکیده
منابع مشابه
The Largest Eigenvalue Of Sparse Random Graphs
We prove that for all values of the edge probability p(n) the largest eigenvalue of a random graph G(n, p) satisfies almost surely: λ1(G) = (1 + o(1))max{ √ ∆, np}, where ∆ is a maximal degree of G, and the o(1) term tends to zero as max{ √ ∆, np} tends to infinity.
متن کاملLargest sparse subgraphs of random graphs
For the Erdős-Rényi random graph Gn,p, we give a precise asymptotic formula for the size α̂t(Gn,p) of a largest vertex subset inGn,p that induces a subgraph with average degree at most t, provided that p = p(n) is not too small and t = t(n) is not too large. In the case of fixed t and p, we find that this value is asymptotically almost surely concentrated on at most two explicitly given points. ...
متن کاملThe largest eigenvalue of nonregular graphs
We give an upper bound for the largest eigenvalue of a nonregular graph with n vertices and the largest vertex degree ∆.
متن کاملA tight bound of the largest eigenvalue of sparse random graph
We analyze the largest eigenvalue and eigenvector for the adjacency matrices of sparse random graph. Let λ1 be the largest eigenvalue of an n-vertex graph, and v1 be its corresponding normalized eigenvector. For graphs of average degree d log n, where d is a large enough constant, we show λ1 = d log n + 1 ± o(1) and 〈1, v1〉 = √ n ( 1−Θ ( 1 logn )) . It shows a limitation of the existing method ...
متن کاملJu l 2 00 1 On the largest eigenvalue of a sparse random subgraph
We consider a sparse random subraph of the n-cube where each edge appears independently with small probability p(n) = O(n−1+o(1)). In the most interesting regime when p(n) is not exponentially small we prove that the largest eigenvalue is ∆(G)1/2(1+o(1)) = n log 2 log(p−1) × (1+o(1)) almost surely,where ∆(G) is the maximum degree of G. If p(n) is exponentially small but not proportional to 2−n/...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2003
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548302005424