On maximal entries in the principal eigenvector of graphs

By Britta Papendieck, P. Recht. 2000

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Principal eigenvectors of irregular graphs (2007, background): “If G is a connected graph and x is the principal eigenvector of G, then Papendieck and Recht [11] proved that xmax ≤ 1 √2 with equality if and only if G = K1,n−1.”
Eigenvector-centrality - a node-centrality? (2000, methodology): “Maximal entries in the principal eigenvector of graphs in dependence of p are investigated in Papendieck and Recht (2000). We refer to them for the proof of the statements below.”
Eigenvectors and eigenvalues of non-regular graphs (2005, methodology): “The maximal entry of the normalized eigenvector of a graph has been investigated by Papendieck and Recht [6] and Zhao and Hong [9].”
Analytic methods for uniform hypergraphs (2013, background): “Papendieck and Recht [34] showed that if G ∈ G2 (n) and [xi] ∈ Sn−12 is an eigenvector to λ (G) , then x2k ≤ 1/2 for any k ∈ V (G) .”
The maximum spectral radius of C4-free graphs of given order and size (2007, background): “First, a fact implied by Theorem 1 in [16]: Fact 4 Let x be a unit eigenvector to the spectral radius of a graph with some edges.”