A nested if construction in which each nested if is written in the same line as the previous else is called an if-else chain, and is used extensively in many programming problems.

For PHPTR Only Chapter 8 Spectra of Complex Networks 1. Explain why the spectrum of a graph is independent of vertex labeling. Answer: When we change the vertex labeling, i.e., when we permute the vertex labels, the new adja- cency matrix can be written in the form Anew = P?1AP, where P is a permutation matrix and A is old adjacency matrix. Therefore, the new adjacency matrix is similar to the old one. Hence, the eigenvalues of the matrix does not change. 2. Prove

(a) The Laplacian of an undirected graph has non-negative eigenvalues. (b) The eigenvalues of the normalized Laplacian of an undirected graph lie in the interval [0, 2].

Which of the following is NOT required in order to view Web pages?

A. Internet connection B. computing device C. browser D. video player