Quiz Question #1
Figure 1(a) below shows a drawing of a network \(N\). Figures 1(b), 1(c), and 1(d) shows the matrices \(\boldsymbol A\), \(\boldsymbol D\), \(\boldsymbol S\), respectively, and Figure 1(e) shows the vector \(\boldsymbol{k}\). Regarding the figures above, consider the following six propositions: For matrix \(\boldsymbol A\) (shown in Figure 1(b)) entry \(a_{ij} = 1\) if and only if there is a link in network \(N\) connecting node \(i\) to node \(j\). Therefore, \(\boldsymbol A\) is an adjacency matrix of network \(N\). Matrix \(\boldsymbol D\) (shown in Figure 1(c)) can be regarded as a matrix indicating second neighbors (nodes at distance two) of network \(N\), since entry \(d_{ij} \neq \infty\) if and only if nodes \(i\) and \(j\) are second neighbors. Matrix \(\boldsymbol D\) (shown in Figure 1(c)) can be regarded as distance matrix of network \(N\) , since if \(d_{ij} = \infty\) there is no path bet...