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Connectivity Matrix Consider the diagram below. Each node represents a webpage, and line segments represent hyperlinks that connect them. For example, the single directional arrow

Connectivity Matrix Consider the diagram below. Each node represents a webpage, and line segments represent hyperlinks that connect them. For example, the single directional arrow from A3 to 6 indicates there is a hyperlink on page A3 that takes the user to page A6. Similarly, double-sided arrow between A1 and A2 indicates there is a hyperlink on page A1 to page A2, and there is a hyperlink on page A2 to page A1.
We can create a matrix C to represent this network. We put a 1 in the (ij)-th entry if Ai is connected to Aj; we put 0 otherwise.
(a) Build the connectivity matrix C for the network given in the figure.
(b) If C indicates traveling from one webpage to another by following a single hyperlink, then C2=CC indicates traveling from one webpage to another by following two hyperlinks. Calculate C2 and determine (C2)3,4. What does (C2)3,4 represent?
(c) A sequence of n hyperlinks moving from one page to another is called a walk of length n. The (ij)-th entry of C+C2+C3 is the number of walks length at most 3 from Ai to Aj. Calculate C+C2+C3 and (C+C2+C3)1,6. What does (C+C2+C3)1,6 represent?
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