# How Page Rank Can Be Affected By a Websites’s Internal Linking Here, we’ll take a look at how Page Rank can be affected by a website’s internal linking structure. Heretofore, we’ve been looking at how inbound and outbound links affect PageRank, but it’s time to switch gears a little bit.

In general, websites feature a hierarchical, tree-like, “graphic” structure. This hierarchy features a root page, the “parent”, which is almost invariably optimized for the key search phrase. Let’s consider an example with optimized page A, featuring an external inbound link from page X, which has no additional outgoing links and a constant Page Rank of 10. Let’s also assume pages B and C each receive links from A, and also link back to it. Finally, let’s look at a damping factor of d = 0.5. This yields the following equations:

PR(A) = 0.5 + 0.5 (10 + PR(B) + PR (C))

PR(B) = 0.5 + 0.5 (PR(A) / 2)

PR(C) = 0.5 + 0.5 (PR(A) / 2)

If we solve these, we get:

PR(A) = 8

PR(B) = 2.5

PR(C) = 2.5

Clearly, there is something of a discrepancy between the PageRank of A and that of B and C.

It is pretty poor SEO practice to optimize just the root/parent page of the website. This optimizes a single page’s response, but does rather little for the website as a whole, which is obviously counterproductive. A better idea is to optimize each page individually, and a better idea still is to optimize each page for a different search phrase.

Let’s move forward, and assume that our parent page is optimized completely, but that our other pages do not. This gives us a good starting point to investigate the answer to the question, “what is the optimal linking structure for this website? Let’s add a link from B to C, and from C to B. A still has its one external inbound link from X, and X has no other outgoing links, and a constant PR of 10. This leads to the following equations:

PR(A) = 0.5 + 0.5 (10 + PR(B) / 2 + PR(C) / 2)

PR(B) = 0.5 + 0.5 (PR(A) / 2 + PR(C) / 2)

PR(C) = 0.5 + 0.5 (PR(A) / 2 + PR(B) / 2)

. . . Which gives the following PageRank values:

PR(A) = 7

PR(B) = 3

PR(C) = 3

This clearly has the effect of decreasing the PageRank of A, and increasing the Page Ranks of B and C. This is fairly clear – addition of internal links should increase the Page Ranks of the newly linked websites and decrease that of the one that wasn’t newly linked. In general, PR spreads more evenly when a website is organized more hierarchically.

## Better Concentration

We’ve already seen that external outbound links have negative effects on the PR of a site’s pages. Let’s look at another example that involves these. Say we have a website, hierarchically structured, featuring pages A, B, C, and D. A links to B, C, and D, and B, C, and D all link back to A. Additionally, B, C, and D all feature one outbound link. Let’s keep the damping factor where it was before, d = 0.5, to produce the following set of equations:

PR(A) = 0.5 + 0.5 (PR(B) / 2 + PR(C) / 2 + PR(D) / 2)

PR(B) = PR(C) = PR(D) = 0.5 + 0.5 (PR(A) / 3)

. . . Yielding:

PR(A) = 1

PR(B) = 2/3

PR(C) = 2/3

PR(D) = ⅔

Now, let’s assign all the outgoing links to page D. In other words, now B and C have no outbound links, but D has three. This leads to the following Page Rank values:

PR(A) = 17/13

PR(B) = 28/39

PR(C) = 28/39

PR(D) = 28/39

Clearly, we’ve increased the PR for each individual page by concentrating all the outbound links in Page D. This suggests the following strategy for SEO: Concentrate external outbound links in as few pages as possible.

Many webmasters try to exhange links with other websites to increase. We’ve already demonstrated that the addition of links to a closed system adds nothing to the Page Rank of the site under consideration, so it’s a dubious tactic, at best. Somewhat paradoxically, it actually does work in some instances. Let’s take a look at the math to see just how to exploit this for our advantage.

As always, this is best done through example, so let’s consider two websites, 1 and 2. Each is hierarchically structured. Site 1 consists of pages A, B, and C, with A the root, linked to B and C. B and C link back to A. Site 2 is set up the same, with pages D, E, and F. We’ll keep a damping factor of 0.5 and work with the following equations:

PR(A) = 0.5 + 0.5 (PR(B) + PR(C))

PR(B) = PR(C) = 0.5 + 0.5 (PR(A) / 2)

This gives us the following PageRank for site 1:

PR(A) = 4/3

PR(B) = 5/6

PR(C) = ⅚

And these for site 2:

PR(D) = 4/3

PR(E) = 5/6

PR(F) = ⅚

This is our starting point. Now, let’s introduce a link exchange. Page A links to page D, and D links to A. If we run the same calculations, we get the following:

PR(A) = 0.5 + 0.5 (PR(B) + PR(C) + PR(D) / 3)

PR(B) = PR(C) = 0.5 + 0.5 (PR(A) / 3)

PR(D) = 0.5 + 0.5 (PR(E) + PR(F) + PR(A) / 3)

PR(E) = PR(F) = 0.5 + 0.5 (PR(D) / 3)

. . . Yielding:

PR(A) = 3/2

PR(B) = 3/4

PR(C) = 3/4

PR(D) = 3/2

PR(E) = 3/4

PR(F) = ¾

We see that A and D benefit, but all other pages lose Page Rank. This isn’t absolutely advantageous or damaging, so let’s look at when this might be desirable versus when this shouldn’t be done. Clearly, if we want the overall PageRank status to be better, we’d forego link exchange. Put another way, if we’re most concerned with a balanced Page rank across pages, link exchange doesn’t make sense. On the other hand, if you want to prioritize a root page, link exchange might actually be a sensible option.

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