We now normalize connectivity numbers according to the scheme suggested in our report Webometry #1. To recall this, imagine a matrix in which all the rows correspond to the pages of the i-th node, and all the columns correspond to the pages of the j-th node. The number of rows is thus the size (number of pages) of the i-th node, S(i), but call it H for Height. Similarly the number of columns of our matrix is the size of the j-th node, S(j), but call it W, for Width. Then the area of our matrix, an array of small cells of a unit area, is the product of the Height times the Width, H*W. Each small cell in this matrix corresponds to a single chosen page of the i-th node (say A.html) and a single chosen page of the j-th node, say B.html.

Now, let this small cell be colored black if there is one or more links from the page A.html of the i-th node to the page B.html of the j-th node, and otherwise suppose it is white. Do likewise for each of the H*W small cells. Then the total number of black cells is the connectivity number, C(i, j), defined above. And the grayness (relative blackness) of the entire matrix of H*W cells is this number, C(i, j), divided by the total number of cells, H*W, which is none other than the product, S(i) * S(j). This quotient,
s(i, j) = C(i, j)/(S(i)*S(j)),
is the overall grayness of our imaginary matrix of area H*W, and this is the number we call the synergy from the i-th node to the j-th node. The synergy matrix is the N by N square matrix of these relative grayness numbers.