There’s a reason networks are valuable. It is all down to mathematics.

There are two parts to a network. The things in the network and the links between them.

In a network with *x* things, adding another thing — mathematicians would call this an *(x+1)*^{th} node — means there *2x* extra potential connections between nodes.

Take a telephone network: a new subscriber can call all existing subscribers and they can call back.

So the number of possible connections increases with the size of the network.

If the network is commercial one with nodes representing customers and each connection has a fixed value then the value of adding one more customer increases as the size of the network increases.

For a network with *x *nodes, there are *x(x-1) *connections.

When networks get large – so large that *(x-1) *is more or less equal to *x*, the value of the network is *x*^{2 }.

This is why network products and the companies selling them have what mathematicians call exponential growth.

Think of it as the difference between stuffing bank notes under your mattress and or investing it in a compound-interest account.

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