## The Mathematics of Social Networks - The Up and the Down

We have all had the experience. You start off with a social network. You add people. People share things. Very quickly the queue of things to read goes exponential. If the average Facebook subscriber adds 500 friends in the first year, the formula is n to the 500th.

Consider the following numbers for content in such a network. You add 500 people on Linkedin or Facebook. Each person posts one element per day. All of a sudden you have 500 items to read. Even if the ratio is lower – let’s say only 10% post something every day, you have 50 items to read. And then of course, there are the enthusiastic posters, who post more than once a day.

From an annual perspective, 365 days a year and 50 items per day is 18,250 items per year. If it takes you an average of 15 seconds to scan an article, you are still looking at 76 hours a year to scan items. It is therefore, no surprise that what make companies like Linkedin or Facebook grow runs into a wall.

Business strategy always focuses upon value. Financial evaluation models for companies that focus upon acquisition via exponential growth don’t focus on the changing value offering to subscribers. For many subscribers there is a point at which value is not based upon the number of connections but the number of high quality connections. Let me suggest therefore, that in the wild and wooly world of Internet valuations, the number of subscribers may be less important than people currently believe. In fact, if you have too many links on a social network, it is highly lightly that you will either start to trim connections or filter their postings.

Consider the situation of loyal subscribers who obtain great value vs. marginal subscribers or links where you obtain value vs. links who only want to pitch you. In the latter case, the benefit are small.

There’s clearly a trade-off. Basing a business strategy upon rapid growth driven by exponential growth provides one perceived form of value, but there are decreasing returns to scale and at some point negative returns. You have to focus with a laser precision on creating value to offset the dis-economies of scale from being overwhelmed by connections, subscriptions to supplier sites and publications.