Do you have too many or too few friends?

Do we have a natural limitation on the number of friends that we have?


In a previous blog post I argued that my favourite number is the average number of friends that a person might have, known as Dunbar’s Number. You might immediately think “That is highly subjective, not even the definition of a friend or social relation is clear” or “It changes from one person to another”. This is obviously true, but the same questions have been posed by anthropologists, psychologists and sociologists, and they have come to a certain agreement about that subject.

Before jumping directly to the number or its several approximations, let’s think about why it makes sense to put some sort of limit on the number of friends a person will have. From a mathematical point of view, a person has limited resources – in this case are time to spend and brain power (memory) – to spend with people. Clearly, having more “friends” means having less time available to spend with each one of them and less space in your brain to build nice memories of each of them. Picture the following example: you and your partner are planning your wedding and you decide to invite 400 people to a reception that will last for 6 hours. For that massive party, you will have a bit less than a minute to spend with each guest; perhaps just enough time to say “Hello, thank you for coming, hope you enjoyed the salmon and goodbye!” You will spend 6 hours basically just saying hello and goodbye: those are the stakes on the memories that you will have from that special day. To create a better memory and to enjoy a better party, you might decide to go for a smaller celebration. That is the type of process that our brain (possibly subconsciously) performs when we pick, from all the people that we have ever met, the ones we want to engage in a social relationship.

primatesBy analysing the size of a primate’s brain and the size of their social groups, including those of primitive humans, the anthropologist Robin Dunbar estimated in the 1990s that we can maintain around 150 significant and reciprocal social contacts: a number known as Dunbar’s number. He observed that it was a similar number observed in some hunter-gatherer societies, as well as the size of a company in some ancient and modern armies.

Obviously things aren’t as simplistic as saying that “We can have at most 150 friends” and the research doesn’t do that. Psychologists consider a model in which a person is surrounded by concentric circles or layers, in which each relationship is contained within one of the circles: the further away a relationship is from the centre, the less significant it is. Referring to the figure below, a person will have five relationships within the inner circle (nuclear relationships), 15 intimate friends (including the first 5 nuclear relationships), 50 friends (including the first 15 intimate friends) and in total 150 significant social relationships. Everything after that is not considered a significant relationship.

Displayed is a simple model with concentric circles that surround a person. Every relationship can be placed in one of the layers or circles which represent how significant it is for that person.

Displayed is a simple model with concentric circles that surround a person. Every relationship can be placed in one of the layers or circles which represent how significant it is for that person.


There have been other estimates for Dunbar’s number that go up to 290 friends. Statistically speaking, the number of significant social contacts should be considered as a distribution (which simply means that it varies from person to person) If we think of that distribution, Dunbar’s number, the 150 that he suggested more than twenty years ago, is an approximation to the mean of that distribution: the average number of friends a person might have.

partyWhy is that number important? It has been used widely in many fields. In politics and epidemiology it is used to predict how fast an idea or a disease might spread. It has been applied to design office and living spaces for a better urban design. Nowadays it is used by Social Networks in some of their algorithms; and it could be used as a measure to detect if Social Media is in fact making us more sociable or if it is just pushing us towards a less sociable “Like” and “Retweet” society. On a smaller scale, we might use that number to plan a big party: perhaps you and your future wife or husband should avoid inviting more than 150 guests each for your wedding!

Rafael Prieto Curiel is doing a PhD in mathematics and crime. He is interested in mathematical modelling of any social issues, such as road accidents, migration, crime, fear and gossip.

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