There is a limit to how many people you can have in your social network - now a study reveals why, and how many relationships you need to maintain that network.
It has long been accepted that the size of a network in which everyone makes the choice to connect and help each other out is limited by the size of our brain.
"When you have got this network of relationships, there are a lot of things going on in that network. It takes a lot of brain power to actually socially navigate these large networks and there's an upper limit to our ability to do that," said study co-author and complex systems expert Michael Harré from the University of Sydney.
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Now, for the first time, Harré and colleague Mikhail Prokopenko have calculated how that limit - known as Dunbar's Number - is reached.
Their model, published today in the Royal Society journal Interface, which has been tested using real data from small groups in both hunter-gather and modern communities, shows the average minimum number of relationships that need to be maintained by individuals to form cooperative groups.
"For humans the limit is around 132 individuals," Harré said.
The good news is that you don't have to maintain relationships with everyone in the group for it to remain cohesive.
"To connect together a group of 132 individuals we estimate the average number of links each individual has to be able to maintain is between four and five."
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They emphasize this is an average, and that some people will maintain a lot more relationships or even less.
The new model shows that within a group of 132, there are smaller groups consisting of around five, 15 and 45 people. The model shows an interesting relationship between the average number of relationships - or links - per person and the size of the group.
A person in a group of five such as a book club or group of friends needs to maintain an average of one to two links; a person in a group of 15 needs an average of two to three links, and a person in a group of 45 needs an average of three to four links.
"The strength of our result is in showing that it is sufficient to add just one connection per person on average while increasing the size of the group roughly three-fold," Prokopenko said.
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There are many ways this can happen. One person in the group might do all the work, or it can be spread around between the group. The good thing about this is it means you don't have to like or even be friends with people to co-operate them - as long as others in the group do.
"You only have to like enough people to bind the group together."
Cooperative social networks have long been known to operate in hunter-gatherer groups, which bind together to maximize safety and resource sharing.
"They had these free-forming groups which kept the power away from individuals and retained the power with the group," Harré said.
This would have been important in the days when hunter-gatherers needed, say, 15 people to cooperate in the hunting of a mammoth.
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"All you need to do is like two or three people in that group and that's adequate for you to go off and hunt with them," he said.
The new research is the first to explore the network structure of cooperative groups in modern society.
Harré said in the cooperative social network people must maintain not only their direct relationships, but they have to have at least a vague idea about how all the other people in each group are related to each other.
This puts increasing demands on our brain as we process larger and larger groups, which is probably why hierarchical social networks developed in modern societies.
Indeed, the researchers found a hierarchical social network model - in which a leader forces people together in armies or bureaucracies - worked best for groups larger than 132.
"It wasn't until we started moving into things like villages and towns and cities where we got larger and larger bodies that we started getting hierarchies," Harré said.
Prokopenko added: "The increase in the average cognitive demand on each individual, needed to support the rapid growth of egalitarian groups, is no longer justified, and so is replaced by a cognitively simpler hierarchical arrangement.
"For example, it is easier to organize "battalions" [of 500 people] not by interconnecting individuals among "tribes", but rather by a direct hierarchical chain of command."
This originally appeared on ABC Science Online.