Of two network breakdown models, researchers find ‘link deletion’ to be most common.

We all lose touch with people during our lives, but while we might assume that our relationships gradually fade as we drift apart, new research suggests they end far more abruptly.

Network breakdown types

Modelling social networks has become a big research area. There is a lot of work aimed at how we build and maintain social networks, for example about gender differences when it comes to managing networks. Less work has been done to study how the networks break down however.
A new research published on the arXiv investigates network breakdown by studying two models for how our individual relationships disappear. The first model, called ‘link deletion’, represents a sudden death of the relationship. In this model, any relationship can be lost at any time, regardless of how strong the relationship is. This means that you have the same probability of losing a relationship with a distant friend as you do with your partner.
In the second model, called ‘link aging’, all relationships are weakened slightly over time and then only the very weakest ones are lost. So your close friends are safe, but it doesn’t look good for the ex-colleague you haven’t spoken to in years.

Simulating networks

The researchers tested their models by creating lots of fake networks—fake people with fake relationships between them—and then implementing their two models for relationship breakdown to see what happened. The resulting networks looked very different, depending on which model was used.
Networks that used the ‘link aging’ model formed many small groups of people that were strongly connected within the group, but with very few connections between the different groups. This clique structure is expected since it’s only the weak relationships that are deleted in these models, and they occur mainly between different groups.
In the ‘link deletion’ model, the networks were more open. There were fewer groups and stronger connections between people in different groups.

Deleting friends

However, the true test of any model is how well it predicts the real world. To test their two models of relationship breakdown, the researchers compared their fake networks with real networks taken from mobile phone coverage.
They found that the ‘link deletion’ model matched the real data much better than their ‘link aging’ model. In fact, the ‘link aging’ model could not reproduce many of the features of the real networks and the researchers conclude that “link deletion is the major mechanism for deleting ties in real society, while link aging, being presumably present, plays a minor role.”
Apparently we are more brutal with our relationships than we like to think.


Yohsuke Murase, Hang-Hyun Jo, János Török, János Kertész, & Kimmo Kaski (2015). Modeling the role of relationship fading and breakup in social network formation arXiv: 1505.00644v1