Skip main navigation

Local Clustering Co-efficient

Read about how the Local Clustering Co-efficient property of networks helps to find out how well connected an individual is in a social media network.
© University of Southampton 2017

Essential knowledge:

  • The Local Clustering Co-efficient tells us how connected the network is around a particular node. The clustering co-efficient is a fraction, representing the number of connections that exist as a proportion of the number that could exist.

  • So for example, if I have three friends (Derek, Ed, and Freya), then those friends have three potential connections (Derek – Ed, Ed – Freya, Freya – Derek). If only one of those potential connections actually exists (for example if Derek is friends with Ed) then one out of three connections exist, giving me a local clustering co-efficient of 1/3.

You may be interested that:

The local clustering co-efficient is a measure introduced by Watts and Strogatz in 1998 in their work to identify small world networks. It is calculated for each node in the network to examine the existing connections between its neighbouring nodes. In other words, it checks the existing connections between the neighbours of a given node to see whether they form a clique around that node.

Let’s look at the following example to illustrate the clustering co-efficient.

Graph for local clustering coefficient Lets calculate the local clustering co-efficient for the node C:

  • C’s neighbours are A, B, D and E.

  • There is only one existing connection between C’s neighbours, and that is AB.

  • There are six possible connections between its neighbours: AD, AE, BD, BE, DE and the one that is already there which is AB.

So the clustering co-efficient for C is 1/6

The clustering co-efficent is essentially a measure of how densely connected the network is around a particular node. So for example in a social network a person with a high clustering co-efficient is one whose friends tend to be friends with one another, forming a clique.

Thinking about your own social networks, are there ones in which your friends tend not to know one another, or ones in which they do (in other words where you have a particularly high or low clustering co-efficient)?

Optional further reading

  1. Watts, DJ and Strogatz, SH (1998) ‘Collective dynamics of `small-world’ networks’, Nature, vol. 393, no. 6684, pp. 440–442, Jun
© University of Southampton 2017
This article is from the free online

The Power of Social Media

Created by
FutureLearn - Learning For Life

Our purpose is to transform access to education.

We offer a diverse selection of courses from leading universities and cultural institutions from around the world. These are delivered one step at a time, and are accessible on mobile, tablet and desktop, so you can fit learning around your life.

We believe learning should be an enjoyable, social experience, so our courses offer the opportunity to discuss what you’re learning with others as you go, helping you make fresh discoveries and form new ideas.
You can unlock new opportunities with unlimited access to hundreds of online short courses for a year by subscribing to our Unlimited package. Build your knowledge with top universities and organisations.

Learn more about how FutureLearn is transforming access to education