In graph theory, a clustering coefficient is a measure of the extent to which nodes in a graph tend to cluster together and a clique is a group of nodes whereby each pair of nodes shares a connection (every possible link exists). A node's neighbourhood is the induced subgraph of a node and its neighbours (also known as a 1.5 hop network or an ego network).
The local clustering coefficient of a node is the measure of how close a node's neighbourhood is to being a clique. It is the ratio of the number of relationships that exist in the neighbourhood compared to the number of relationships that could possibly exist. It is a measure of a node's interconnectedness.