Clustering Coefficient Functions

By: Katana Graph

July 12, 2022

Clustering Coefficient Functions

The clustering coefficient algorithm is typically used on homogeneous, undirected graphs to determine which nodes cluster together and the likelihood that a node’s neighbors are also connected. For example, if a person’s friends are also friends with each other, the node representing that person has a high clustering coefficient. A low clustering coefficient, on the other hand, indicates a graph is composed of several weak ties. A clustering coefficient might be viewed roughly as the ratio of common friends in a social network compared to all possible connections a person might have.

A clustering coefficient may be thought of as an aggregate density metric, with a focus on "egocentric" networks, i.e., networks constructed from a single point of reference. Identifying the degree to which nodes tend to cluster together is useful for finding patterns within large graphs, which can then be used to simplify visualization or to identify anomalies.

There are two categories that the clustering coefficient can fall under: local and global. Locally, it identifies how close a subset of nodes is to being a complete graph (otherwise known as a clique). Globally, it provides an overall indication of network clustering.

Networks with the highest possible clustering coefficient are described as having a modular structure with the lowest possible distance between the different nodes, indicating a network consisting of disjoint cliques. This is related to — but not the same as — centrality measurements, which focus on nodes’ importance based on the user’s parameters.

Whether used locally or globally, determining the clustering coefficient of nodes is a step towards identifying structural holes in a network. If expected connections are missing between nodes, the flow of information in a network could be hindered by a lack of routes to get from A to B. Whether you apply this to cybersecurity, internal network efficiency, recommendations, or other processes depends on the specific use case.

On large graphs, calculating clustering coefficients can require unrealistically long compute times. The Katana Graph Intelligence Platform supports a range of carefully-defined algorithms optimized to run as fast as possible, allowing users to express business needs precisely while experiencing better performance than other platforms can provide.

Katana Graph, in collaboration with Intel, has designed a high-performance, easy-to-use graph analytics Python library that includes highly optimized, parallel implementations of important graph analytics algorithms such as Local Clustering Coefficient. The library provides interoperability with pandas, scikit-learn, Apache Arrow, and libraries in the Intel AI software stack.

Turn Data into Breakthroughs

Our beginnings in cutting-edge research and scientific analysis have had a powerful effect on who we are today, and continuous improvement is at our core. Katana Graph continually watches for new use cases for its graph intelligence platform. We work closely with clients to see a big-picture view of where the highest value challenges lie, ensuring that our scalable graph analytics can facilitate innovation in a rapidly evolving business landscape. To discover how the Katana Graph Intelligence Platform can serve your big data needs, please contact us.

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