### Publication

**2017**"The ground truth about metadata and community detection in networks"- Leto Peel*,
Daniel B. Larremore*, and
Aaron Clauset. Science Advances
**3**(5) e1602548. - [PDF][Science Advances][Supplement].
- *equal contribution

### Code

In the paper, we describe two algorithms. Implementations of the Blockmodel Entropy Significance Test (BESTest) and the neoSBM are written in MATLAB and Python respectively.

- Code for the Blockmodel Entropy Significance Test (MATLAB).
- Code for the neoSBM (Python).

If you are interested in porting the neoSBM to MATLAB or the BESTest to Python, please do so! We would be happy to acknowledge your contribution here!

### Data

In the paper, we refer to data from the Zachary Karate Club, the Lazega Lawyers, and the Malaria *var* genes. Below, we provide our copies of those datasets and the correct citations for each.

- [Karate Club .txt data]
- W. W. Zachary, An information flow model for conflict and fission in small groups, J. Anthropol. Res. pp. 452-473 (1977).
- [Lazega Lawyers .mat data]
- E. Lazega, The collegial phenomenon: The social mechanisms of cooperation among peers in a corporate law partnership (Oxford University Press on Demand, 2001).
- [Malaria var .txt and .mat data]
- D. B. Larremore, A. Clauset, C. O. Buckee, A network approach to analyzing highly re- combinant malaria parasite genes, PLoS Comput Biol 9, e1003268 (2013).

### Abstract

Across many scientific domains, there is a common need to automatically extract a simplified view or coarse-graining of how a complex system's components interact. This general task is called community detection in networks and is analogous to searching for clusters in independent vector data. It is common to evaluate the performance of community detection algorithms by their ability to find so-called *ground truth* communities. This works well in synthetic networks with planted communities because such networks' links are formed explicitly based on those known communities. However, there are no planted communities in real world networks. Instead, it is standard practice to treat some observed discrete-valued node attributes, or metadata, as ground truth. Here, we show that metadata are not the same as ground truth, and that treating them as such induces severe theoretical and practical problems. We prove that no algorithm can uniquely solve community detection, and we prove a general No Free Lunch theorem for community detection, which implies that there can be no algorithm that is optimal for all possible community detection tasks. However, community detection remains a powerful tool and node metadata still have value so a careful exploration of their relationship with network structure can yield insights of genuine worth. We illustrate this point by introducing two statistical techniques that can quantify the relationship between metadata and community structure for a broad class of models. We demonstrate these techniques using both synthetic and real-world networks, and for multiple types of metadata and community structure.

### Get in touch

larremore(at)santafe.edu