# Modularity Background - Teradata Vantage

## Teradata® Vantage Machine Learning Engine Analytic Function Reference

Product
Release Number
1.0
8.00
Published
May 2019
Language
English (United States)
Last Update
2019-11-22
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Product Category

Community detection and identification is important for understanding network dynamics. In this context, a community (also called a module, group, or cluster) refers to a subset of a network consisting of nodes that are more highly interconnected with each other than they are with nodes that are not part of the community. Identifying these communities can be valuable in many different network analysis problems. For example, diffusion of information or disease is faster within a densely connected social community than within a more loosely connected group.

Modularity is a measure of the quality of a division of a network into communities, or modules. It is defined by the following equation, which compares the density of links within communities to the density of links between communities. Modularity is a numeric value between 1 and -1, with values closer to 1 indicating better community formation (that is, a division of the network with dense within-community connections and sparse between-community connections).

The ML Engine Modularity function is based on the algorithm described in the paper Fast unfolding of communities in large networks; VD Blondel, JL Guillaume, R Lambiotte, E Lefebvre; Journal of Statistical Mechanics: Theory and Experiment, Volume 2008, October 2008.

## Modularity Equation

In the modularity equation:
• A ij is the weight of the edge between nodes i and j.
• k i is the sum of the weights of the edges of node i.
• m is the total weight of all edges in the network. For an unweighted network, the weight of each edge is 1.
• δ(c i ,c j ) is 1 when nodes i and j are in the same community, and 0 otherwise.

This modularity equation is equivalent to the preceding one:

## Use Cases

Field What Modularity Analysis Identifies
Social network analysis
• Communities of acquaintances
• Circles of influence
Telecom
• Groups of customers where most communications happen within the group
Banking and finance
• Business relationships, such as supply chains or capital chains
• Potentially fraudulent transactions or communications
Web site optimization
• Pages with similar subjects
• Pages likely to be accessed in the same session
Retail
• Target customers for specific products
• Product recommendations for specific customers
• Products that are becoming more or less popular (forecasting)
Public health
• People who may be at risk for a disease or condition
Computer network security
• Systems at risk for a virus or malware attack