# Detecting And Using Base Clusters For Modularity Maximization

## Advisor Information

Sanjukta Bhowmick

## Location

Milo Bail Student Center Council Room

## Presentation Type

Oral Presentation

## Start Date

8-3-2013 3:15 PM

## End Date

8-3-2013 3:30 PM

## Abstract

A network is said to exhibit community structure if the nodes of the network can be easily grouped into set of nodes, such that each group is densely connected internally [1] but sparsely connected with other groups. Most real world networks exhibit community structure and determining communities is an important analysis tool in many application including sociology, epidemiology and biological networks. A popular technique for detecting communities is based on computing the modularity of the network [1]. Modularity computes how well are vertices in a group connected as opposed to being randomly connected. In general, high modularity indicates good partition of network into communities. Maximizing modularity is a NP- hard problem [1]. However, all modularity based algorithm for detecting community structure are affected by the order in which the vertices in the network are processed. Therefore, detecting communities or clusters in real world graph becomes increasingly difficult. Our goal is to find the subnetwork that is invariant across different orderings. We introduce the concept of base cluster, that is, a group of vertices that are always partitioned to the same community independent of the perturbations to the input. We develop a preprocessing step that identifies stable base cluster and empirically show that number of base clusters in a network affects the range of modularity values obtained. In particular, base clusters can also help determine strong communities in the network.

Detecting And Using Base Clusters For Modularity Maximization

Milo Bail Student Center Council Room

A network is said to exhibit community structure if the nodes of the network can be easily grouped into set of nodes, such that each group is densely connected internally [1] but sparsely connected with other groups. Most real world networks exhibit community structure and determining communities is an important analysis tool in many application including sociology, epidemiology and biological networks. A popular technique for detecting communities is based on computing the modularity of the network [1]. Modularity computes how well are vertices in a group connected as opposed to being randomly connected. In general, high modularity indicates good partition of network into communities. Maximizing modularity is a NP- hard problem [1]. However, all modularity based algorithm for detecting community structure are affected by the order in which the vertices in the network are processed. Therefore, detecting communities or clusters in real world graph becomes increasingly difficult. Our goal is to find the subnetwork that is invariant across different orderings. We introduce the concept of base cluster, that is, a group of vertices that are always partitioned to the same community independent of the perturbations to the input. We develop a preprocessing step that identifies stable base cluster and empirically show that number of base clusters in a network affects the range of modularity values obtained. In particular, base clusters can also help determine strong communities in the network.