Title: MOG: Mapper on Graphs for Relationship Preserving Clustering,
Abstract: The interconnected nature of graphs often results in difficult to interpret
clutter. Typically techniques focus on either decluttering by clustering nodes
with similar properties or grouping edges with similar relationship. We propose
using mapper, a powerful topological data analysis tool, to summarize the
structure of a graph in a way that both clusters data with similar properties
and preserves relationships. Typically, mapper operates on a given data by
utilizing a scalar function defined on every point in the data and a cover for
scalar function codomain. The output of mapper is a graph that summarize the
shape of the space. In this paper, we outline how to use this mapper
construction on an input graphs, outline three filter functions that capture
important structures of the input graph, and provide an interface for
interactively modifying the cover. To validate our approach, we conduct several
case studies on synthetic and real world data sets and demonstrate how our
method can give meaningful summaries for graphs with various complexities