# Analyzing and Visualizing Scalar Fields on Graphs

## TL;DR

This paper introduces a novel visualization method for scalar graphs that transforms network data into terrain maps, revealing relationships between attributes and topology, scalable to large graphs, and useful for data science insights.

## Contribution

The paper presents a new terrain map-based visualization technique for scalar graphs, capturing multi-attribute relationships and scaling to large networks.

## Key findings

- Effective visualization of scalar graphs reveals key network structures.
- Method scales to graphs with millions of nodes.
- Demonstrated usefulness on real-world data science tasks.

## Abstract

The value proposition of a dataset often resides in the implicit interconnections or explicit relationships (patterns) among individual entities, and is often modeled as a graph. Effective visualization of such graphs can lead to key insights uncovering such value. In this article we propose a visualization method to explore graphs with numerical attributes associated with nodes (or edges) -- referred to as scalar graphs. Such numerical attributes can represent raw content information, similarities, or derived information reflecting important network measures such as triangle density and centrality. The proposed visualization strategy seeks to simultaneously uncover the relationship between attribute values and graph topology, and relies on transforming the network to generate a terrain map. A key objective here is to ensure that the terrain map reveals the overall distribution of components-of-interest (e.g. dense subgraphs, k-cores) and the relationships among them while being sensitive to the attribute values over the graph. We also design extensions that can capture the relationship across multiple numerical attributes (scalars). We demonstrate the efficacy of our method on several real-world data science tasks while scaling to large graphs with millions of nodes.