Visualizing spreading phenomena on complex networks

TL;DR

This paper introduces a scalable visualization algorithm for large complex networks that highlights spreading phenomena from a focal node's perspective, aiding interactive exploration of network dynamics.

Contribution

A novel three-stage layout algorithm enabling interactive visualization of spreading processes in networks with millions of nodes from a single node perspective.

Findings

Effective visualization of citation dynamics in large collaboration networks.

Scalable algorithm suitable for networks with millions of nodes.

Enhanced understanding of local influence in spreading phenomena.

Abstract

Graph drawings are useful tools for exploring the structure and dynamics of data that can be represented by pair-wise relationships among a set of objects. Typical real-world social, biological or technological networks exhibit high complexity resulting from a large number and broad heterogeneity of objects and relationships. Thus, mapping these networks into a low-dimensional space to visualize the dynamics of network-driven processes is a challenging task. Often we want to analyze how a single node is influenced by or is influencing its local network as the source of a spreading process. Here I present a network layout algorithm for graphs with millions of nodes that visualizes spreading phenomena from the perspective of a single node. The algorithm consists of three stages to allow for an interactive graph exploration: First, a global solution for the network layout is found in spherical space that minimizes distance errors between all nodes. Second, a focal node is interactively selected, and distances to this node are further optimized. Third, node coordinates are mapped to a circular representation and drawn with additional features to represent the network-driven phenomenon. The effectiveness and scalability of this method are shown for a large collaboration network of scientists, where we are interested in the citation dynamics around a focal author.