Title: Visualizing spreading phenomena on complex networks,
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.