Evolutionary Events in a Mathematical Sciences Research Collaboration Network

TL;DR

This paper analyzes the evolution of the mathematics research collaboration network from 1985 to 2009, revealing significant shifts and differences between subfields using network diagnostics and modeling.

Contribution

It introduces a dynamic analysis approach using sliding windows to study network evolution and identifies major structural shifts and subnetwork differences.

Findings

Network structure shows occasional dramatic shifts.

Major subnetworks ('pure' and 'applied') evolve differently.

Two significant events marked major changes in the network.

Abstract

This study examines long-term trends and shifting behavior in the collaboration network of mathematics literature, using a subset of data from Mathematical Reviews spanning 1985-2009. Rather than modeling the network cumulatively, this study traces the evolution of the "here and now" using fixed-duration sliding windows. The analysis uses a suite of common network diagnostics, including the distributions of degrees, distances, and clustering, to track network structure. Several random models that call these diagnostics as parameters help tease them apart as factors from the values of others. Some behaviors are consistent over the entire interval, but most diagnostics indicate that the network's structural evolution is dominated by occasional dramatic shifts in otherwise steady trends. These behaviors are not distributed evenly across the network; stark differences in evolution can be observed between two major subnetworks, loosely thought of as "pure" and "applied", which approximately partition the aggregate. The paper characterizes two major events along the mathematics network trajectory and discusses possible explanatory factors.