Review of graph invariants for quantitative analysis of structure dynamics

Abstract

In this work we review graph invariants used for quantitative analysis of evolving graphs. Focusing on graph datasets derived from structural pattern recognition and complex networks fields, we demonstrate how to capture relevant topological features of networks. In an experimental setup, we study structural properties of graphs representing rotating 3D objects and show how they are related to characteritics of undelying images. We present how evolving strucure of Autonomous Systems (ASs) network is reflected by non-trivial changes in scalar graph descriptors. We also inspect characteristics of growing tumor vascular networks, obtained from a simulation. Additionally, the overview of currently used graph invariants with several possible groupings is provided. © 2012 Springer Berlin Heidelberg.