Spectral Graph Analysis: A Unified Explanation and Modern Perspectives

Understand

Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few.

• Spectral graph theory provides a set of useful techniques and models for understanding `patterns of interconnectedness' in a graph.
• Our prime focus in this paper is on the following question: Is there a unified explanation and description of the fundamental spectral graph methods? There are at least two reasons to be interested in this question.
• Firstly, to gain a much deeper and refined understanding of the basic foundational principles, and secondly, to derive rich consequences with practical significance for algorithm design.