Spectral Variation of Normalised Laplacian for Various Network Models

Many network models have been proposed to mimic real-world systems when they become too large and complex to be described explicitly. Since the models inherit similar structural properties to the real-world network, by studying their nodes and links, many network properties can be identified. While most of the tools used to study their structural properties are coming from graph theory, spectral analysis is another method that can be used to reveal the structural inheritance properties of a network. In this work, we performed spectral analysis on network models, namely Erdo-Renyi (ER), Watts-Strogatz (WS), Barabasi Albert (BA), grids and growing geometrical network (GGN) with the undirected and directed connection. The eigenvalue spectrum of the normalised Laplacian was computed for each model and used in spectral plots, Cheeger constant and energy measurement. Results from the spectral measures have revealed specific characteristics for different models, which in turn make them easier to be recognised.