ABSTRACT

This chapter introduces the key technique that we will develop and use to analyze social networks with rich semantics for the relationships between nodes. The first main way to understand a graph is Graph drawing, collections of algorithmic ways to display, visualize, or render a graph in a way that humans can directly and easily understand. The second main way to understand a graph is spectral embedding Spectral embedding. The advantage of spectral approaches over graph drawing is that the construction comes with strong guarantees about the quality of the embedding. The spectral embedding begins from the Laplacian matrix, computes an eigendecomposition, and uses k of the eigenvectors as the coordinates for the position of each point. The spectral embedding technique can be applied to the new, larger graph and embed it in a single geometric space Geometric space. The distances between the positions of embedded nodes tells how similar the corresponding nodes are in the context of the entire social network.