https://ieeexplore.ieee.org/abstract/document/7835917
There are many varieties of spectral clustering, most notably, by changing the type of Laplacian used. Using the unnormalized Laplacian Lun as described above is known as unnormalized spectral clustering. Two popular variations that are based around normalized Laplacians are the normalized random walk spectral clustering [5] and normalized symmetric spectral clustering [2] that use Lrw and Lsym respectively:
\(\text{L}_{rw}=\text{D}^{-1}\text{L}_{un}\)
\(\text{L}_{sym}=\text{D}^{-1/2}\text{L}_{un}\text{D}^{-1/2}\)

Whey the spectrum is calculated for the Lapliacian of the similarity graph, rather than on the similarity graph itself?

due to useful spectral properties exhibited by the graph Laplacian (ref: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.96.2577) "The second smallest Laplacian eigenvalue lamda_2 plays a special role. Recently its applications to several difficult problems in graph theory were discovered (e.g., the expanding properties of graphs, the isoperimetric number, and the maximum cut problem)."

Data Clustering Algorithms and Applications

https://www.taylorfrancis.com/books/e/9781315373515/chapters/10.1201/9781315373515-7
This chapter introduces the basic formulations of nonnegative matrix factorization (NMF) and outlines the theoretical foundations on NMF for clustering and presents the equivalence results between NMF and various clustering methodologies. It demonstrates the NMF clustering capabilities and analyzes the advantages of NMF in clustering analysis. The chapter provides an outline on the NMF algorithm development and discusses several practical issues in NMF algorithms. The intrinsic alternating minimization in NMF algorithms is nonconvex, even though the objective function is convex with respect to one set of variables. The chapter also provides an overview of many different NMF variants and examines the advances on using NMF-based methods for solving many other clustering problems including co-clustering, semisupervised clustering, and consensus clustering and discusses future research directions. Co-clustering algorithms aim at clustering different types of data simultaneously by making use of the dual relationship information such as the term-document matrix and the gene-sample matrix.
Compute the normalised mutual information between two lists

Normalized mutual information (NMI)