X = {x1, … , xN}: a set of data points
S = (sij)i,j=1,…,N: the similarity matrix in which each element indicates the similarity sij  between two data points xi and xj

The goal of clustering is to divide the data points into several groups such that points in the same group are similar and points in different groups are dissimilar.

Modeling the dataset as a graph

The clustering problem in graph perspective is then formulated as a partition of the graph such that nodes in the same sub-graph are densely connected/homogeneous and sparsely connected /heterogeneous to the rest of the graph.

Distances and similarities are reverse to each other. In the following, only talk about similarities, everything also works with distances.
Dynamic Attributed Network