please solve this and give me a detailed example i assumed that i have 10 persons for each vetices and they connect to each other 14 edges which is the connection how can i found the adjency matrix , the clustering and the laplacian ...etc please solve it correctly thanks for the hard work

You will look at the graph representing an individual's profile on a social network. The profile has a certain number of "friends". Some of these friends know each other and are friends with each other as well. This friendship network can be represented as a graph with nodes being friends and edges showing the friendship connection between the individuals. The goal of clustering is to separate this graph into components which are tightly connected within themselves and have fewer connections to the outside (the so-called communities). The method you will explore in this project is based on the theorem by M. Fiedler (you may "google" to find it), who has shown that for a connected graph (meaning that there is a path between any two vertices) the eigenvector corresponding to the second smallest eigenvalue of the Laplacian of the graph allows the graph to be split into two maximally interconnected components. Choose your own graph of social network (see details below in PD2). Your task is to apply the above-mentioned method to find such a clustering. PD2: Choose any simple connected graph that represents a social network. The graph must have at least 10 vertices and at least 14 edges. Explain how a social network is represented using the adjacency matrix. Solve the data clustering problem as described in the formulation of the problem above by finding the Laplacian and its eigenvalues-eigenvectors. By identifying the eigenvector that corresponds to the second smallest eigenvalue of the Laplacian, provide the clustering choice. (YOu may use MATLAB for your computations)