=================================================================================

The most popular Graph Network Tools are:
         i) Networkit. NetworKit is an open-source toolkit for large-scale network analysis with its goal for analyzing huge networks with hundreds of thousands to billions of edges. These are used to calculate network analysis such as degree sequences, clustering coefficients, and centrality measures. The features of the Networkit are:
           i.a) Interactive Workflow Pipeline.
           i.b) High Performance.
           i.c) Easy Integration and scalability.
         ii) Igraph.
         iii) Graph-tool.
         iv) Networkx.
         v) Pyvis. The pyvis library in Python is meant for quick generation of visual network graphs with minimal Python code. This library is designed as a wrapper around the popular Javascript visJS.

============================================

igraph for clustering and network: Code:
         
       Output:    
         
         

============================================

igraph for clustering and network: Code:
         
       Output:    
         

============================================

igraph for network and tree (note: the output file is in pdf format evern though it can be output to other image formats, e.g. png and gif, but those images in such formats are not clear): Code:
         
       Output: