How to represent a dataset as a linked list-like graph?
The graph resulting from this kind of dataset is also known as a Network Graph and the kind of analysis you are trying to do is known as Social Network Analysis.

There are many prominent Python libraries for visualization and subsequent analysis of network graphs. The most widely used is NetworkX. It is easy to add nodes and directed edges in a NetworkX graph and visualize them with Matplotlib.

Installing NetworkX is a prerequisite.

pip install networkx

The following code creates a NetworkX DiGraph object, adds edges(and thereby nodes) to it and plots the graph. 

import networkx as nx
from matplotlib import pyplot as plt
G = nx.DiGraph()
G.add_edges_from([(1, 3), (2, 3), (2, 4), (4, 1)])
nx.draw(G)    


Hopefully, this should get you started :)