Network Graph are composed of nodes (individuals) and edges (connections). Nodes that are highly connected appear closer on chart. Networks can be directed or undirected, showing a connection or a flow.
Network diagrams allow to visualize relationships between a group of entities, describing how things are interconnected. Customizing nodes appearance allows to compare with an expected structure.
Several R libraries are available. Igraph is the most important allowing to make every type of customisation. NetworkD3 allows to draw interactive network, ggnet2 and ggnetwork are other interesting libraries.