Each node is named uniquely and knows who it is connected to. The List of connections allows for a Node to be connected to an arbitrary number of other nodes.
public class Node {
public String name;
public List<Edge> connections;
}
Each connection is directed, has a start and an end, and is weighted.
public class Edge {
public Node start;
public Node end;
public double weight;
}
A graph is just your collection of nodes. Instead of List<Node> consider Map<String, Node> for fast lookup by name.
public class Graph {
List<Node> nodes;
}