Please Help: How to represent graphs for pathfinding

Hi, I am quite new to pathfinding, I understand that I have to use graphs, but I have difficulty on understanding how to represnt the graph in java. I need to represent nodes and edges, and state which nodes are connected to each other and the cost (distance) associated for travelling between those two nodes. So that I can later use a pathfinding strategy to find the shortest path.
I would be very grateful if anyone can guide me in this matter, on saying what kind of data structure is suitable, possibly using a little example.
Thank you.

Adjacency list
Edge list
Adjacency matrix
Incidence matrixWhat you need to do is to isolate the graph representation in a Graph class and then try to figure out what aspects of a graph you're interested in (what kind of methods you'd like to be available in Graph). Sometimes one specific representation will be perfect for your needs but sometime you'll need a combination of different representations. You can start with the representation you find easiest to handle maybe a 2D matrix where the rows/colums represent from/to nodes, and the elements are the costs. Later if you discover you need something else you need to make changes to Graph only.

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