Representing a graph in JSON

Question

Inspired by this question, I'm trying to represent a DAG in JSON. My case includes edges and nodes that contain some data (rather than just strings as in this example). I was thinking of a spec like this:

{
    "graph": {
        "a": ["b", "c"],
        "b": ["c"]
        "c"
    },

    "nodes": {
        "a": {
            "name": "Adam"
        },
        "b": {
            "name": "Bob"
        },
        "c": {
            "name": "Caillou"
        }
    },

    "edges": {
        // how to do the same for edges?
        // ie: how to query edges ?
    }
}

One idea I had was to make the keys of the edges be the concatenation of the two vertex ids that it connects. For example, ab, ac, and bc are the three edges in this graph. I want to know if there's a more standard way of doing this.

EDIT: This is what I'm thinking of now

{
    "graph": {
        "a": {
            "data": {
                // a's vertex data
            },
            "neighbors": {
                "b": {
                    "data": {
                        // data in edge ab
                    }
                },
                "c": {
                    "data": {
                        // data in edge ac
                    }
                }
            }
        },
        "b": {
            "data": {
                // b's vertex data
            },
            "neighbors": {
                "c": {
                    "data": {
                        // data in edge bc
                    }
                }
            }
        },
        "c": {
            "data": {
                // c's vertex data
            }
        }
    }
}

Answer 1

Since the DAG's edges hold data, they better have their own identifiers, just like the nodes. That is, the json representation should be composed of three components:

1. Node records: mapping each node identifier to the node's data.
2. Edge records: mapping each edge identifier to the edge's data.

3. Adjacency lists: mapping each node identifier to an array of edge identifiers, each corresponds to an edge going out of the node.

   DAG = {
     "adjacency": {
       "a": ["1", "2"],
       "b": ["3"]
     },
     "nodes": {
       "a": {
         // data
       },
       "b": {
         // data
       },
       "c": {
         // data
       }
     },
     "edges": {
       "1": {
         "from": "a", "to": "b",
         "data": {
           // data
         }
       },
       "2": {
         "from": "a", "to": "b",
         "data": {
           // data
         }
       },
       "3": {
         "from": "b", "to": "c",
         "data": {
           // data
         }
       }
     }
   }