Validate JsonSchema itself. Is it correct JSON Schema?

Question

NB! I don't want to validate JSON against JSON Schema!

I have 2 JSON files:

1. JSON Schema file:

{
    "title" : "SomeTitle",
    "type":"object",
    "properties":{
        "City" : {"type" : "string", "editType" : "textarea"}
    }    
}

2. JSON File:

{
    "Elements": [{
            "name": "XYZ",
            "cities": ["XY", "QW", "ER", "TY"]
        }, {
            "name": "ASD",
            "cities": ["AS", "SD", "DF"]
        }
    ]
}

I want to validate these 2 files if they can be used as JSON Schema.

E.g:

First file -> true (Means that it can be used as JSON Schema)
Second file -> false

I have tried:

1) JSchema schema = JSchema.Parse(stringSchema); // It parses without any exception, and Valid property is null

2) James Newton-Kings answer

No luck, How can I validate JSON Schema itself?