There is the Thematic Approach to modeling.
I believe using the thematic approach with graph constructs (i.e. binary relationships) is also sometimes referred to as the Davidsonian or Neo-Davidsonian approach.
This approach calls for creating an identity for an event, as a simple node, and then describing the event by using as it as the subject of a number of individually simple thematic relationships like has-patient, has-agent, etc... You can have time relations as well, perhaps in your case has-begin-time and has-end-time.
One advantage of this approach is that it works with primitive modeling environments, like RDF, that don't support any more than binary subject-verb-object relationships, and also ones that don't support higher order statements (e.g. statements about statements). This approach supports optional/missing information quite well (and without use of nulls as you might find an relational model with lots of attributes in table where nulls might be found for missing/optional information).
However, a disadvantage is the explosion of edges, and possible increase in complexity of queries.
All-in-all from a mathematical point of view this is similar to your approach using higher order vertexes (a vertex that can refers to another vertex), so it comes down to standardizing on terminology, and on the capabilities of your modeling environment (e.g. whether higher order is supported).
However, if your modeling system does not support multiple edges between the same subject and object (in the same direction, using the same verb/relation), then using your vertex-based approach you would not necessarily be able differentiate between different attendances of the same person to the same school — whereas with the thematic approach you could (since using nodes for events instead of edges, assuming you can simply create a new node unique to other nodes).