The concept you are describing, where the graviton field forms a "web" that is deformed by objects and affects spacetime directly, is closer to the traditional understanding of gravity in the framework of general relativity rather than the exchange of gravitons.
In general relativity, gravity is described as the curvature of spacetime caused by the presence of mass and energy. Massive objects deform the fabric of spacetime, and other objects moving within this curved spacetime experience what we perceive as the force of gravity.
In this framework, the gravitational interaction is not mediated by particles like the other fundamental forces (such as electromagnetism or the weak and strong nuclear forces) that are mediated by gauge bosons. Instead, it is the curvature of spacetime itself that governs the motion of objects.
The concept of gravitons, on the other hand, arises from attempts to unify general relativity with quantum mechanics, resulting in a theory called quantum gravity. In quantum gravity, gravitons are hypothetical particles that would mediate the gravitational interaction at a quantum level, similar to how photons mediate the electromagnetic interaction.
However, a complete and consistent theory of quantum gravity that incorporates both general relativity and quantum mechanics is still an active area of research and has not yet been achieved. The nature of the graviton and its role in the quantum description of gravity is still a subject of theoretical investigation.
In summary, while the idea of a web-like graviton field that directly affects spacetime is an interesting concept, it does not align with the current understanding of gravity in the framework of general relativity or the known properties of gravitons.