If an input port on a subcomposition node has a constant value with no cables going into it, the constant value travels into the subcomposition through the corresponding published input port when the composition starts and whenever you edit the constant value.
The data travels from the published input port to any input ports that are directly connected to it by a cable. This is a rare case in which data can travel without an event. The data reaches the input ports on nodes but does not cause the nodes to execute.
In the example below, the Generate Checkerboard Image subcomposition’s width and height input ports are set to the constant values 1920 and 1080. The subcomposition outputs a 1920x1080 image.
It’s important to realize that the data travels only through the cable from the published input port to the next node, no farther. With the below variation on Generate Checkerboard Image, the subcomposition no longer outputs an image of size specified by width and height. Why? Because the constant values 1920 and 1080 only flow as far as the Multiply node’s input ports. They don’t cause the Multiply node to execute and pass its data along to the Make Checkerboard Image node.
To fix the composition above, you could add an event cable from the time published input port to each of the Multiply nodes. This would ensure that the Multiply nodes provide the halved width and height to Make Checkerboard Image whenever Make Checkerboard Image needs them, even if width and height have constant values.
As long as the published input port connects directly to the node’s input port, you can use a constant value to control a node that fires events. In the example below, editing the subcomposition node’s Seconds input port would affect the firing rate of the Fire Periodically node inside of it.