Hello Michael,
And welcome to the forum. I'll say the same thing as qwerty, just using more words.

An MDG Technology is EA's deployment format (basically an XML file) for adaptations.
An MDG Technology contains profiles, profiles contain stereotypes. An EA stereotype may define a shape script, which determines how the element or connector is drawn.
In your case, you would need one element stereotype for your components, and one connector stereotype for your connectors.
You have a problem in that element shape scripts can't check any properties of other elements than the one being drawn, which you'd need to do in this case to determine what activities each component is connected to. However, if all else fails a shape script can call an Add-In (which you would then have to write), which can pull any information out of the database.
What qwerty is suggesting with the tagged values is a different way of expressing the relationship: use tagged values (of the RefGuidList type) instead of the connectors to represent the active sectors. An advantage with this approach is that no connectors are drawn, so they don't need to be hidden. A disadvantage is that since there's no connector, finding all applications for a certain sector becomes difficult.
If that's not a concern, the tagged values approach is definitely the way I would go. And if it's a concern but a minor one, you can always create a custom repository search query.
HTH,
/Uffe