The essential characteristics of the http based web are that by default everyone is anonymous, and everyone can get to everything. Its "free" and the trend is for the parts that are not free and anonymous to move in that direction. For example, you can now buy stuff on eBay Express without having to sign up for an eBay account, and there are fewer newspaper sites requiring paid subscriptions, since they are losing audience to the free sites.
However, the essential characteristics of the Skype peer to peer network are the opposite of the Internet. Everyone has a clear identity and no-one can get to anything without asking for permission or being invited. I think this truly a different paradigm for building systems.
Everyone on Skype is plugged into the public key encryption infrastructure (PKI) which provides a secure identity as well as secure communications between peers. However, to communicate with other peers you need to know them and have permission. For me the most interesting capability on Skype is the application to application messaging API (ap2ap) that enables a new class of distributed applications that leverage the social network formed by the mesh of Skype contact lists.
The upshot of this is that some things that are easy on the Internet are difficult on Skype, and vice versa. There is a temptation to take something that we know works on the web, and try to make something similar on Skype ap2ap, but that is pointless, just use the web! Look for things that really don't work well on the web, or look for web-based systems that connect a few people but need an expensive back-end or don't scale. This is the start of something interesting....
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