There is no doubt the social web has changed the way we use the internet and interact with each other. I believe a foundation of this "new web" is the social graph - which is sometimes referred to as the friend graph. Although Facebook may have won the "friend graph" (for now), other valuable relationship graphs exist and I don't believe they will all be owned by Facebook. As a VC, I'm on the lookout for companies defining and harnessing these graphs via network effects as i believe there will be a few more mega platform companies created : )
Before exploring some ideas on these other graphs, let's recap what is a graph, its components, and why its important. As Wikipedia states, graphs are mathematical relationships to model pairwise relationships between objects in a certain collection. Graphs can be used to model many physical, biological, and social systems - from epidemics to viral propagation of marketing messages in a community. We could graph relationships for any set of objects (e.g. a family of appliances or brands for certain product categories), but the most interesting ones are human relationships given how important they are in communication, information, entertainment, and commerce. The speed and relevance of a message traversing a network formed by a relationship graph vs a "dumb" network (e.g. emailing a marketing list) is profound as we have seen firsthand from the spread of messages, videos, and photos on youtube, Facebook, and twitter.
What's In A Graph
Human beings are defined by our relationships and the information, entertainment, and commerce we consume are influenced by people in our networks. I argue that a friend graph is simply one important network (and arguably the most valuable) and there are others that are valuable and unique. The uniqueness can be described after understanding the components of the graph - two of these are defined well by this article in ReadWrite Web and one other element defined below as "Activities".
1) People's Identity - this is the online data typically in a profile that describes who we are. Facebook designed a great system which encourages and rewards users to share an accurate view of a person's real world identity - which may be the most valuable for many applications. That said, an individual can have other identities which partially expose their real world traits (e.g. work identity) or entirely different identities which are aspirational (e.g. a Level 60 Warrior in World of Warcraft). These could result in different relationship graphs with different connections between identities. I would argue that it is difficult to manage these different identities and relationships in one place let alone all the privacy settings for each type. This is one argument why other networks/graphs can succeed outside of the friend graph dominated by Facebook.
2) Types of Relationships - this is the type of link between identities and also the strength of that link. We have lots of different relationships in our lives - our friends (dominated by Facebook), our family, people involved in our hobbies, our work, our academic relationships, and experts who help us (directly or indirectly by reading/watching them). Even if we define ourselves by one real world identity, we have several graphs that are different with varying connections and strengths. Facebook owns the friend graph but what i share and expose on Facebook is not what i want to share with all these other relationships. Another reason why Facebook can't satisfy all our needs.
3) Activities - depending on the identity and the type of relationship, there should be different activities relevant for each network and thus a potentially very different feature set for each. An extreme example is the World of Warcraft community vs your Facebook community. In WoW, a user has a fantasy identity and relationships to achieve goals in the game (forming guilds to slay dragons, pillage towns, etc). The activities are real-time, graphic intensive, and follow the story arc created by the characters and their relationships. This feature set is obviously very different than Facebook but both are valuable "graphs" to own. In fact, WoW has much higher engagement per user than Facebook as diehards immerse themselves in this fantasy world for dozens of hours per week - giving some more satisfaction than the real world!
When we think about the combination of identities and relationships that a person has in their life, you can see how there are possibilities for many "graphs" and thus networks to fluorish. I don't think they all have the same economic value or frequency of use in our lives - but they are valuable.
Other Graph Opportunities
Here are some other graphs aside from Facebook's friend graph that i think will be important:
1) Professional Graph - this graph uses our work identity (which is more of a resume vs our personal likes and interests) and connects to others important in our work. It feels like the clear winner is Linkedin (trading over $7B in market cap as of today). The challenge is lower frequency as you don't need to tap into your professional graph everyday (although linked in is changing that with its own version of social news) but each visit is more valuable given the demographic and context. Linkedin has done a solid job differentiating from facebook with a unique news feed, graph connections, and activities for its members.
2) Social Discovery Graph - this graph is about discovering new people to build relationships online. This could use your real world identity but is likely a combination of some elements of the real world (e.g. your photo) with other aspirational elements that could be more fantasy. The relationships are those created by online activities - conversing about topics with others, flirting online, and playing games together. The opportunity here could be massive for two reasons. First, most of the 7 billion people in this world don't have a plethora of meaningful relationships or daily exciting lives in the real world and are seeking satisfaction online - where there are no geographic or socio-economic barriers. Second, these new online relationships can be worth a lot. Mayfield company Tagged (a leader in social discovery) has shown that it can achieve higher ARPUs than Facebook for its online games as users are highly motivated to look good in front of new people and not embarrassed to spend money on virtual items in front of online friends. An example of a massive company in China that combines social discovery and social utility/communication is Tencent ($42B market cap).
3) Family Graph - this is defined by the genealogical relationships between individuals - of course real world profies are used and the relations are family based. The information and communications along this graph are quite different than what one would share with friends which give a unique opportunity vs Facebook. A challenge is frequency as the need or desire to communicate with relatives up and down your family tree is not daily or weekly. Geni has tried to own this family tree graph but without much success in terms of growth. The immediate family household may be a sub-opportunity that has much higher frequency but i haven't seen that cracked yet (cozi is one startup giving it a shot).
4) Interest Graph - you may have a lot in common with your friends but what about the people out there that share your individual passions or interests that you aren't friends with? They could be role models (e.g. Tony Horton of P90x for fitness fanatics) or others sharing an experience or interest (e.g. the people doing the 90 day P90x program). This graph could be very different than the friend graph and the conversations, info, and activity would be highly focused and in many cases not as frequent. Bulletin boards and group websites (e.g. yahoo groups) have tried to satisfy this need but they typically aren't building a graph and allowing users to connect via many interests. Ning is probably the closest one I am aware of. I think this is a very valuable graph but its unclear how independent it will be from facebook as improvements in their groups and events features could satisfy 80% of the use cases and often your friends overlap with interests. That said, its not easy managing different communities on facebook which could be an opening for a new startup.
5) Broadcast Graph - this graph is less of a 2 way connection - its more about a person or entity having followers that consume content from the author. Newspapers, magazines, blogs, and now twitter are great examples. I feel like this space is well covered. There will be an interesting graph created here (as evidenced by twitter) that is different than your friend graph - and could be worth billions as well.
6) Neighbor Graph - this is a relatively open space - its about connecting neighbors to communicate, share news, reccomendations, local commerce, and coordinate activities. Most people don't have a good way to communicate with neighbors despite being so close (do you know the emails of all your neighbors?) and since they spend most of their time and money in their neighborhood. I think this graph is very unique to facebook in both the relationships and activities aspects. The information you share about your neighborhood is not so relevant to all your facebook friends. The frequency could be high if news is a key driver (I find myself diligently reading my hyperlocal newsletter - Patch by AOL - everyday). Blockboard is a startup that is taking an interesting mobile-centric run at this space. I'm actively looking for opportunities here.
In summary, graphs are powerful new constructs to build communities for communication, information, and commerce. Facebook seems to own the valuable friend graph but I believe there are a number of other large opportunities to create platform businesses. The building blocks of identity, relationships, and activities are used differently for each opportunity and its hard for facebook to cover all use cases without hurting its core proposition. There are likely other "graph" opportunities that i haven't covered here - i'm interested in hearing from you on both the ideas above and your own!