Hashgraph is an alternative to Nakamoto consensus which has efficiency as a priority

Hashgraph works similar to Iota in that it uses a similar topology but the prime mechanism for Hashgraph is that it uses a gossip protocol. A gossip protocol could be described as Alice, who tells two friends, who tell two friends, propagating a message. The hashgraph is a new data structure which is a hybrid of a hash and a graph:

Hashgraph is interesting because it is extremely efficient. The concept of the gossip propagation in Hashgraph is interesting because the hashgraph itself is included in the gossip.

A few concepts of note about Hashgraph:

• "Gossip - information spreads by each member repeatedly choosing another member at random, and telling them all they know" 
• "Hashgraph - a data structure that records who gossiped to whom, and in what order. "
• "Gossip about gossip - the hashgraph is spread through the gossip protocol. The information being gossiped is the history of the gossip itself, so it is “gossip about gossip”. This uses very little bandwidth overhead beyond simply gossiping the transactions alone. "
• "Virtual voting - every member has a copy of the hashgraph, so Alice can calculate what vote Bob would have sent her, if they had been running a traditional Byzantine agreement protocol that involved sending votes. So Bob doesn’t need to actually her the vote. Every member can reach Byzantine agreement on any number of decisions, without a single vote ever being sent."
  

As you can see the way Hashgraph works is significantly different from how Bitcoin works. Bitcoin security is based on economic assumptions but is extremely very inefficient. In fact, Bitcoin tends to concentrate power away from it's users and into cartels which can be considered a systemic risk. Proof of Stake has similar risks but the difference is at least with Proof of Stake you get the efficiency gains in exchange for the same risk of concentration of power around cartels. Hashgraph does not require mining and is a variation of Proof of Stake. It would be interesting to see how Hashgraph compares in efficiency to DPOS but this would require testing.

Conclusion

Hashgraph looks interesting because it is dramatically more efficient than any Proof of Work. It also on the surface looks to be secure in the sense that it does produce Byzantine Fault Tolerance, but it also seems to suffer the same flaws of any Proof of Stake consensus. In general it has to be studied more as a lot of questions remain unanswered but it is a viable alternative to Nakamoto consensus and has ideas which can be improved upon.



References

1. http://www.swirlds.com/downloads/SWIRLDS-TR-2016-02.pdf
2. https://en.wikipedia.org/wiki/Hashgraph 

3. http://www.swirlds.com/downloads/SWIRLDS-TR-2016-01.pdf

4. http://iotatoken.com/IOTA_Whitepaper.pdf