1. UNIVERSITY OF JYVÄSKYLÄ Power-law Networks InBCT 3.2 Peer-to-Peer communication Cheese Factory -project http://tisu.it.jyu.fi/cheesefactory Researcher M.Sc. Mikko Vapa University of Jyväskylä Agora Center mikvapa@jyu.fi

2. Highway map Flight map

3. UNIVERSITY OF JYVÄSKYLÄ 2002 Maps and their route distribution Highway routes follow normal distribution: But because of hubs like Helsinki flight routes have different characteristics. This structure is called power-law distribution: γ = degree exponent

4. UNIVERSITY OF JYVÄSKYLÄ 2002 Power-law structured network Power-law network of 50 nodes Nodes 1, 2, 3 and 4 are the most visible hubs

5. UNIVERSITY OF JYVÄSKYLÄ 2002 History of Power-law Networks Despite that power-law networks have been out there since life was born they were just recently discovered (in 1999 World Wide Web was found to be a power-law network) In a short time many other network maps were found to follow power-law distribution: –Internet routers and cables –Social networks (only 6 hops between any people in the world) –Companies (Nokia as a hub with many small subcontractors) –Molecules and chemical reactions in living organisms (H 2 O, ATP, ADP and CO 2 molecules as hubs) –Peer-to-peer networks (Gnutella diagnosed as the first one) During years 2000-2002 researchers came into a conclusion that this structure is universal and dominates all forms of life and organisation in complex systems and societies

6. UNIVERSITY OF JYVÄSKYLÄ 2002 Characteristics of Power-law network Fault-tolerant meaning that no matter how many nodes fail the network stays connected Short network distance between any node in the network meaning that searching can be done efficiently Still unclear: –How do these networks emerge? research on evolution of networks is needed –What is the most efficient way to search these networks? new search algorithms are needed Reference: Barabási, A.-L., ”Linked – The New Science of Networks”, Perseus Publishing, 2002