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Researcher M.Sc. Mikko Vapa University of Jyväskylä Agora Center mikvapa@jyu.fi

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. Highway map. Flight map. Maps and their route distribution.

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Researcher M.Sc. Mikko Vapa University of Jyväskylä Agora Center mikvapa@jyu.fi

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  1. Power-law NetworksInBCT 3.2 Peer-to-Peer communicationCheese Factory -projecthttp://tisu.it.jyu.fi/cheesefactory Researcher M.Sc. Mikko VapaUniversity of Jyväskylä Agora Center mikvapa@jyu.fi

  2. Highway map Flight map

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

  5. 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 (H2O, ATP, ADP and CO2 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. 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 EUROOPAN UNIONI

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