Jiang Zhang (Beijing Normal University)
Abstract. Many complex systems are open — they exchange matter, energy, and information with environment. Flow network is a weighted directed graph with a source and a sink, depicting flux distributions on networks in the steady state of an open flow system. Energetic food webs, global trade networks, input-output network, and clickstreams are flow network models of energy flows between species, goods flows between countries, money or value flows between industrial sectors, and attention flow between websites, respectively. These flow networks share some common properties, such as dissipation law, gravity law, scale-free weight distributions, and generalized Kleiber law for their growth, etc. They also have distinct characters. For example, we compare hiearchicality of international trading flow networks for different products, and relate the hiearchicality of a flow network with the complexity of a product. In another example, we show how distinct patterns emerge for different online communities if we embed their attention networks in Euclidean space according to a novel random walk based distance notion. Finally, we make perspective on general principles of the co-evolution between flows and networks.