Exploring complex networks by thermal flux spreading

Thermal conduction physical method based on finite element model (FEM) is utilized in searching for the shortest path between two nodes in complex networks. The thermal flux matrix of nodes is constructed, and the element with the maximal value in each node thermal flux vector indicates one section of the shortest path to the source node. Theoretical analysis and experimental results show that the strategy can avoid the problem of bringing high flux of inquiring data packet into network and the correct shortest path form source node to any other nodes can be found simultaneously. The shortest path from the source node to any other nodes can be found in time O(mt/Deltat), where m is the number of edges, t is the conduction time, Deltat is the integral interval, which is essentially in linear time with m, and all the shortest path between any two nodes can be found in time O(nmt/2Deltat).