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A heterogeneous continuous time random walk is an analytical formalism forstudying and modeling diffusion processes in heterogeneous structures onmicroscopic and macroscopic scales. In this paper we study both analyticallyand numerically the effects of spatio-temporal heterogeneities onto thediffusive dynamics on different types of networks. We investigate how thedistribution of the first passage time is affected by the global topologicalnetwork properties and heterogeneities in the distributions of the traveltimes. In particular, we analyze transport properties of random networks anddefine network measures based on the first-passage characteristics. Theheterogeneous continuous time random walk framework has potential applicationsin biology, social and urban science, search of optimal transport properties,analysis of the effects of heterogeneities or bursts in transportationnetworks.

Structural and temporal heterogeneities on networks