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In this paper, we present an overview of different types of random walkstrategies with local and non-local transitions on undirected connectednetworks. We present a general approach to analyzing these strategies bydefining the dynamics as a discrete time Markovian process with probabilitiesof transition expressed in terms of a symmetric matrix of weights. In the firstpart, we describe the matrices of weights that define local random walkstrategies like the normal random walk, biased random walks, random walks inthe context of digital image processing and maximum entropy random walks. Inaddition, we explore non-local random walks like L\'evy flights on networks,fractional transport and applications in the context of human mobility.Explicit relations for the stationary probability distribution, the mean firstpassage time and global times to characterize the random walk strategies areobtained in terms of the elements of the matrix of weights and its respectiveeigenvalues and eigenvectors. Finally, we apply the results to the analysis ofparticular local and non-local random walk strategies; we discuss theirefficiency and capacity to explore different types of structures. Our resultsallow to study and compare on the same basis the global dynamics of differenttypes of random walk strategies.

Random walks on weighted networks: Exploring local and non-local navigation strategies