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We give a rigorous and self-contained survey of the abelian sandpile model and rotor-router model on finite directed graphs, highlighting the connections between them. We present several intriguing op...
This paper studies the continuous-time distributed optimization of a sum of convex functions over directed graphs. Contrary to what is known in the consensus literature, where the same dynamics works ...
Abstract: We consider the normalized Laplacian for directed graphs with positive and negative edge weights. We derive basic spectral properties of the normalized Laplacian and identify extremal eigenv...
We investigate Riemann-Roch theory for directed graphs. The Riemann-Roch criteria of Amini and Manjunath is generalized to all integer lattices orthogonal to some positive vector. Using a generalized...
A directed graph is set-homogeneous if, whenever U and V are isomorphic finite subdigraphs, there is an automorphism g of the digraph with U^g=V. Here, extending work of Lachlan on finite homogeneous...
We study the resilience of random and pseudorandom directed graphs with respect to the property of having long directed cycles. For every 0 < < 1/2 we find a constant c = c( ) such that the followin...

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