We introduce and study analogues of expander hyperfinite graph sequences in the context directed acyclic graphs, which we call "extender" "hypershallow" sequences, respectively. Our main result is a probabilistic construction non-hypershallow sequences.

The Laplacian matrix and its pseudo-inverse for a strongly connected directed graph is fundamental in computing many properties of graph. Examples include random-walk centrality betweenness measures, average hitting commute times, other connectivity measures. These measures arise the analysis social computer networks. In this short paper, we show how linear system involving may be solved time n...

We consider generalisations of tree width to directed graphs, that attracted much attention in the last fifteen years. About their relative strength with respect to “bounded width in one measure implies bounded width in the other” many problems remain unsolved. Only some results separating directed width measures are known. We give an almost complete picture of this relation. For this, we consi...

this paper deals with leader-following and leaderless consensus problems of high-order multi-input/multi-output (mimo) multi-agent systems with unknown nonlinear dynamics in the presence of uncertain external disturbances. the agents may have different dynamics and communicate together under a directed graph. a distributed adaptive method is designed for both cases. the structures of the contro...