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Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given ‘far away’ observations. Several theoretical results (a...
We present a simple and efficient algorithm for randomly generating simple graphs without small cycles. These graphs can be used to design high performance Low-Density Parity-Check (LDPC) codes. ...
We generalize a theorem of Knuth relating the oriented spanning trees of a directed graph G and its directed line graph LG. The sandpile group is an abelian group associated to a directed graph, whose...
We show how to exploit symmetries of a graph to efficiently compute the fastest mixing Markov chain on the graph (i.e., find the transition probabilities on the edges to minimize the second-largest ei...
We consider two graph optimization problems called vector domination and total vector domination. In vector domination one seeks a small subset S of vertices of a graph such that any vertex outside S ...
In this paper a convergent series expansion is constructed to solve the prescribed mean curvature equation ±∇·(∇u/p1 ± |∇u|2) = nH for n-dimensional hypersurfaces in Rn+1 (+ sign) an...
A graph has the unique path property $\rm UPP_n$ if there is a unique path of length $n$ between any ordered pair of nodes. This paper reiterates Royle and MacKay's technique for constructing orderly ...

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