Path homology of directed hypergraphs

Persistent Path Homology of Directed Networks

Directed domination in oriented hypergraphs

ErdH{o}s [On Sch"utte problem, Math. Gaz. 47 (1963)] proved that every tournament on $n$ vertices has a directed dominating set of at most $log (n+1)$ vertices, where $log$ is the logarithm to base $2$. He also showed that there is a tournament on $n$ vertices with no directed domination set of cardinality less than $log n - 2 log log n + 1$. This notion of directed domination number has been g...

Persistent Path Homology of Directed Networks Samir Chowdhury and Facundo

While standard persistent homology has been successful in extracting information from metric datasets, its applicability to more general data, e.g. directed networks, is hindered by its natural insensitivity to asymmetry. We study a construction of homology of digraphs due to Grigor’yan, Lin, Muranov and Yau, and extend this construction to the persistent framework. The result, which we call pe...

Partial line directed hypergraphs

The partial line digraph technique was introduced in [7] in order to construct digraphs with a minimum diameter, maximum connectivity, and good expandability. To find a new method to construct directed hypergraphs with a minimum diameter, we present in this paper an adaptation of that technique to directed hypergraphs. Directed hypergraphs are used as models for interconnection networks whose v...

Directed Moore Hypergraphs

For graphs with maximum degree A and diameter D, an upper bound on the number of vertices is 1 + AxF:-,‘(A 1)‘. This bound is called the Moore bound for graphs and the graphs that attain it are called Moore graphs. Similar bounds for directed graphs and for hypergraphs have been defined and the existence of directed Moore graphs and of Moore hypergraphs has been studied. In this article, we def...