11 citations · 28 across the 15 of their papers we have counts for
4 papers · 1 filter
Avalanche homology of digraphs via sandpile dynamics
Henri Riihimäki, Jason P. Smith
We introduce avalanche homology as a new (di)graph homology theory, based on the dynamics of the sandpile model. Avalanche homology is the simplicial homology of the avalanche comp…
An application of neighbourhoods in digraphs to the classification of binary dynamics
Pedro Conceição, Dejan Govc, Jānis Lazovskis +3
A binary state on a graph means an assignment of binary values to its vertices. For example, if one encodes a network of spiking neurons as a directed graph, then the spikes produc…
Complexes of Tournaments, Directionality Filtrations and Persistent Homology
Dejan Govc, Ran Levi, Jason P. Smith
Complete digraphs are referred to in the combinatorics literature as tournaments. We consider a family of semi-simplicial complexes, that we refer to as "tournaplexes", whose simpl…
Computing persistent homology of directed flag complexes
Daniel Luetgehetmann, Dejan Govc, Jason Smith +1
We present a new computing package Flagser, designed to construct the directed flag complex of a finite directed graph, and compute persistent homology for flexibly defined filtrat…