230 citations · 253 across the 4 of their papers we have counts for
4 papers
Fundamental groups of random clique complexes
Armindo Costa, Michael Farber, Danijela Horak
We study fundamental groups of clique complexes associated to random graphs. We establish thresholds for their cohomological and geometric dimension and torsion. We also show that…
Interlacing inequalities for eigenvalues of discrete Laplace operators
Danijela Horak, Jürgen Jost
The term interlacing refers to systematic inequalities between the sequences of eigenvalues of two operators defined on objects related by a specific oper- ation. In particular, kn…
Spectra of combinatorial Laplace operators on simplicial complexes
Danijela Horak, Jürgen Jost
We first develop a general framework for Laplace operators defined in terms of the combinatorial structure of a simplicial complex. This includes, among others, the graph Laplacian…
Persistent Homology of Complex Networks
Danijela Horak, Slobodan Maletic, Milan Rajkovic
Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topologic…