Given a graph $ G $ and a positive integer $ k $, the Graphlet Sampling problem asks to
sample a connected induced $ k $-vertex subgraph of $ G $ uniformly at random. Graphlet …

We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs
(or graphlets) of rooted, bounded degree graphs. Our algorithm utilizes a vertex-percolation …

Simplicial complexes are higher-order combinatorial structures which have been used to
represent real-world complex systems. In this paper, we focus on the local patterns in …

We address the problem of computing the distribution of induced connected subgraphs, aka
graphlets or motifs, in large graphs. The current state-of-the-art algorithms estimate the motif …

We study the following problem: Given an integer k≥ 3 and a simple graph G, sample a
connected induced k-vertex subgraph of G uniformly at random. This is a fundamental graph …

We study the graphlet sampling problem: given an integer k≥ 3 and a graph G=(V, E),
sample a connected induced k-node subgraph of G (also called k-graphlet) uniformly at …

We introduce a novel statistical measure for MCMC-mean estimation, the inter-trace
variance ${\rm trv}^{(\tau_ {rel})}({\cal M}, f) $, which depends on a Markov chain ${\cal M} …

We study the problem of approximately counting cliques and near cliques in a graph, where
the access to the graph is only available through crawling its vertices; thus typically seeing …

The mixing time of random walks on a graph has found broad applications across both
theoretical and practical aspects of computer science, with the application effects depending …

We theoretically analyze our model and show how to bound the growth rate of some
characteristics of the graph, such as degree of vertices. Leveraging our theoretical results …