Related papers: How to Count Triangles, without Seeing the Whole G…
The switch chain is a well-studied Markov chain which generates random graphs with a given degree sequence and has uniform stationary distribution. Motivated by the high number of triangles seen in some real-world networks, we study a…
In modern graph analytics, the shortest path is a fundamental concept. Numerous \rrev{recent works} concentrate mostly on the distance of these shortest paths. Nevertheless, in the era of betweenness analysis, the counting of the shortest…
We identify the scaling limit of random intersection graphs inside their critical windows. The limit graphs vary according to the clustering regimes, and coincide with the continuum Erdos--Renyi graph in two out of the three regimes. Our…
Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of…
We study the problem of approximating the $3$-profile of a large graph. $3$-profiles are generalizations of triangle counts that specify the number of times a small graph appears as an induced subgraph of a large graph. Our algorithm uses…
Sampling random nodes is a fundamental algorithmic primitive in the analysis of massive networks, with many modern graph mining algorithms critically relying on it. We consider the task of generating a large collection of random nodes in…
Graphlets are induced subgraph patterns and have been frequently applied to characterize the local topology structures of graphs across various domains, e.g., online social networks (OSNs) and biological networks. Discovering and computing…
Counting the number of small subgraphs, called motifs, is a fundamental problem in social network analysis and graph mining. Many real-world networks are directed and temporal, where edges have timestamps. Motif counting in directed,…
A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…
Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance…
The triad census is an important approach to understand local structure in network science, providing comprehensive assessments of the observed relational configurations between triples of actors in a network. However, researchers are often…
Crowd counting has recently attracted increasing interest in computer vision but remains a challenging problem. In this paper, we propose a trellis encoder-decoder network (TEDnet) for crowd counting, which focuses on generating…
Solving SharpSAT problems is an important area of work. In this paper, we discuss implementing Tetris, an algorithm originally designed for handling natural joins, as an exact model counter for the SharpSAT problem. Tetris uses a simple…
We study the minimum degree necessary to guarantee the existence of perfect and almost-perfect triangle-tilings in an $n$-vertex graph $G$ with sublinear independence number. In this setting, we show that if $\delta(G) \ge n/3 + o(n)$ then…
To capture the inherent geometric features of many community detection problems, we propose to use a new random graph model of communities that we call a Geometric Block Model. The geometric block model builds on the random geometric graphs…
From social science to biology, numerous applications often rely on graphlets for intuitive and meaningful characterization of networks at both the global macro-level as well as the local micro-level. While graphlets have witnessed a…
Mining dense subgraphs is an important primitive across a spectrum of graph-mining tasks. In this work, we formally establish that two recurring characteristics of real-world graphs, namely heavy-tailed degree distributions and large…
In this paper we give a simple polynomial-time algorithm to exactly count the number of Euler Tours (ETs) of any Eulerian graph of bounded treewidth. The problems of counting ETs are known to be #P-complete for general graphs (Brightwell…
We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, for various models of random (multi)graphs. For our proofs we introduce the notion of \emph{patchworks} to describe the possible…
We initiate the study of combinatorial algorithms for Triangle Detection in $H$-free graphs. The goal is to decide if a graph that forbids a fixed pattern $H$ as a subgraph contains a triangle, using only "combinatorial" methods that…