Related papers: Consistency Thresholds for the Planted Bisection M…
We consider two closely related problems: planted clustering and submatrix localization. The planted clustering problem assumes that a random graph is generated based on some underlying clusters of the nodes; the task is to recover these…
Empirical observations suggest that in practice, community membership does not completely explain the dependency between the edges of an observation graph. The residual dependence of the graph edges are modeled in this paper, to first…
Finding community structures in networks is important in network science, technology, and applications. To date, most algorithms that aim to find community structures only focus either on unipartite or bipartite networks. A unipartite…
We establish sufficient conditions of exact and almost full recovery of the node partition in Bipartite Stochastic Block Model (BSBM) using polynomial time algorithms. First, we improve upon the known conditions of almost full recovery by…
We consider random recursive trees that are grown via community modulated schemes that involve random attachment or degree based attachment. The aim of this paper is to derive general techniques based on continuous time embedding to study…
In this paper, we consider networks consisting of a finite number of non-overlapping communities. To extract these communities, the interaction between pairs of nodes may be sampled from a large available data set, which allows a given node…
We give a polynomial-time algorithm that finds a planted clique of size $k \ge \sqrt{n \log n}$ in the semirandom model, improving the state-of-the-art $\sqrt{n} (\log n)^2$ bound. This $\textit{semirandom planted clique problem}$ concerns…
The problem of finding the largest induced balanced bipartite subgraph in a given graph is NP-hard. This problem is closely related to the problem of finding the smallest Odd Cycle Transversal. In this work, we consider the following model…
We introduce a random recursive tree model with two communities, called balanced community modulated random recursive tree, or BCMRT in short. In this setting, pairs of nodes of different type appear sequentially. Each node of the pair…
Understanding information exchange and aggregation on networks is a central problem in theoretical economics, probability and statistics. We study a standard model of economic agents on the nodes of a social network graph who learn a binary…
The problem of detecting communities in a graph is maybe one the most studied inference problems, given its simplicity and widespread diffusion among several disciplines. A very common benchmark for this problem is the stochastic block…
The theoretical information threshold for the planted clique problem is $2\log_2(N)$, however no polynomial algorithm is known to recover a planted clique of size $O(N^{1/2-\epsilon})$, $\epsilon>0$. In this paper we will apply a standard…
Relations between discrete quantities such as people, genes, or streets can be described by networks, which consist of nodes that are connected by edges. Network analysis aims to identify important nodes in a network and to uncover…
We consider the problem of distributed learning, where a network of agents collectively aim to agree on a hypothesis that best explains a set of distributed observations of conditionally independent random processes. We propose a…
Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment,…
We study the problem of community detection (CD) on Euclidean random geometric graphs where each vertex has two latent variables: a binary community label and a $\mathbb{R}^d$ valued location label which forms the support of a Poisson point…
Given an undirected graph with edge costs and node weights, the minimum bisection problem asks for a partition of the nodes into two parts of equal weight such that the sum of edge costs between the parts is minimized. We give a polynomial…
Revealing underlying relations between nodes in a network is one of the most important tasks in network analysis. Using tools and techniques from a variety of disciplines, many community recovery methods have been developed for different…
Bipartite networks composed of dichotomous node sets are ubiquitous in nature and society. Partly for simplicity's sake, many studies have focused on their projection onto their unipartite versions where one only needs to care about a…
In this paper, a new information theoretic framework for graph matching is introduced. Using this framework, the graph isomorphism and seeded graph matching problems are studied. The maximum degree algorithm for graph isomorphism is…