Related papers: Efficient Algorithms for Exact Graph Matching on C…
A relevant, sometimes overlooked, quality criterion for communities in graphs is that they should be well-connected in addition to being edge-dense. Prior work has shown that leading community detection methods can produce poorly-connected…
Spectral algorithms are an important building block in machine learning and graph algorithms. We are interested in studying when such algorithms can be applied directly to provide optimal solutions to inference tasks. Previous works by…
We study graph matching between two correlated networks in the almost fully seeded regime, where all but a vanishing fraction of vertex correspondences are revealed. Concretely, we consider the correlated stochastic block model and assume…
Signed graphs encode similarity and dissimilarity relationships among different entities with positive and negative edges. In this paper, we study the problem of community recovery over signed graphs generated by the signed stochastic block…
Stochastic block models (SBMs) are a very commonly studied network model for community detection algorithms. In the standard form of an SBM, the $n$ vertices (or nodes) of a graph are generally divided into multiple pre-determined…
We propose an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each vertex. For two Erd\H{o}s-R\'enyi graphs $\mathcal{G}(n,q)$ whose edges are…
Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…
Community detection in networks is a fundamental problem in machine learning and statistical inference, with applications in social networks, biological systems, and communication networks. The stochastic block model (SBM) serves as a…
A significant problem in analysis of complex network is to reveal community structure, in which network nodes are tightly connected in the same communities, between which there are sparse connections. Previous algorithms for community…
There has been a recent interest in understanding the power of local algorithms for optimization and inference problems on sparse graphs. Gamarnik and Sudan (2014) showed that local algorithms are weaker than global algorithms for finding…
Graphs provide a natural way to represent data by encoding information about objects and the relationships between them. With the ever-increasing amount of data collected and generated, locating specific patterns of relationships between…
This paper deals with the problem of graph matching or network alignment for Erd\H{o}s--R\'enyi graphs, which can be viewed as a noisy average-case version of the graph isomorphism problem. Let $G$ and $G'$ be $G(n, p)$ Erd\H{o}s--R\'enyi…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
Graph alignment in two correlated random graphs refers to the task of identifying the correspondence between vertex sets of the graphs. Recent results have characterized the exact information-theoretic threshold for graph alignment in…
The network alignment (or graph matching) problem refers to recovering the node-to-node correspondence between two correlated networks. In this paper, we propose a network alignment algorithm which works without using a seed set of…
Computing fixed-radius near-neighbor graphs is an important first step for many data analysis algorithms. Near-neighbor graphs connect points that are close under some metric, endowing point clouds with a combinatorial structure. As…
Considering the worst-case scenario, junction tree algorithm remains the most general solution for exact MAP inference with polynomial run-time guarantees. Unfortunately, its main tractability assumption requires the treewidth of a…
This paper proposes a novel scalable community-based neural framework for graph learning. The framework learns the graph topology through the task of community detection and link prediction by optimizing with our proposed joint SBM loss…
In this paper we consider alignment of sparse graphs, for which we introduce the Neighborhood Tree Matching Algorithm (NTMA). For correlated Erd\H{o}s-R\'{e}nyi random graphs, we prove that the algorithm returns -- in polynomial time -- a…
Community detection is the problem of identifying dense communities in networks. Motivated by transitive behavior in social networks ("thy friend is my friend"), an emerging line of work considers spatially-embedded networks, which…