Graph Inference with Effective Resistance Queries

• URL: http://arxiv.org/abs/2502.18350v1
• Date: Tue, 25 Feb 2025 16:37:25 GMT
• Title: Graph Inference with Effective Resistance Queries
• Authors: Huck Bennett, Mitchell Black, Amir Nayyeri, Evelyn Warton,
• Abstract summary: We study graph inference using an oracle that returns the effective resistance (ER) between a pair of vertices.<n>Although it is known that an $n$-vertex graph can be uniquely reconstructed from all possible ER queries, little else is known.
• Score: 2.2349172369559156
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The goal of graph inference is to design algorithms for learning properties of a hidden graph using queries to an oracle that returns information about the graph. Graph reconstruction, verification, and property testing are all types of graph inference. In this work, we study graph inference using an oracle that returns the effective resistance (ER) between a pair of vertices. Effective resistance is a distance originating from the study of electrical circuits with many applications. However, ER has received little attention from a graph inference perspective. Indeed, although it is known that an $n$-vertex graph can be uniquely reconstructed from all $\binom{n}{2}$ possible ER queries, little else is known. We address this gap with several new results, including: 1. $O(n)$-query algorithms for testing whether a graph is a tree; deciding whether two graphs are equal assuming one is a subgraph of the other; and testing whether a given vertex (or edge) is a cut vertex (or cut edge). 2. Property testing algorithms, including for testing whether a graph is vertex- or edge-biconnected. We also give a reduction to adapt property testing results from the bounded-degree model to our ER query model. This yields ER-query-based algorithms for testing $k$-connectivity, bipartiteness, planarity, and containment of a fixed subgraph. 3. Graph reconstruction algorithms, including an algorithm for reconstructing a graph from a low-width tree decomposition; a $\Theta(k^2)$-query, polynomial-time algorithm for recovering the adjacency matrix $A$ of a hidden graph, given $A$ with $k$ of its entries deleted; and a $k$-query, exponential-time algorithm for the same task. We also compare the power of ER queries and shortest path queries, which are closely related but better studied. Interestingly, we show that the two query models are incomparable in power.

Related papers

• Efficient Graph Matching for Correlated Stochastic Block Models [7.320365821066744]
  We study learning problems on correlated block models with two balanced communities.<n>Our main result gives the first efficient algorithm for graph matching in this setting.<n>We extend this to an efficient algorithm for exact graph matching whenever this is information-theoretically possible.
  arXiv  Detail & Related papers  (2024-12-03T18:36:45Z)
• A Graph is Worth $K$ Words: Euclideanizing Graph using Pure Transformer [47.25114679486907]
  We introduce GraphsGPT, featuring a Graph2Seq encoder that transforms Non-Euclidean graphs into learnable Graph Words. A GraphGPT decoder reconstructs the original graph from Graph Words to ensure information equivalence.
  arXiv  Detail & Related papers  (2024-02-04T12:29:40Z)
• A Near-Optimal Best-of-Both-Worlds Algorithm for Online Learning with Feedback Graphs [21.563733343861713]
  We consider online learning with feedback graphs, a sequential decision-making framework where the learner's feedback is determined by a directed graph over the action set. We present a computationally efficient algorithm for learning in this framework that simultaneously achieves near-optimal regret bounds in both and adversarial environments.
  arXiv  Detail & Related papers  (2022-06-01T15:14:32Z)
• AnchorGAE: General Data Clustering via $O(n)$ Bipartite Graph Convolution [79.44066256794187]
  We show how to convert a non-graph dataset into a graph by introducing the generative graph model, which is used to build graph convolution networks (GCNs) A bipartite graph constructed by anchors is updated dynamically to exploit the high-level information behind data. We theoretically prove that the simple update will lead to degeneration and a specific strategy is accordingly designed.
  arXiv  Detail & Related papers  (2021-11-12T07:08:13Z)
• Graphon based Clustering and Testing of Networks: Algorithms and Theory [11.3700474413248]
  Network-valued data are encountered in a wide range of applications and pose challenges in learning. We present two clustering algorithms that achieve state-of-the-art results. We further study the applicability of the proposed distance for graph two-sample testing problems.
  arXiv  Detail & Related papers  (2021-10-06T13:14:44Z)
• Random Subgraph Detection Using Queries [29.192695995340653]
  The planted densest subgraph detection problem refers to the task of testing whether in a given (random) graph there is a subgraph that is unusually dense. In this paper, we consider a natural variant of the above problem, where one can only observe a relatively small part of the graph using adaptive edge queries. For this model, we determine the number of queries necessary and sufficient (accompanied with a quasi-polynomial optimal algorithm) for detecting the presence of the planted subgraph.
  arXiv  Detail & Related papers  (2021-10-02T07:41:17Z)
• Random Graph Matching with Improved Noise Robustness [2.294014185517203]
  We propose a new algorithm for graph matching under probabilistic models. Our algorithm recovers the underlying matching with high probability when $alpha le 1 / (log log n)C$. This improves the condition $alpha le 1 / (log n)C$ achieved in previous work.
  arXiv  Detail & Related papers  (2021-01-28T02:39:27Z)
• Adversarial Linear Contextual Bandits with Graph-Structured Side Observations [80.95090605985042]
  A learning agent repeatedly chooses from a set of $K$ actions after being presented with a $d$-dimensional context vector. The agent incurs and observes the loss of the chosen action, but also observes the losses of its neighboring actions in the observation structures. Two efficient algorithms are developed based on textttEXP3.
  arXiv  Detail & Related papers  (2020-12-10T15:40:07Z)
• Inverse Graph Identification: Can We Identify Node Labels Given Graph Labels? [89.13567439679709]
  Graph Identification (GI) has long been researched in graph learning and is essential in certain applications. This paper defines a novel problem dubbed Inverse Graph Identification (IGI) We propose a simple yet effective method that makes the node-level message passing process using Graph Attention Network (GAT) under the protocol of GI.
  arXiv  Detail & Related papers  (2020-07-12T12:06:17Z)
• Scalable Deep Generative Modeling for Sparse Graphs [105.60961114312686]
  Existing deep neural methods require $Omega(n2)$ complexity by building up the adjacency matrix. We develop a novel autoregressive model, named BiGG, that utilizes this sparsity to avoid generating the full adjacency matrix. During training this autoregressive model can be parallelized with $O(log n)$ synchronization stages.
  arXiv  Detail & Related papers  (2020-06-28T04:37:57Z)
• Graph Pooling with Node Proximity for Hierarchical Representation Learning [80.62181998314547]
  We propose a novel graph pooling strategy that leverages node proximity to improve the hierarchical representation learning of graph data with their multi-hop topology. Results show that the proposed graph pooling strategy is able to achieve state-of-the-art performance on a collection of public graph classification benchmark datasets.
  arXiv  Detail & Related papers  (2020-06-19T13:09:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.