# Spectral Methods for Immunization of Large Networks

arXiv: https://arxiv.org/abs/1711.00791 · HTML: https://mlsanity.com/paper/1711.00791/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2017.

## Built on by (most cited first, 9 of 9)

- [Spike2Vec: An Efficient and Scalable Embedding Approach for COVID-19 Spike Sequences](https://mlsanity.com/paper/2109.05019/) (2021)
- [A k-mer Based Approach for SARS-CoV-2 Variant Identification](https://mlsanity.com/paper/2108.03465/) (2021)
- [Efficient Approximate Kernel Based Spike Sequence Classification](https://mlsanity.com/paper/2209.04952/) (2022)
- [Effective and scalable clustering of SARS-CoV-2 sequences](https://mlsanity.com/paper/2108.08143/) (2021)
- [Robust Representation and Efficient Feature Selection Allows for Effective Clustering of SARS-CoV-2 Variants](https://mlsanity.com/paper/2110.09622/) (2021)
- [Computing Graph Descriptors on Edge Streams](https://mlsanity.com/paper/2109.01494/) (2021)
- [Efficient Classification of SARS-CoV-2 Spike Sequences Using Federated Learning](https://mlsanity.com/paper/2302.08688/) (2023)
- [Characterizing SARS-CoV-2 Spike Sequences Based on Geographical Location](https://mlsanity.com/paper/2110.00809/) (2021)
- [Spread Control Method on Unknown Networks Based on Hierarchical Reinforcement Learning](https://mlsanity.com/paper/2308.14311/) (2023)

## Abstract (arXiv)

Given a network of nodes, minimizing the spread of a contagion using a limited budget is a well-studied problem with applications in network security, viral marketing, social networks, and public health. In real graphs, virus may infect a node which in turn infects its neighbor nodes and this may trigger an epidemic in the whole graph. The goal thus is to select the best k nodes (budget constraint) that are immunized (vaccinated, screened, filtered) so as the remaining graph is less prone to the epidemic. It is known that the problem is, in all practical models, computationally intractable even for moderate sized graphs. In this paper we employ ideas from spectral graph theory to define relevance and importance of nodes. Using novel graph theoretic techniques, we then design an efficient approximation algorithm to immunize the graph. Theoretical guarantees on the running time of our algorithm show that it is more efficient than any other known solution in the literature. We test the performance of our algorithm on several real world graphs. Experiments show that our algorithm scales well for large graphs and outperforms state of the art algorithms both in quality (containment of epidemic) and efficiency (runtime and space complexity).