III: Small: Collaborative Research: Resilience Analysis for Core Decomposition in Real-World Networks

The resilience of a network is generally defined as its ability to continue performing well when it is subject to failures and attacks. Designing and developing graph analysis algorithms that are robust against missing data, incomplete network observation, or errors in data collection is essential in many real-world applications. One fundamental and important class of graph analysis methods are those that find the dense regions in a given network. These methods have applications in bioinformatics, social network analysis, router network monitoring, visualization, and other areas. Core decomposition, a powerful and efficient algorithm for finding dense subgraphs, has been proven to be extremely useful in understanding the structure of complex networks from a variety of domain. However, it is notoriously non-robust against small changes in the network structure. This project will explore and characterize the robustness of core decomposition process and develop attack (and corresponding defense) strategies to manipulate the network to hinder the core decomposition analysis. The outcome of this research will allow for increased understanding of the accuracy core decomposition analyses on real-world networks, and propose new, related decompositions that are more robust against noise or missing data. The project will be performed in three parts: 1) Exploring and characterizing the robustness of core decomposition to develop a variety of techniques and metrics to quantify the robustness, 2) Developing graph modification 'attack' strategies to tamper with a network's core structure by adding/deleting nodes or edges -- the project considers three types of attacks: those targeting nodes' core numbers, the subgraphs induced by the core decomposition, and the hierarchy induced by the core decomposition, 3) Developing corresponding strategies to defend against the attacks on a network's core structure. Given the wide application space of core decomposition, this project will increase the robustness of algorithms for describing the hierarchical structure of a network, detecting central nodes, spotting the anomalies, and speeding up algorithms for other tasks, like community detection. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.