# The Network Nullspace Property for Compressed Sensing of Big Data over Networks

## TL;DR

This paper introduces the network nullspace property, a new condition linking network structure and sampling geometry, enabling accurate recovery of graph signals from limited data in large network datasets.

## Contribution

It proposes the network nullspace property, a novel criterion for signal recovery that integrates network topology and sampling design, advancing compressed sensing in network-structured data.

## Key findings

- Defines the network nullspace property for graph signals
- Provides conditions for accurate signal recovery
- Suggests sampling strategies based on network topology

## Abstract

We present a novel condition, which we term the net- work nullspace property, which ensures accurate recovery of graph signals representing massive network-structured datasets from few signal values. The network nullspace property couples the cluster structure of the underlying network-structure with the geometry of the sampling set. Our results can be used to design efficient sampling strategies based on the network topology.