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Abstract:
Uncovering the topological properties of the brain network is essential for understanding brain function. Typically network structure is inferred from observations of a tiny fraction of the system, resulting in a severe subsampling of the whole network. How this inevitable subsampling influences the inferred network properties, such as the widely used small-world index, remains mostly unknown. The small-world index is defined as a clustering coefficient divided by diameter. For random, small-word, and scale-free networks we demonstrate analytically and numerically that the subsampling preserves the clustering coefficient. However, the diameter is strongly influenced by the subsampling, biasing the inference of small-worldness in subsampled networks. Our primary goal is to understand how to correct for such bias rigorously. Brain networks have a highly complex structure that is not captured by simple random networks we consider in theoretical studies. For a more realistic comparison, we investigate functional networks extracted from the High-Density Multi-Electrode Array recordings from cortical cultures using transfer entropy. The extracted network contains 4096 nodes, allowing for a further subsampling. We demonstrate that already the thresholding procedure used for extraction of the binary network is strongly influenced by subsampling.
