Fig. 4: Redundancy in some real-world networks.
Amount of symmetry present on a typical (full) network measure for our test networks (Table 1). The predicted values, \({c}_{\text{full}}={\left({n}_{{\mathcal{G}}}/{n}_{{\mathcal{Q}}}\right)}^{2}\) coincide (up to 0.01%) with the compression ratio (shown as “actual”) obtained by our lossless compression algorithm for the shortest path distance, and communicability (exponential matrix), for our smallest seven networks (memory limit in our computer). After decompression, we recover the original matrix exactly for the shortest path distance, and up to a small numerical error (1.16 × 10−4 mean relative error) for communicability.
