Fig 1.
(a) Average hop count during a greedy search for different dimensionality Euclidian data and English words database with edit distance, demonstrating the logarithmic scaling. (b) Degree distribution for the GH algorithm networks with PA for different degree cutoffs (kc).
Fig 2.
Comparison of the GH model to the GH model with PA.
(a) Number of distance computations per a greedy search for GH network with PA for different degree cutoffs (kc). (b) Average hop count during a greedy search for GH network with PA for different degree cutoffs. The inset shows the decay of greedy hop slope with an increase of the degree cutoff. Both plots are presented for Euclid data with d = 2, M = 12.
Fig 3.
2D network constructed by the GH algorithm with M = 5 for clustered d = 2 Euclidian data.
The inset shows scaling of the modified greedy algorithm average hop count.
Fig 4.
(a) Average number of greedy algorithm hops scaling for the first 104 elements given as start and target nodes (red) and all elements used for search (black). The first 104 elements form a rich club that ignores more newly added elements. The results are presented for Euclidian data with d = 2, M = 20. (b) Cartoon of Voronoi partition for connections of a single greedy search step. Newly added elements (green) cause only local changes in Voronoi partitioning, so if the target element lies outside the current element connections, it falls into Voronoi partition of rich club’s elements (blue), thus ignoring local connections at greedy search.