{"paper":{"title":"Diffusion dynamics and synchronizability of hierarchical products of networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.AO","authors_text":"Per Sebastian Skardal","submitted_at":"2017-04-10T12:47:06Z","abstract_excerpt":"The hierarchical product of networks represents a natural tool for building large networks out of two smaller subnetworks: a primary subnetwork and a secondary subnetwork. Here we study the dynamics of diffusion and synchronization processes on hierarchical products. We apply techniques previously used for approximating the eigenvalues of the adjacency matrix to the Laplacian matrix, allowing us to quantify the effects that the primary and secondary subnetworks have on diffusion and synchronization in terms of a coupling parameter that weighs the secondary subnetwork relative to the primary su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02834","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}