The novel Radial Graphlet Distribution Distance is effective, and comparable in performance to state-of-the-art methods, and the easy-to-compute Joint Degree Distance is a viable alternative to graphlet-based distances, especially for measuring randomness in sets of very large networks.
Under stochastic block models, it is proved that stronger topological disruptions incur asymptotically larger distances almost surely in both inter-community and intra-community split settings.
S. Bhattacharyya, Huiyan Sang, Bani Mallick· 0 citations
The findings indicate that the Eppstein-Wang algorithm provides a practical and scalable solution for average distance estimation, with higher reliability on unipartite graphs compared to bipartite graphs.
It is proved that the related symmetry-breaking problems of maximal independent set (MIS) and maximal matching (MM) are substantially harder: a lower bound of $\Omega\left(\frac{\log\log n}{\log\log\log n}\right)$ for MIS and MM on HRGs is established.
Yannic Maus, Janosch Ruff, Sonia Simons et al.· 0 citations
It is proved that both the maximum common edge subgraph and the graph edit distance remain NP-hard, even when both graphs are paths, even when one graph is a path and the other is a tree.
The joint asymptotic distribution of any finite collection of network moments in random graphs sampled from a graphon, which includes both the nondegenerate case as well as the degenerate case, provides the higher-order fluctuation theory for subgraph counts in the graphon model.
Anirban Chatterjee, S. Dan, B. Bhattacharya· Annals of Statistics· 0 citations