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.
Abstract
Comparing graph partitions is fundamental to the analysis of network-structured data, yet existing measures for comparing graph partitions typically rely on graph-agnostic indices that treat vertices as exchangeable, ignoring the underlying graph topology that encodes essential information about community cohesion and separation. We propose a general construction of graph-informed distances that compares vertex partitions through induced edge partitions and yields valid metrics on the space of contiguous graph partitions. As special cases, we develop graph-informed versions of variation of information and the van Dongen distance together with a binary cut-based companion distance, and show that these distances satisfy a natural local graph-aware refinement criterion. Under stochastic block models, we prove that stronger topological disruptions incur asymptotically larger distances almost surely in both inter-community and intra-community split settings. These results provide a simple and principled framework to compare graph partitions while respecting the underlying graph structure.
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.
Bram Mornie, D. Colle, P. Audenaert et al.· Computing· 0 citations
This work generalizes three distance-based topological measures, namely closeness centrality, betweenness centrality and node eccentricity, using this new hypergraph distance, and shows that hypergraphs can be divided into three distinct classes, corresponding to the possible dominance of specific orders of interaction over their general metric structure.
E. Vasilyeva, L. Tupikina, D. Musatov et al.· Chaos, Solitons & Fracta...· 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.
This approach demonstrates that models trained on small-scale random graphs learn to extract universal distance-preserving features, achieving robust generalization to large-scale, real-world networks that match or exceed the fidelity of classical, exact landmark-based embeddings.
This paper presents a comparative analysis of two variants of a classical algorithm for finding the shortest path in a connected graph. The first variant uses an adjacency matrix (AM) to verify the existence of an edge (arc) between two vertices, while the second variant performs the same verification using an adjacency list (AL). The objective of this study is to examine how graph density affects the performance of the two algorithmic modifications depending on the data structure used. A total of 95 graphs were analyzed, grouped into five sets from 100 to 500 in increments of 100. For each group, 19 graphs were generated with densities ranging from 5% to 95% in increments of 5%. The methodology includes analyzing the number of iterations, assignments, and comparisons executed by the algorithms for all graphs. The initial hypothesis assumed that the total number of operations would always be lower when using an AL instead of an adjacency matrix, regardless of graph density. The results demonstrate that this assumption is incorrect: for densities above 82%, the total number of operations is lower when using an adjacency matrix, whereas the AL is more efficient for densities below 82%, with its efficiency increasing as density decreases. These findings are particularly important for mobile technologies, as they support the design of more efficient pathfinding solutions that optimize performance and energy consumption in mobile applications.
V. Kralev, Radoslava Kraleva, Aleksandra Popova· International Journal of Int...· 0 citations
We present an exact algorithmic framework for enumerating all maximum common subgraphs shared by multiple vertex- and edgelabeled graphs, motivated by molecular-graph comparison in cheminformatics and computational chemistry and, more generally, by comparison problems on labeled networks. The framework addresses maximum common induced subgraphs (MCIS), maximum common edge subgraphs (MCES), and their connected variants under labelpreserving matching. Algorithmically, it combines labeled modular- product constructions with a modified Bron–Kerbosch clique-enumeration procedure that retains the maximal intermediate candidates needed for exact multi-graph reduction. To improve practical performance, we incorporate pruning of redundant type-0 product edges and similarity-based ordering of the input graphs. Formal correctness proofs, benchmarks on the ZINC and ChEMBL22 molecular datasets, and a publicly available implementation show that the framework yields a reproducible exact method for labeled-network comparison that is practically usable on the studied molecular instance sizes.
Unknown authors· Match-communications in Math...· 0 citations