Aug 2026· Entropy· Vol 28· 0 citations· 37 references
Medicine
TL;DR
The results show that smaller clusters are generally more vulnerable to attacks on central nodes, whereas larger and less centralized clusters retain more topological efficiency.
Abstract
Cluster structures are widespread in complex networks, yet conventional network-level measures do not distinguish the accessibility provided inside a cluster from that provided through its external links. This study asks how these two topological contributions can be measured consistently and how rapidly they deteriorate under different node-removal mechanisms. We define internal and external cluster efficiency by combining edge volume, relative cluster size, and a harmonic shortest-path factor based on the mean reciprocal distance rather than the reciprocal of an arithmetic mean distance. The measures are evaluated together with a Cluster Robustness Index (CRI) and Structural Resilience Entropy (SRE) on Barabási–Albert and Lancichinetti–Fortunato–Radicchi networks and five empirical network topologies under six attack strategies. The results show that smaller clusters are generally more vulnerable to attacks on central nodes, whereas larger and less centralized clusters retain more topological efficiency. A source-level audit also shows that replacing the reciprocal of the arithmetic mean distance by the arithmetic mean of reciprocal distances changes most normalized trends only slightly; the clearest quantitative changes occur in the weighted-average efficiency panels. Intra-cluster edge addition increases internal efficiency by 1–5% and CRI-based robustness by up to 11.9%, while cross-cluster edge rewiring improves external efficiency by up to 2.45% and CRI-based robustness by up to 2.33% under the tested targeted attacks. The reported quantities are structural proxies derived from unweighted network topology; they do not represent observed flow, transmission speed, recovery dynamics, or domain-specific functionality. The framework therefore supports cluster-level vulnerability diagnosis and topology-oriented reinforcement without making claims beyond the available network data.
Determining network structures that are neither local nor global is an area of research that has received considerable attention. The study of these intermediate structures has been primarily concerned with the detection of network communities but also includes the examination of network roles, core and peripheral structure, etc. In an increasingly relevant line of research, persistent homology has also been used to analyze the shape of a network in terms of the network’s cycle structure and its higher-dimensional analogues. In this work, we bring these two perspectives together by introducing a non-parametric partition of a network derived from its persistent homology. This partition, which we call the network’s persistence partition, is defined using the concept of a
persistence surface
, assigning to each node a measure of its individual persistence relative to its position in the network. We examine the extent to which this partition aligns with standard notions of network roles defined via combinatorial equivalence. We then compare how persistence partitions relate to communities and to the core–periphery structure of a network. Our analysis draws on both real and synthetic networks and demonstrates that persistent homology can reveal distinctive structural features that are not detected by conventional methods.
Abigail Jenkins, N. Callor, Z. Boyd et al.· PLOS Complex Systems· 0 citations
The analysis of random walks on networks often relies on global quantities that average over nodes, thereby masking local differences in diffusion speed. This study introduces a vertex-level quantity Hi, defined as the finite-window fitted scaling exponent of the mean squared resistance distance ⟨Ωi2(t)⟩∼Cit2Hi from a given node i. We found nodes with Hi values below 0.5 (echo effect) and above 0.5 (catapult effect). The exponent is computed exactly via matrix powers of the transition matrix. We systematically evaluate Hi on several synthetic network families, generalized Sierpiński graphs, Newman-Watts small-world networks, and a custom grid-path-complete graph, and on two real-world networks (international E-road network and western U.S. power grid). We found nodes with Hi values less than 0.5 (subdiffusive regime) and greater than 0.5 (apparent superdiffusion) in both model networks and real-world networks. Analysis of model networks shows that when a node has an echo effect, its Hi value is less than 0.5, whereas when it has a catapult effect, its Hi value is greater than 0.5. In the two real networks, most nodes are in the subdiffusive regime and the overall heterogeneity of the local diffusion exponents is low, as indicated by Rényi indices of 0.0835 (E-road network) and 0.0555 (power grid). Comparisons with classical centrality measures indicate that Hi provides information not captured by those measures. The local diffusion exponent offers a vertex-level, dynamics-based tool for identifying structural bottlenecks and node roles, complementing global network characterizations.
Heterogeneous information networks serve as one of the most important platforms in the fields of big data and artificial intelligence. Node similarity analysis is a fundamental yet crucial task. To explicitly distinguish the number of differing items and the total magnitude of interaction information between nodes of the same type under arbitrary meta-paths, while enabling flexible weighting between these two aspects, this paper proposes a similarity algorithm that formulates node similarity as a convex combination of vector norms. The proposed algorithm requires only the interaction information between typed nodes and does not depend on the type of metapath. It satisfies desirable properties including non-negativity, symmetry, self-maximum and boundedness. Experimental results on two real-world datasets demonstrate its superiority: on the Association for Computing Machinery Digital Library Dataset, the proposed algorithm achieves an average Silhouette of 0.67 on the paper-author-paper meta-path, outperforming PathSim and HeteSim by over 139%, and maintains a Calinski-Harabasz index approximately 6.6 times that of PathSim on the optimal paper-subject-paper meta-path. On the Internet Movie Database Dataset, it attains an average Silhouette of 0.77, which is 5.1 times and 3.0 times those of PathSim and HeteSim, respectively. Furthermore, the algorithm exhibits strong robustness, with minimal performance fluctuation across different meta-paths and clustering algorithms, whereas baseline methods suffer severe degradation. These results validate the efficiency and robustness of the proposed algorithm under various complex scenarios.
Wujie Hu, Wenhu Qin, Xuechun Liu et al.· IEEE International Conferenc...· 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
Identifying influential nodes in complex networks is a fundamental problem with applications in information diffusion, epidemic control, infrastructure robustness, and biological systems. Traditional approaches rely on structural centrality measures, such as degree, betweenness, closeness, and PageRank, which quantify node importance based on network connectivity. However, these measures do not explicitly account for diffusion dynamics and the structural impact of node removal, where both spreading capability and network resilience play a critical role. In this paper, we propose a unified framework that jointly captures diffusion-based influence and structural resilience. We first introduce an SIR-based centrality in which node influence is defined by its spreading capability, while resilience is quantified by measuring the change in total network diffusion after node removal. To address the computational cost of this formulation, we propose the Resilient-Influential Node (RIN) centrality, which efficiently approximates the unified objective by combining classical centrality measures with a Laplacian-based structural adjustment. Experimental results on multiple real-world networks, using SIR-based rankings as ground truth, show that the proposed RIN framework provides a consistent and principled characterization of influential and resilient nodes across diverse network structures.
Afra Kurudirek, Ibrahim Filik, Sravan Sakhamuri et al.· 2026 International Conferenc...· 0 citations
This study introduces a new ranking framework that integrates a quasi-Laplacian structural measure with a gravity-inspired aggregation process and demonstrates that the proposed framework consistently outperforms existing techniques in terms of accuracy, resolution, and computational simplicity.