Jun 2026· Nature Communications· Vol 17· 0 citations· 67 references
Medicine
TL;DR
A statistical filter that benchmarks node-level bipartite clustering against degree-preserving randomizations to classify nodes as geometric (signal) or degree constrained noise is introduced, offering a simple, scalable way to disentangle structure from noise in bipartite networks.
Abstract
Real bipartite networks combine degree-constrained random mixing with structured connectivity balancing short and long range connections, effectively accounted for by geometric network models. We introduce a statistical filter that benchmarks node-level bipartite clustering against degree-preserving randomizations to classify nodes as geometric (signal) or degree constrained noise. In synthetic mixtures with known ground truth, the filter achieves high classification accuracy and sharpens inference of latent geometric parameters. Applied to four empirical systems –metabolism, online group membership, plant-pollinator interactions, and languages– the filter isolates recurrent neighborhoods while removing ubiquitous or weakly co-occurring entities. Filtering exposes a compact geometric backbone that disproportionately sustains connectivity under percolation and preserves downstream classifier accuracy in node-feature tasks, offering a simple, scalable way to disentangle structure from noise in bipartite networks. Real bipartite networks combine structured relations with non-specific connectivity. Here, authors introduce a clustering-based node-level filtering method that extracts the transitivity backbone, identifying meaningful structure that sustains connectivity and preserves predictive performance.
Predicting the percolation threshold of highly clustered networks from local statistics remains difficult, because short loops break the independence assumption underlying tree-like message passing. Existing remedies address loopy connectivity either through prescribed local motifs in random-graph ensembles or through a single network's realized topology, leaving an ensemble-level treatment of arbitrary connectivity patterns absent. Here, we develop a loopy message-passing framework for random clustered graph ensembles based on generalized-edge statistics, which characterize overlap patterns among the neighborhoods of different nodes. This yields a progressively refined approximation scheme based on neighborhoods of increasing size around each node. The low-order approximations recover previous equations for random network ensembles, and the new result that yields refined threshold prediction is developed by the second-order approximation. We show that the effectiveness of this framework depends not only on short-cycle density but also on the internal consistency of generalized edges. To diagnose this effectiveness, we introduce the generalized-edge closure coefficient (GECC) to quantify this consistency. Because GECC is computed entirely from local statistics and does not rely on any percolation calculation, it serves as an a priori diagnostic for the reliability of the approximation. Using synthetic and real networks, the threshold is evaluated via the second-order and lower-order approximations. Comparisons with Monte Carlo simulations show that GECC captures key structural features that strongly affect the percolation threshold. These results establish ensemble-based loopy message passing as an efficient route for predicting the percolation threshold in large clustered networks.
Collective behaviors such as infrastructure failures and social adoption propagate through groups governed by fixed quorum requirements rather than by pairwise contacts. However, it remains unclear how absolute group- and individual-level thresholds jointly shape cascades in higher-order networks. Here we show that a dual-threshold bootstrap percolation model on random hypergraphs separates a connected active backbone from large-scale endogenous activation. A seed-driven giant component emerges continuously at a structural percolation threshold, whereas macroscopic amplification ignites only at a higher dynamical tipping point, creating a metastable safety margin in which communication is possible without systemic outbreak. This decoupling reflects an asymmetric division of labor: the group quorum
M
acts as a source-side filter, while the individual barrier
K
serves as a receiver-side gatekeeper. On homogeneous substrates, the structural onset is protected to leading order against
K
, but heterogeneous connectivity erodes this protection. Our framework provides a basis for predicting cascade risk and designing targeted node- and group-level interventions in complex systems.
Network comparison plays a central role in characterizing structural differences and cross-network correlations in complex systems. In many real-world settings, however, interactions are inherently signed, with positive and negative links altering both connection semantics and structural organization. This challenges conventional comparison methods built upon unsigned assumptions, which are unable to adequately capture such heterogeneity. To address this limitation, we introduce a network comparison method based on Signed Communicability Embedding (SCE). SCE employs the matrix exponential of the signed adjacency matrix to capture the cumulative contributions of positive and negative walks across multiple scales. Network-level dissimilarity is then quantified through discrepancies in pairwise node distances within the resulting embedding space, thereby integrating topological structure and relation polarity into a unified measure. To further ensure consistency across networks, a spectral correction strategy is incorporated to mitigate scale-induced bias. Extensive experiments on diverse real-world signed networks show that SCE yields stable and discriminative performance under a variety of perturbation scenarios, particularly in capturing structural shifts induced by negative edge changes. Additional analyses based on null models and network clustering further show that SCE not only disentangles differences arising from topology and sign configurations but also organizes networks into distinct structural regimes, reflecting variations in connectivity density, local closure, and signed interaction heterogeneity. Overall, SCE provides a coherent and interpretable approach to network comparison in complex signed systems.
Connectivity is a fundamental concept in network science, characterizing how interactions propagate through indirect pathways. While numerous connectivity metrics exist, such as shortest paths, effective resistance and minimum cut, each highlighting distinct structural features, their relationships remain largely fragmented. Here we show that these classical notions arise as limiting cases of a unified statistical-physics framework based on the random cluster (RC) model, which interprets connectivity as a principled synthesis of series and parallel transmission. By tuning its parameters, the RC model not only recovers classical connectivity measures but also extrapolates into unexplored regimes, leading to emergent notions of connectivity which yield practical tools for network learning tasks. In particular, RC connectivity naturally encodes the kinetics of growing paths, enhancing learning performance in dynamical settings such as epidemic spreading and neurodynamics. By linking structural, dynamical, and learning-based perspectives, RC connectivity establishes a general and interpretable foundation for the analysis of networked systems. Network connectivity is traditionally described by distinct measures like shortest paths or effective resistance. Here, authors introduce a unified statistical physics framework based on the random cluster model that encompasses these classical notions and defines a continuous family of new connectivity measures, offering a powerful tool to analyze structure and dynamics in complex networks.
Community detection is essential for uncovering the functional organization of complex networks. While traditional methods often rely on edge density, motif-based approaches use higher-order structural patterns to identify communities. However, existing research frequently employs conventional motifs, such as triangles or 4-node cliques, or lacks validation against networks with ground-truth communities. This study addresses these limitations by systematically evaluating eight small motifs across both synthetic and real-world networks with known community structures. We propose a framework that transforms unweighted graphs into weighted representations by assigning weights to node pairs based on their co-occurrence frequency within specific graphlets, while also preserving information about the original edges, rather than creating a potentially sparse (hyper)network. Thus, graphlet adjacency captures the topological complexity of a node by accounting for both its direct edges and the local connectivity patterns of its neighbors; this higher-order information is vital for accurate community detection. Our results demonstrate that graphlet-based weighting significantly enhances community detection in networks. We find that no single "universal" motif optimizes performance across all real-world networks. Rather than favoring only dense, clique-based structures, our findings highlight that simpler motifs can also provide strong performance in networks. These results suggest that relying exclusively on cliques may overlook critical connectivity patterns, offering a new perspective on how higher-order structures define communities in networks.
Anastasiia Dziuba, Jure Pražnikar· Journal of Intelligence and...· 0 citations
Identifying influential nodes in complex networks is a fundamental challenge with broad applications in areas such as social network analysis, communication infrastructure, transportation systems, and information networks. Existing ranking methods typically rely on combinations of structural features-such as degree, k-shell index, and neighborhood connectivity-to estimate a node's importance. However, many of these approaches suffer from key limitations, including insufficient accuracy, low resolution in distinguishing nodes with similar influence, dependence on tunable parameters, and high computational complexity, which restrict their practicality in large-scale or real-world networks. This study introduces a new ranking framework that integrates a quasi-Laplacian structural measure with a gravity-inspired aggregation process. The core idea is to construct a strengthened representation of each node's structural role using only simple yet informative attributes-namely degree and k-shell index-and then evaluate its local influence through a short-range interaction mechanism. The proposed approach is designed to be free of tunable parameters, interpretable, and computationally efficient, requiring only a small fixed gravity radius (R=3), which makes it suitable for large and diverse networks. Experiments conducted on nine real-world networks and compared against eight state-of-the-art methods demonstrate that the proposed framework consistently outperforms existing techniques in terms of accuracy, resolution, and computational simplicity. These results highlight the effectiveness of the gravity-quasi-Laplacian paradigm as a reliable and scalable tool for identifying influential nodes in complex networks.