Typically, past works on urban mobility have leveraged origin–destination analysis to capture where people travel, often leaving the sequence and structure of their trips unaddressed, thereby limiting the diagnosis of accessibility inequalities. We address this gap by integrating process mining and network science, applying both frameworks to Call Detail Records (CDRs) from the Lisbon Metropolitan Area. From 2.7 million reconstructed trips, we construct case-centric event logs and discover Directly-Follows Graphs (DFGs) for morning commuting in each of the 18 municipalities. We represent these DFGs as weighted directed networks and compare them using eight complementary metrics, including degree-distribution Wasserstein distance, flow correlation, Jensen–Shannon divergence, and a composite complexity index. This reveals systematic structural heterogeneity that aggregated OD analysis cannot detect. Lisbon city emerges as a structural outlier, with the highest modal diversity and most complex DFG topology, whereas most peripheral municipalities are dominated by private car use. Geographic proximity does not guarantee temporal accessibility: median commutes between neighbouring municipalities such as Sintra and Cascais exceed 25 min, indicating infrastructure gaps. Municipalities cluster into spatially coherent groups defined by shared mobility process structures−a northern suburban cluster, a southern Tagus cluster, and an outlying Lisbon cluster−patterns that are consistent across structural and temporal metrics. Inferred commuting patterns align strongly with 2021 Census data (Pearson r = 0.94, Spearman ρ = 0.90), supporting the validity of the approach. We show that process mining and network science are complementary: process mining yields structured event representations and modal sequencing, while network science offers robust tools for structural comparison. However, DFG structures represent only mode–destination transitions, not full multimodal trip chains, a limitation to be addressed in future works.
Most financial-network studies infer links from market co-movement or observed exposures. We ask a prior measurement question: do the firms identified as central remain central when interfirm proximity is defined in different accounting spaces? Using listed firms from mainland China and Hong Kong over 2006–2023, we construct annual weighted, undirected similarity networks from year-standardized accounting ratios. The design compares a GLOBAL layer based on the full ratio vector, RISK and RETURN layers, and a family of single-ratio networks. Euclidean distances are transformed into continuous similarity weights, and weighted eigenvector centrality measures recursive prominence within each representation. The composite layers display a stable topological ordering: average density is 0.286 in GLOBAL, 0.384 in RISK, and 0.457 in RETURN. Yet cohesion and centrality concentration do not move together. GLOBAL is the least dense composite layer but has the largest top-10 centrality share (11.07
This work investigates whether early-career collaboration structures among musicians can predict long-term artistic success. Using MusicBrainz and Spotify data, we construct a large-scale collaboration network and model the generative processes underlying tie formation using Exponential Random Graph Models (ERGMs). We show that structural tendencies such as triadic closure, homophily, and productivity-driven exposure shape early collaboration, while weak ties are underrepresented relative to structural expectations. Using these insights, we engineer interpretable features and learned graph embeddings to predict long-term success, measured by Spotify follower count. Our findings demonstrate that early-network connectivity—particularly weak ties, cross-community bridging, and deviations from expected structural patterns—adds predictive signal beyond metadata baselines.
Community detection algorithms such as Louvain frequently produce clusters that are internally disconnected or poorly connected, limiting their utility in downstream network analysis. The Well-Connected Clusters (WCC) and Connectivity Modifier (CM) algorithms address this by post-processing any input clustering to enforce a user-defined edge connectivity criterion through recursive minimum cut bisection. While prior work demonstrated shared-memory parallel implementations of WCC and CM in Chapel on graphs with up to two billion edges, scalability remains constrained by single-node memory capacity and by the separate subgraph-construction preprocessing pass used in the original pipeline. This paper presents distributed-memory parallel implementations of WCC and CM in both C++ with MPI and Chapel with multi-locale execution. The central contribution is an architectural redesign that integrates subgraph generation into the Leiden clustering step, eliminating the separate WCC/CM subgraph preprocessing pass. Each compute node receives only its assigned subgraph files and executes a fully independent pipeline without ever loading the full graph. Connected component computation is parallelized within each node and distributed across nodes via round-robin assignment, and memory-mapped I/O accelerates file loading throughout. Experiments on ten real-world networks spanning up to 2.1 billion edges show that the C++ distributed implementation achieves up to 65× speedup over the original baseline on graphs where both complete successfully. The Chapel distributed implementation is integrated into Arachne, an open-source graph analytics framework built on the Arkouda platform, available at https://github.com/Bears-R-Us/arkouda-njit. It achieves broader graph coverage than the C++ distributed implementations, successfully processing billion-edge configurations including Open-Alex and Open-Citations on which all C++ distributed implementations fail, while Wikipedia-Links remains unsuccessful for both implementations. On successful configurations, Chapel distributed delivers speedups up to 19.7× at CPM 0.001 and up to 55.8× at CPM 0.01 over the Chapel shared-memory reference, with one reported slowdown on Livejournal WCC at CPM 0.001. Failures on a subset of large graphs are associated with memory leaks and data races in VieCut.
Stress in the global financial system propagates through multiple channels, including interbank credit and funding, overlapping portfolios, and bank–firm exposures. Multilayer networks represent these channels as interdependent layers, enabling analysis of how shocks transmit and amplify within and across channels. Yet many studies collapse these channels into a single layer, and stress tests often examine channels in isolation, in both cases removing cross-channel feedback and understating systemic vulnerability. This can lead to inadequate capital and liquidity buffers, overly optimistic risk assessments, and poorly targeted interventions. The synthesis in this review shows how multilayer financial networks are constructed and quantifies how much single-layer proxies underestimate systemic vulnerability, distilling the evidence into a practical Map–Monitor–Test–Intervene workflow that serves researchers designing multilayer propagation studies, practitioners assessing portfolio and counterparty risks, and supervisors calibrating stress tests. We synthesise 112 studies (2015-2025) across six domains: Bank–firm Networks, Corporate Networks, Global Trade and Supply-Chain Networks, Interbank Networks, Financial Markets, and Global Systemic Risks. Reported magnitudes include up to 90% understatement of systemic risk when a single exposure layer is analysed in isolation, up to 50% of systemic risk missed when overlapping portfolios are omitted, and critical leverage thresholds overstated by 45% to 300% when cross-channel interactions are ignored. Three findings recur: layers encode distinct mechanisms, so one layer is often a poor proxy for another, with overlay aggregation hiding feedback; cross-layer coupling amplifies losses and tightens stability margins; and systemic importance depends on the state of the financial system, concentrating in a small minority of institutions that bridge multiple channels. Collapsing channels is no longer a harmless simplification when stability judgements, risk management, and policy decisions depend on how financial stress propagates.
Composite risk instruments compress multiple indicators into a single severity score. This is operationally efficient, but it obscures how risk factors are organised and how equifinal pathways generate the same total score. We propose a network-based framework to examine configuration-level heterogeneity among score-equivalent cases. Using 17,272 administrative assessments from a criminological risk instrument, we analyse item co-occurrence within narrow, overlapping score windows to hold overall severity constant. Recurrent configurations are detected via clustering based on Jaccard similarity, their stability is evaluated across windows, and their internal structures are estimated using Ising network models. Identical scores map onto distinct and recurring network architectures, showing that relational structure contains substantively relevant information beyond additive scoring. More broadly, the framework illustrates how network psychometrics can uncover latent structural heterogeneity in applied measurement instruments and in other administrative score-based systems.
Community detection is essential for analysing the structural organization schemes of complex networks that are encountered in social, biological, and communication systems. Five prominent community detection techniques, namely, the random node head technique (RNHT), the highest-degree node head technique (HDNHT), the Louvain community detection technique, the max–min technique, and the newly proposed degree–distance centroid community detection technique, were compared in this study. The DDC–CD approach uniquely combines the node degree and shortest-path distance metrics to select optimal centroids, thereby promoting the formation of balanced, well-separated community structures. Experiments were carried out on four real-world datasets—Facebook, Power-Grid, Wiki-Vote, and Gnutella—using three key evaluation metrics: the average fitness value, modularity, and runtime. The DDC–CD method consistently produced the lowest average fitness values (0.240 for Facebook, 0.340 for Power-Grid, 0.190 for Wiki-Vote, and 0.280 for Gnutella), reflecting minimal intercommunity connectivity. It also achieved higher modularity values for most datasets (0.531 for Facebook, 0.731 for Power-Grid, 0.141 for Wiki-Vote, and 0.227 for Gnutella), indicating the superior structural quality of its identified communities. While the runtime of DDC–CD was marginally higher than those of the RNHT and HDNHT, it remained computationally efficient and offered a more balanced trade-off relative to those of the max–min and Louvain techniques. In summary, the degree–distance centroid community detection technique surpassed the existing methods by generating compact, cohesive, and well-defined communities, demonstrating improved accuracy and stability.
Average consensus (AC) strategies have played a key role in every system that employs cooperation by means of distributed computations. To promote consensus, an N-agent network can repeatedly combine certain node estimates until their mean value is reached. Such algorithms are commonly formulated as (global) recursive matrix–vector products of size N, where consensus can be attained either asymptotically or in finite time. In this paper, we revisit some existing approaches in these directions and propose new iterative and exact extensions to the problem. This is carried out by interplaying with standalone conterparts, while underpinned by the so-called eigenstep method of finite-time convergence, which we generalize to directed graphs with arbitrary combination matrices. Also, by formulating the AC from a linearly-constrained problem, we compute the solution via an exact algorithm that requires as little as 𝒪(N) additions in overall complexity. For undirected graphs, the latter compares favorably to existing schemes that require 𝒪(KN^2) multiplications to deliver the AC, where K refers to the number of distinct eigenvalues of the underlying graph Laplacian matrix.
Abstract Research on voting behavior in the European Parliament (EP) has long shown that legislative alignments are structured by multiple ideological dimensions whose salience varies across policy areas and political contexts. Building on this literature, this study maps coalition structures in the EP’s 9th term (2019–2024) using a co-voting network backbone approach applied to roll-call vote data. By extracting statistically significant co-support relationships among Members of the European Parliament (MEPs), we identify how coalition configurations realign across major policy areas and cannot be reduced to a single left–right divide. The results reveal pronounced issue-dependent coalition patterns: larger and governing groups, including EPP and S&D, exhibit fragmented coalition behavior, aligning with different partners depending on the policy domain. Votes on the institutional development of the Union highlight a pro- and anti-European integration dimension that cuts across traditional ideological alignments without fully replacing them. Despite facing unprecedented challenges—including Brexit, the COVID-19 pandemic, Russia’s war against Ukraine, and a period of record inflation—the EP maintained its transnational character: ideological affinity and party group membership, rather than nationality, remain the primary drivers of voting alignment. Rather than revising established accounts of the EP’s ideological space, this study contributes a complementary network-based perspective that makes coalition cohesion, fragmentation, and cross-group alignment structurally and visually explicit.
Community detection is an unsupervised learning problem with many applications. In this study, we present Constrained Voting Consensus (CVC), a new ensemble clustering method that is designed to combine multiple clusterings, some of which may only cover a small portion of the network. We demonstrate that combining several dense subgraph clustering methods with standard methods within this ensemble approach produces a more accurate clustering than its constituent clustering methods. We also compare CVC to other ways of combining sets of clusterings, including the median consensus method, and show that CVC achieves higher accuracy and has better robustness. Furthermore, CVC can scale to very large networks with millions of vertices.
Abstract Despite numerous initiatives aimed at enhancing the Semantic Web and IoT interoperability, semantic interoperability continues to be a primary barrier in large-scale IoT deployments; as disparate devices, data formats, and contextual representations must exchange meaningful information. The proposed solution will address this issue by developing a unified deep learning framework for integrating representation learning, temporal reasoning, causal alignment, and distributed consensus for maintaining a consistent semantic representation of information across dynamically changing environments. Unlike existing approaches that have relied on static ontology alignments, the proposed framework continually adapts to changes in the context (e.g., device updates, new terms), to maintain a robust and scalable level of cross-system communication and knowledge transfer in process. Using multi-ontology benchmarks and real-world sensor datasets, we empirically evaluate the effectiveness of our proposed approach and demonstrate significant performance improvements in key interoperability tasks. Specifically, the proposed framework achieves a semantic alignment accuracy of 92.5% between two heterogeneous ontologies, a drift detection accuracy of 89.4% in detecting changes in temporal sensor streams, and a federated semantic agreement rate of 94.1% across distributed nodes without requiring the sharing of raw data samples. These results demonstrate strong performance in maintaining a consistent semantic representation of information over time, across differing contexts, and in accordance with privacy constraints. The federated agreement metric is a novel measure used in this paper to quantify the proportion of nodes that converge to a common semantic interpretation following iterative updates, thus providing a means for assessing the degree of semantic coherence at the system level sets. The observed performance enhancements derive from combining several mechanisms, as opposed to optimizing a single strategy. The context-aware embeddings provide accurate alignment of semantic representations at the outset, while the temporal modeling preserves the stability of the semantic representation as the meanings of the data evolve, causal mapping provides a mechanism for transferring knowledge across environments, and the decentralized learning mechanisms support scalability in distributed IoT deployments. Collectively, these mechanisms provide a coherent semantic layer upon which reliable reasoning and decision-making processes can operate in dynamic IoT environments.
In this study, we consider the classical susceptible–infectious–susceptible (SIS) model on heterogeneous networks and introduce a mixture of truncated zeta (MTZ) distributions to model degree heterogeneity more flexibly. We refer to the resulting framework as the MTZ-SIS model. Based on this distributional specification, we formulate a corresponding SIS model under the heterogeneous mean-field (HMF) approximation and use analytical moment properties of the MTZ distribution to investigate the associated epidemic threshold. As with standard HMF approaches, the framework is exact only for locally tree-like networks and should otherwise be interpreted as an approximation. To enable inference from empirical network data, we further develop a projection-based parameter estimation procedure combined with the L-BFGS-B optimization algorithm. The resulting method, termed Parameter Expansion Search, jointly estimates the power-law exponent and mixture weights while accommodating structural sparsity. Numerical results demonstrate that the proposed estimation procedure achieves high accuracy and stability, and that the MTZ-SIS model provides a more flexible and realistic representation of degree heterogeneity, thereby offering a useful framework for modeling epidemic dynamics on heterogeneous networks.
The Second World War (1933–1945) was the backdrop for the most prolific looting of cultural goods in recorded history, during which Nazi officers confiscated an estimated one-fifth of all art in Europe. The present study offers the first analysis of the social networks which facilitated the movement of these looted goods during and after the war based on the provenance database Proveana. Managed by the German Lost Art Foundation, Proveana holds records on individuals, events, collections, and organisations, and visualises the immediate relationship networks around each entity. This study has extracted these data, reconstructed all relationships contained in the database, and conducted social network analysis (SNA) on the resulting network. Findings from SNA indicate that the network is moderately efficient, with easy and quick interactions despite its large size. A single component comprises 94
The dynamic nature of user preferences poses significant challenges for recommender systems, necessitating models that can effectively capture both short-term fluctuations and long-term behavioral patterns. Traditional graph-based approaches and existing time-aware models often fail to fully integrate hierarchical temporal dependencies, leading to suboptimal recommendation performance. In this paper, we propose a novel Hierarchical Time-aware Graph Neural Network (HTGNN) framework that incorporates multi-scale temporal dynamics to enhance recommendation accuracy. HTGNN constructs a hierarchical representation of user-item interactions over time, enabling it to model evolving preferences with greater granularity. Our experimental results across multiple benchmark datasets demonstrate that HTGNN consistently outperforms state-of-the-art models, achieving superior ranking quality and user satisfaction. These findings underscore the effectiveness of HTGNN in advancing personalized recommendation systems by bridging the gap between temporal modeling and hierarchical learning.
In dynamic social networks, the frequent changes in nodes and links pose significant challenges for community detection. Traditional community detection methods encounter with issues such as random behavior, high time complexity, or low efficiency across time steps. This paper presents a novel framework, called DyGraphSage, which integrates an enhanced GraphSage model with a Temporal GRU to identify community structures. DyGraphSage begins by defining both conventional and newly introduced structural features and employing GraphSage embeddings to learn network representations and detect communities in the initial snapshot. To address temporal evolution, two strategies are proposed for updating node labels in subsequent time steps. Primarily, a new semi-supervised method is introduced to efficiently update labels when only minor structural changes occur between consecutive snapshots. Alternatively, when substantial modifications are detected, the model retrains itself using an adaptive thresholding mechanism. A new efficient equation is proposed to compute the threshold (θ) dynamically, based on node structures and their connections across previous and current network snapshots. This process allows the model to manage community updates using adjusted weights and biases, eliminating the need for reinitialization. Experimental results demonstrate that DyGraphSage outperforms several state-of-the-art dynamic community detection algorithms, particularly in terms of NMI and ARI metrics.
Network alignment seeks to identify corresponding nodes across graphs, a task that is challenging when structural signals are weak or noisy. Existing optimization-based methods offer strong accuracy but do not scale well, while embedding-based methods are efficient yet often less precise. We propose SST-Align, a hybrid alignment framework that combines the strengths of both paradigms: a topology-driven initialization followed by self-supervised representation learning. Across six real-world datasets, SST-Align achieves competitive or superior node-mapping accuracy compared to strong graph alignment baselines. Under increasing structural noise, SST-Align remains robust and typically matches the performance of non-pretrained methods. We further demonstrate that SST-Align generalizes to heterogeneous networks through a simple extension incorporating node-type awareness.
Homophily has recently been studied in higher-order networks such as hypergraphs, yet existing measures are mostly limited to static settings and do not address cases in which node categories vary over time. In many real-world applications, nodes have basic categories, while their relevance to group interactions may change with time-varying activation levels, suggesting the need to treat categories in a temporal manner. In this paper, by naturally extending homophily indices developed for static hypergraphs, we propose an analytical framework for measuring higher-order homophily in temporal hypergraphs with time-varying node categories. The proposed method enables the quantification of higher-order homophily for individual categories and further for category pairs in a unified manner. We first conduct experiments on synthetic temporal hypergraphs where categories are associated with fluctuating activation levels. These experiments highlight differences between higher-order homophily patterns evaluated under the proposed framework and those evaluated on the aggregated static hypergraph, revealing situations in which conventional static indices may overlook important time-dependent characteristics. We then apply the framework to real-world hypergraphs derived from collective human activities observed in social media, demonstrating that explicitly accounting for temporal variations in node categories reveals higher-order homophily patterns that remain hidden in conventional static approaches.
This paper introduces a control-theoretic framework for graph sparsification aimed at constructing sparse subgraphs that retain the learning capacity of the original graph, reducing structural complexity while maintaining downstream performance. We refer to these sparse graphs as learning backbones. Our approach leverages the zero-forcing (ZF) phenomenon, a dynamic process on graphs with applications in networked system control, to construct a tree that retains key dynamical properties. By exploiting the hypothesized relationship between these properties and the attributes required for effective graph-based learning, we generate the desired learning backbones. We evaluate the proposed approach on graph classification benchmarks across nine datasets and six baseline models, showing that the proposed sparsification strategy substantially reduces edge density while largely preserving classification performance, and in certain cases exhibits robustness in noisy settings. Additionally, we extend the learning backbone framework by incorporating node distance metrics as a complementary control-based sparsification strategy. Finally, we analyze the impact of edge sparsification by progressively removing edges until reaching the ZF-based learning backbone and employ the network usable information (NUI) metric to assess the learning process across varying edge densities.
The response of a network to connectivity disruption is central to understanding its robustness. While such questions have been thoroughly studied in terms of global cohesion, many questions remain open regarding the impact on local connectivity. Specifically, networks with different topologies display different distributions of small motifs, and it remains unclear how local connectivity patterns link to structural weaknesses within a network. This study presents a principled approach for assessing random connectivity disruptions among the nodes of a network to identify its structural vulnerabilities. Leveraging recent findings on random walks for exact local topology recollection, we introduce a method for quantifying changes within the (l)-hop neighborhood of the nodes. We derive vulnerability profiles for the nodes and introduce a new index that aggregates neighboring nodes’ vulnerabilities in a distance dependent weighting. Our conducted experiments show that structural weaknesses of a network are distributed across localized regions, where vulnerabilities are most likely driven by immediate neighborhoods of the nodes.
This study experimentally analyzes how the design of preprocessing structures for network traffic data influences the explanation quality of artificial intelligence models. Unlike previous studies that focused on improving detection accuracy or architectural complexity, this work demonstrates that even under identical training conditions, differences in input preprocessing strategies can lead to significant variations in model explainability. To this end, four preprocessing-based input structures were compared: (1) tabular inputs based on session features, (2) payload-only inputs using unstructured text, (3) a simple hybrid combination of tabular and payload inputs, and (4) a rule-based natural language structure that integrates rule-transformed tabular features with payload data. All models were trained on the same dataset under identical configurations, with detection performance evaluated using AUROC and F1-score, and explanation quality assessed through Comprehensiveness, Sufficiency, and Deletion–Insertion AUC. Experimental results show that detection performance remained similar across all four structures, but the rule-based model consistently achieved the highest explanation quality across all metrics. In particular, Integrated Gradients analysis revealed the formation of clear semantic cross-references between indicator expressions in the rule sentences and attack cues in the payload, indicating that the model effectively learned to integrate behavioral context and content evidence. These findings demonstrate that the design of network preprocessing structures is a key factor determining model interpretability and explanation fidelity, and emphasize the importance of data representation–oriented approaches for advancing toward explainable and trustworthy security AI systems.
