Why do many modern neural-network-based graph generative models fail to reproduce typical real-world network characteristics, such as high triangle density?

In sensitive applications involving relational datasets, protecting information about individual links from adversarial queries is of paramount importance. In many such settings, the available data are summarized solely through the degrees of the nodes in the network. We adopt the $β$ model, which is the prototypical statistical model adopted for this form of aggregated relational information, and study the problem of minimax-optimal parameter estimation under both local and central differential privacy constraints. We establish finite sample minimax lower bounds that characterize the precise dependence of the estimation risk on the network size and the privacy parameters, and we propose simple estimators that achieve these bounds up to constants and logarithmic factors under both local and central differential privacy frameworks. Our results provide the first comprehensive finite sample characterization of privacy utility trade offs for parameter estimation in $β$ models, addressing the classical graph case and extending the analysis to higher order hypergraph models. We further demonstrate the effectiveness of our methods through experiments on synthetic data and a real world communication network.

Community detection, or network clustering, is used to identify latent community structure in networks. Due to the scarcity of labeled ground truth in real-world networks, evaluating these algorithms poses significant challenges. To address this, researchers use synthetic network generators that produce networks with ground-truth community labels. RECCS is one such algorithm that takes a network and its clustering as input and generates a synthetic network through a modular pipeline. Each generated ground truth cluster preserves key characteristics of the corresponding input cluster, including connectivity, minimum degree, and degree sequence distribution. The output consists of a synthetically generated network, and disjoint ground truth cluster labels for all nodes. In this paper, we present two enhanced versions: RECCS+ and RECCS++. RECCS+ maintains algorithmic fidelity to the original RECCS while introducing parallelization through an orchestrator that coordinates algorithmic components across multiple processes and employs multithreading. RECCS++ builds upon this foundation with additional algorithmic optimizations to achieve further speedup. Our experimental results demonstrate that RECCS+ and RECCS++ achieve speedups of up to 49x and 139x respectively on our benchmark datasets, with RECCS++'s additional performance gains involving a modest accuracy tradeoff. With this newfound performance, RECCS++ can now scale to networks with over 100 million nodes and nearly 2 billion edges.

One of the most persistent challenges in network science is the development of various synthetic graph models to support subsequent analyses. Among the most notable frameworks addressing this issue is the Artificial Benchmark for Community Detection (ABCD) model, a random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs similar to the well-known LFR model but it is faster, more interpretable, and can be investigated analytically. In this paper, we use the underlying ingredients of ABCD and introduce its variant, mABCD, thereby addressing the gap in models capable of generating multilayer networks. The uniqueness of the proposed approach lies in its flexibility at both levels of modelling: the internal structure of individual layers and the inter-layer dependencies, which together make the network a coherent structure rather than a collection of loosely coupled graphs. In addition to the conceptual description of the framework, we provide a comprehensive analysis of its efficient Julia implementation. Finally, we illustrate the applicability of mABCD to one of the most prominent problems in the area of complex systems: spreading phenomena analysis.

Why do many modern neural-network-based graph generative models fail to reproduce typical real-world network characteristics, such as high triangle density?

Why do many modern neural-network-based graph generative models fail to reproduce typical real-world network characteristics, such as high triangle density?

Graph Neural Networks (GNNs) excel in diverse tasks, yet their applications in high-stakes domains are often hampered by unreliable predictions. Although numerous uncertainty quantification methods have been proposed to address this limitation, they often lack \textit{rigorous} uncertainty estimates. This work makes the first attempt to introduce a distribution-free and model-agnostic uncertainty quantification approach to construct a predictive interval with a statistical guarantee for GNN-based link prediction. We term it as \textit{conformalized link prediction.} Our approach builds upon conformal prediction (CP), a framework that promises to construct statistically robust prediction sets or intervals. We first theoretically and empirically establish a permutation invariance condition for the application of CP in link prediction tasks, along with an exact test-time coverage. Leveraging the important structural information in graphs, we then identify a novel and crucial connection between a graph's adherence to the power law distribution and the efficiency of CP. This insight leads to the development of a simple yet effective sampling-based method to align the graph structure with a power law distribution prior to the standard CP procedure. Extensive experiments demonstrate that for conformalized link prediction, our approach achieves the desired marginal coverage while significantly improving the efficiency of CP compared to baseline methods.