arXiv subjects

Qingying Zhang

Publications and source records attributed to Qingying Zhang.

6 recordsLinked to original sources

arXiv2026

Vertex-subgraph eigenvector centrality for connected induced subgraphs

Eigenvector centrality evaluates the importance of vertices through adjacency relations, while higher-order subgraph structures provide additional information for centrality analysis. This motivates the simultaneous evaluation of vertices and subgraphs within a unified spectral framework. In this paper, we propose vertex-subgraph eigenvector centrality (VSC), which jointly determines the centralities of vertices and connected induced subgraphs of order three. The vertex centrality depends on the centralities of the subgraphs containing it and those of the other vertices in these subgraphs, whereas the subgraph centrality depends on the centralities of its constituent vertices. To distinguish induced paths P3 from triangles K3, the capacity of each subgraph is defined as its number of edges. The resulting coupled nonlinear eigenvalue equations are represented by a fourth-order symmetric nonnegative tensor. We prove that this tensor is weakly irreducible for every connected graph with at least three vertices, which guarantees the existence and uniqueness, up to scaling, of a positive Perron eigenvector. Numerical experiments on four real-world networks compare VSC with classical centrality measures and show that capacity weighting has a greater effect on subgraph rankings than on vertex rankings.

cs.SI↗

arXiv2026

Windowed and Quantized Group-Based ADMM for Distributed Optimization in Heterogeneous Edge Networks

Distributed optimization in edge networks is constrained by heterogeneous client computing capabilities and limited communication resources. We propose the Windowed and Quantized Group-Based Alternating Direction Method of Multipliers (WQ-GADMM) to coordinate group updates under limited activation capacity and reduce communication costs. Clients are grouped by estimated computation time. Each window activates a limited number of groups per round, and the cloud updates the global model after all groups have updated once. The method quantizes both downlink and uplink model exchanges to reduce communication costs and allows bounded model staleness and inexact proximal local updates. For smooth nonconvex objectives, we establish an average squared Karush-Kuhn-Tucker residual bound under the stated assumptions and parameter conditions. The bound consists of a term that decreases with the iteration count and a quantization-dependent error term. Experiments on MNIST and CIFAR-10 show that 12-bit communication reduces communication volume and simulated wall-clock time while maintaining test accuracy comparable to full precision. The 12-bit configuration also maintains complete group coverage and achieves shorter mean group inter-completion gaps than the evaluated baselines.

cs.DC↗

arXiv2026

P-GADMM: Parallel Group-Based ADMM for Asynchronous Optimization in Heterogeneous Edge Networks

The Alternating Direction Method of Multipliers (ADMM) is widely used for distributed optimization, but its synchronous implementation can suffer from efficiency loss in heterogeneous edge networks, where fast clients or groups need to wait for slower ones before global updates can be completed. Existing group-based ADMM methods reduce communication overhead through grouping, but their grouping rules usually focus on data similarity or network topology and do not explicitly account for computation heterogeneity. To address this issue, this paper proposes Parallel Group-Based ADMM (P-GADMM) for distributed optimization in heterogeneous edge networks. P-GADMM forms computation-aware edge groups according to client computational capabilities and local data sizes, which reduces training-speed variation within each group. It further combines edge-level aggregation with bounded asynchronous coordination at the cloud, allowing active groups to participate in global updates without waiting for slower groups while controlling stale group information through a delay threshold. For strongly convex group objectives, we establish convergence guarantees for an idealized form of P-GADMM under bounded group-level staleness, showing a time-averaged convergence behavior up to a staleness-induced asymptotic error neighborhood. Experiments show that P-GADMM reduces wall-clock training time compared with representative baselines while maintaining comparable final accuracy.

cs.DC↗

arXiv2026

The eigenvector centrality of hypergraphs

A hypergraph is called uniform when every hyperedge contains the same number of vertices, otherwise, it is called non-uniform. In the real world, many systems give rise to non-uniform hypergraphs, such as email networks and co-authorship networks. A uniform hypergraph has a natural one-to-one correspondence with its adjacency tensor. In 2019, Benson proposed the eigenvector centrality of uniform hypergraphs via its adjacency tensor. In this paper, we define an adjacency tensor for hypergraphs and propose the eigenvector centrality for hypergraphs. When the hypergraph is uniform, our proposed eigenvector centrality reduces to Benson's. When each edge of the uniform hypergraph contains exactly two vertices, our proposed centrality reduces to the eigenvector centrality of graphs. We conducted experiments on several real-world hypergraph datasets. The results show that, compared to traditional centrality measures, the proposed centrality measure provides a unique perspective for identifying important vertices and can also effectively identify them.

cs.SI↗

arXiv2025

Perron-Frobenius theorem for dual tensors and its applications

The Perron-Frobenius theorem of nonnegative matrices is a classical result on spectral theory of matrices, which has wide applications in many domains. In this paper, we give the Perron-Frobenius theorem for dual tensors, that is, a dual tensor with weakly irreducible nonnegative standard part has a positive dual eigenvalue with a positive dual eigenvector. We give an explicit formula for the dual part of the positive dual eigenvector by using generalized inverses of an $M$-matrix. By considering the natural correspondence between tensors (matrices) and hypergraphs (graphs), some basic properties on the positive dual eigenvalue and positive dual eigenvector of hypergraphs are obtained. As applications, we introduce dual centrality measures for vertices of graphs and hypergraphs. By introducing a dual perturbation, vertices that are tied under eigenvector centrality can be effectively distinguished. In our numerical experiments, by perturbing specific structures, we successfully differentiated vertices in regular graphs and hypergraphs that were previously indistinguishable.

math.CO↗

arXiv2024

The subgraph eigenvector centrality of graphs

Let $G$ be a connected graph and let $F$ be a connected subgraph of $G$ with a given structure. We consider that the centrality of a vertex $i$ of $G$ is determined by the centrality of other vertices in all subgraphs contain $i$ and isomorphic to $F$. In this paper we propose an $F$-subgraph tensor and an $F$-subgraph eigenvector centrality of $G$. When the graph is $F$-connected, we show that the $F$-subgraph tensor is weakly irreducible, and in this case, the $F$-subgraph eigenvector centrality exists. Specifically, when we choose $F$ to be a path $P_1$ of length $1$(or a complete graph $K_2$), the $F$-eigenvector centrality is eigenvector centrality of $G$. Furthermore, we propose the $(K_2,F)$-subgraph eigenvector centrality of $G$ and prove it always exists when $G$ is connected. Specifically, the $P_2$-subgraph eigenvector centrality and $(K_2,F)$-subgraph eigenvector centrality are studied. Some examples show that the ranking of vertices under them differs from the rankings under several classic centralities. Vertices of a regular graph have the same eigenvector centrality scores. But the $(K_2,K_3)$-subgraph eigenvector centrality can distinguish vertices in a given regular graph.

math.CO↗