Theoretical relations between basic centrality measures in real-world networks

Mikhail Tuzhilin

Home/Archive/arXiv

arXiv · 2611.01957

Theoretical relations between basic centrality measures in real-world networks

Mikhail Tuzhilin

View original source ↗Read source document ↗Export metadata ↓

Abstract

We establish new relationships among several fundamental measures of real-world networks, including the average clustering coefficient, the global clustering coefficient, the average shortest-path length and degree centrality, closeness centrality, betweenness centrality and ksi-centrality. We further develop the theory of $j$-neighborhood centrality, which encompasses degree centrality and ksi-centrality as special cases.

Explore related subjects

cs.SI math.CO

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Mikhail Tuzhilin. 2026-11-01. Theoretical relations between basic centrality measures in real-world networks. https://arxiv.org/abs/2611.01957

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

When Platforms Pay Users to Correct Misinformation: Revenue Incentives and Governance Capacity in Weibo Annotations

Crowdsourced misinformation governance systems such as Community Notes and Weibo Annotations depend on sustained corrective labor. How monetary incentives shape participation and subsequent governance outcomes remains poorly understood. We conduct a mixed-methods study of Weibo Annotations, analyzing 102,994 posts and 431,407 comments from 2023--2026, alongside interviews with 15 contributors. We find concentrated corrective labor, limited observed display, and weak quality--engagement alignment. Policy introduction was associated with sharp increases in contributor participation and annotation production. Model-assisted quality followed its expected trajectory, evidence for additional display growth was inconclusive, and engagement per annotation fell below expectation. Public discussions and interviews reveal substantial verification demands, difficult-to-interpret review processes, uneven platform knowledge, and gaps in contributor protection. We identify four recurring bottlenecks in governance orchestration: participation, review, reach, and protection. Effective incentive design therefore depends on whether platforms can support these downstream processes as corrective labor expands.

cs.SI↗

arXiv2026

BaCon: Band-Concentrated Exponential Random Graph Models

Exponential-family random graph models ERGMs provide a parametric interpretable framework for modeling real graphs including the Web and social networks Fitted ERGMs may suffer from degeneracy matching observed graph statistics in expectation does not guarantee that the observed graph and similar ones are highly probable under the fitted distribution We introduce Band-Concentrated ERGMs BaCon a framework that avoids degeneracy by imposing a probabilistic constraint requiring at least $1-δ$ of the distribution probability mass to lie on the set of graphs with statistics within an $\varepsilon$-tolerance band around the observed statistics BaCons maximumentropy distribution still belongs to the exponential family while including a factor checking for inclusion in the tolerance band We derive the exact Metropolis-Hastings acceptance rule for this target and use a practical stochastic approximation procedure with a smoothed band membership during fitting Experiments on social networks across increasingly challenging model specifications show that BaCon substantially increases the probability mass assigned to graphs whose statistics are close to the observed ones while remaining estimable for specifications where standard ERGM estimation fails These results demonstrate that probability mass constraints are a principled way to mitigate degeneracy while retaining the benefits of exponential-family graph models

cs.SI↗

arXiv2026

Community detection in complex networks via node similarity, graph representation learning, and hierarchical clustering

Community detection is a significant challenge in analysing real graphs, including social, citation, biological, and many other networks. This article proposes three new, general, hierarchical frameworks to deal with this task. The introduced approach supports various linkage-based clustering algorithms, vertex proximity matrices, and graph representation learning models. We compare 364 module combinations on Stochastic Block Model graphs and real-life datasets. We observe that our best pipelines (Wasserman-Faust and the mutual information-based PPMI proximity, as well as the deep learning-based DNGR representations) perform competitively with the state-of-the-art Leiden and Louvain algorithms. At the same time, unlike the latter, they remain hierarchical. Thus, they output a series of nested partitions of all possible cardinalities which are compatible with each other. This feature is crucial when the number of correct partitions is unknown in advance, and we show that it is obtained at near-zero practical cost in terms of partition quality. On graphs composed of many small communities, our pipelines are more accurate than the reference solutions. Nevertheless, the downside of our approach is its time complexity, which confines the framework to networks of some 10000 vertices on personal machines.

cs.SI↗