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New random graph model favors sparse clique structures

By PulseAugur Editorial · [1 sources] ·

Researchers have developed a new exponential random graph model that incorporates soft clique constraints. This model assigns higher probabilities to graphs with fewer r-cliques, controlled by a positive weight parameter. The study proves that for large graphs, the model asymptotically favors partitions into r-1 parts of roughly equal size, with edge densities around 1/2 between parts and below a specified epsilon within parts. These structural properties remain consistent regardless of the weight assigned, as long as it is positive. AI

RANK_REASON Academic paper published on arXiv detailing a new mathematical model for graph theory. [lever_c_demoted from research: ic=1 ai=0.1]

Read on arXiv cs.AI →

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New random graph model favors sparse clique structures

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Academic paper published on arXiv detailing a new mathematical model for graph theory. [lever_c_demoted from research: ic=1 ai=0.1]
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COVERAGE [1]

  1. arXiv cs.AI TIER_1 English(EN) · Yasmin Tousinejad, Vera Koponen ·

    Exponential random graph models with soft clique constraints

    arXiv:2608.30869v1 Announce Type: cross Abstract: Let $r\geq3$ be fixed, and let $\mathbf{G}_n$ be the set of all simple graphs with vertex set $[n]=\{1,\ldots,n\}$. We consider an exponential random graph model which gives higher probability to $G \in \mathbf{G}_n$ than to $H \i…

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