We study the efficient generation of random graphs with a prescribed expected degree sequence, focusing on rank-1 inhomogeneous models in which vertices are assigned weights and edges are drawn independently with probabilities proportional to the product of endpoint weights. We adopt a temporal viewpoint, adding edges to the graph one at a time up to a fixed time horizon, and allowing for self-loops or duplicate edges in the first stage. Then, the simple projection of the resulting multigraph recovers exactly the simple Norros--Reittu random graph, whose expected degrees match the prescribed targets under mild conditions. Building on this representation, we develop an exact generator based on \textit{edge-arrivals} for expected-degree random graphs with running time $O(n+m)$, where $m$ is the number of generated edges, and hence proportional to the output size. This removes the typical vertex sorting used by widely-used fast generator algorithms based on \textit{edge-skipping} for rank-1 expected-degree models, which leads to a total running time of $O(n \log n + m)$. In addition, our algorithm is simpler than those in the literature, easy to implement, and very flexible, thus opening up to extensions to directed and temporal random graphs, generalization to higher-order structures, and improvements through parallelization.

翻译：我们研究了具有给定期望度序列的随机图的高效生成问题，重点关注秩-1非齐次模型，该模型中顶点被赋予权重，边以与端点权重乘积成正比的概率独立生成。采用时间视角，我们逐步向图中添加边直至固定时间范围，并在初始阶段允许自环或重复边。随后，所得多重图的简单投影恰好恢复了简单Norros-Reittu随机图，在温和条件下其期望度与预设目标一致。基于这一表示，我们开发了一种基于\textit{边到达}的精确生成器，用于期望度随机图，其运行时间为$O(n+m)$（其中$m$为生成边数），因此与输出规模成正比。这一方法省去了广泛使用的基于\textit{边跳跃}的秩-1期望度模型快速生成算法中典型的顶点排序步骤，后者总运行时间为$O(n \log n + m)$。此外，我们的算法比文献中现有方法更简洁、易于实现且极具灵活性，从而可推广至有向图和时间随机图，扩展至高阶结构，并通过并行化实现性能优化。