With the rapid advancement of generative models, general-purpose generation has gained increasing attention as a promising approach to unify diverse tasks across modalities within a single system. Despite this progress, existing open-source frameworks often remain fragile and struggle to support complex real-world applications due to the lack of structured workflow planning and execution-level feedback. To address these limitations, we present ComfyMind, a collaborative AI system designed to enable robust and scalable general-purpose generation, built on the ComfyUI platform. ComfyMind introduces two core innovations: Semantic Workflow Interface (SWI) that abstracts low-level node graphs into callable functional modules described in natural language, enabling high-level composition and reducing structural errors; Search Tree Planning mechanism with localized feedback execution, which models generation as a hierarchical decision process and allows adaptive correction at each stage. Together, these components improve the stability and flexibility of complex generative workflows. We evaluate ComfyMind on three public benchmarks: ComfyBench, GenEval, and Reason-Edit, which span generation, editing, and reasoning tasks. Results show that ComfyMind consistently outperforms existing open-source baselines and achieves performance comparable to GPT-Image-1. ComfyMind paves a promising path for the development of open-source general-purpose generative AI systems.

Abstract Reliability evaluation of interconnection networks is of significant importance to the design and maintenance of interconnection networks. The component connectivity is an important parameter for the reliability evaluation of interconnection networks and is a generalization of the traditional connectivity. The $g$-component connectivity $c\kappa _g (G)$ of a non-complete connected graph $G$ is the minimum number of vertices whose deletion results in a graph with at least $g$ components. Determining the $g$-component connectivity is still an unsolved problem in many interconnection networks. Let $Q_{n,k}$ ($1\leq k\leq n-1$) denote the $(n, k)$-enhanced hypercube. In this paper, let $n\geq 7$ and $1\leq k \leq n-5$, we determine $c\kappa _{g}(Q_{n,k}) = g(n + 1) - \frac{1}{2}g(g + 1) + 1$ for $2 \leq g \leq n$. The previous result in Zhao and Yang (2019, Conditional connectivity of folded hypercubes. Discret. Appl. Math., 257, 388–392) is extended.

Summary Suppose that G = (V(G), E(G)) is a connected graph and D(G) is the diameter of G. For two distinct vertices a1, b1 ∈ V, κ(a1, b1), defined as local connectivity of a1 and b1, is the maximum value of independent paths from a1 to b1 in G. Similarly, λ(a1, b1) is local edge connectivity of a1 and b1. For some t ∈ [1, D(G)], ∀ a1, b1 ∈ V, a1 is distinct to b1, and distance of a1 and b1 is d(a1, b1) = t, if κ(a1, b1) or (λ(a1, b1)) = min {d(a1), d(b1)}, then G is called t‐distance optimally (edge) connected. For all integers 0 < k ≤ t, if G is k‐distance optimally connected, then we call that G is t‐distance local optimally connected. Similarly, we have the definition of t‐distance local optimally edge connected graphs. The t‐distance connectivity κd(G, t) of G is urn:x-wiley:15320626:media:cpe4787:cpe4787-math-0001 The distance connectivity of G is defined as κd(G) = (κd(G, 1), κd(G, 2), …, κd(G, D(G))). Then, λd(G, t) and λd(G) can be defined similarly. Using the number of (edge) independent vi‐vj paths to replace the number 1, we generalize the adjacency matrix to the (edge) path matrix. In this research, we characterize the distance connectivity of graphs with D(G) ≤ 2, Cartesian product of k‐regular graphs, and the regular graphs. We also determine the eigenvalues of path matrix of some graphs and give some problems about distance connectivity.