Language-encoded network topology enables large language models to reason about complex networks

Networks describe systems in biology and beyond, from protein interactions and social relationships to power grids and citation records. Reasoning about such systems requires understanding their structure: which elements are central, which connections bridge separate communities, and how it changes when elements are removed. Although large language models (LLMs) excel at natural language, they struggle with such questions when networks are given as edge lists, sentences or measurement tables, because their structural meaning must be inferred. Here we introduce BioGlyph, which compiles network topology into an interpretable and transferable language of structural roles. BioGlyph combines graph partitioning and structural measurements to identify roles such as hubs, community cores and cross-community connectors, and fixed rules to translate them into a universal vocabulary. The representation describes each element through its structural role, supporting evidence and semantic consequences, leaving both the network and the LLM unchanged. Across twenty networks spanning five domains, BioGlyph substantially improves open LLMs' ability to answer structural reasoning questions, outperforming edge-based, numerical and learned representations by up to 26 percentage points in system accuracy. Ablations show that the gain comes from explicitly encoding structural roles in semantically interpretable terms. The gain is more prominent in dense, community-structured networks and diminishes in sparse networks whose topology is more readily inferred from text. In a budding-yeast protein-interaction network, BioGlyph exposes biological organization: cross-community connectors are enriched for essential genes, whereas peripheral proteins are depleted. BioGlyph thus provides an interpretable representation for both language models and scientists to reason about network structure.

Photonic reservoir computing with complex networks

Photonic reservoir computing has attracted increasing attention as a fast and low-cost approach for time-series prediction. Photonic reservoir computing utilizes the high speed, broad bandwidth, and spatial parallelism of light. However, the effect of the internal connection structure (network topology) on the computing performance has not been investigated for large-scale photonic reservoirs. In this study, we experimentally and numerically demonstrate photonic reservoir computing using a spatial light modulator to systematically evaluate the relationship between the network topology and the performance of reservoir computing. We introduce complex network structures such as small-world and scale-free network topologies of the internal nodes in the reservoir. We perform the memory capacity measurement and the one-step-ahead prediction task of the chaotic time series to compare the performance. We found that the small-world network exhibits the maximum memory capacity and the best prediction performance. Our numerical calculations reveal that the performance of the time-series prediction can be optimized by changing the rewiring probability of the network and the leak rate of the reservoir. We also implement photonic human brain network as a reservoir, which is designed by the connectomes of human brain activities. We found that the network topology strongly affects the performance of reservoir computing, and the small-world network structure outperforms the other configurations.

Spectral Dynamics of Semantic Drift in Clinical Multi-Agent Language Model Networks

The integration of iterative LLMs within multi-agent diagnostic frameworks requires a rigorous quantitative reevaluation of underlying communication topologies. Frequently used architectural paradigms depend on scale-free or small-world networks, assuming optimal communication efficiency. Our study mathematically dismantles that assumption for semantic data. By mapping multi-agent communication uncertainty trajectories onto a 768-dimensional Bio_ClinicalBERT embedding space via an analytical isotropic variance proxy using Barab'asi--Albert (BA) and Watts--Strogatz (WS) networks, we prove that structural bottlenecks compromise diagnostic safety. Our phase transition matrices illustrate that localized dense cliques confine hallucinated data, preventing global consensus and forcing the system toward a permanent entropy saturation threshold of $H_{\infty} \approx 5.947$. As a result, we measure a severe terminal cosine similarity degradation of 53.29%, completely overwriting the original ground-truth. Moreover, the terminal semantic drift reveals a catastrophic variance amplification of 51.81% ($ρ= 1.5181$) in highly clustered architectures, proving total system unpredictability when compared to Erdős--R'enyi configurations ($ρ= 1.0766$). Instead of reducing errors, hub-centric systems autonomously compound localized hallucinations. By introducing dynamic spectral monitoring operating at an $\mathcal{O}(N^3)$ time complexity and imposing a strict lower bound on algebraic connectivity ($λ_{2_{min}}$) via the continuous eigen-decomposition of the graph Laplacian, we present a mathematically rigorous technique to ensure global state diffusion. Securing the reliability of autonomous medical diagnostics necessitates treating topological stability as a non-negotiable quantitative imperative.

An LLM-Based Framework for Intent-Driven Network Topology Design

Designing deployable and resilient network topologies from natural language requirements remains a challenging problem in network automation. This work investigates the ability of Large Language Models (LLMs) to generate structurally valid and constraint-compliant network topologies through a constraint-driven pipeline combining hierarchical modeling and systematic validation. The framework is evaluated via a multimodel comparison of proprietary and open-weight LLMs across four realistic network scenarios released as a public dataset. We assess structural correctness using node and edge F1-scores against reference topologies, and evaluate resilience through server and content connectivity metrics. In addition, we analyze common failure modes, including interface mismatches and directional inconsistencies in generated topologies. Overall, this work provides a systematic benchmark for understanding how LLMs handle structural and resilience constraints in topology synthesis, and supports informed model selection for AI-driven network design.

Contagion Networks: Evaluator Preference Propagation in Multi-Agent LLM Systems

When large language models serve as evaluators in multi-agent systems, their strategy preferences -- whether induced by explicit prompts or by shared architectural priors -- propagate through the agent network. We introduce Contagion Networks, a formal framework for measuring how evaluator preferences spread across interacting LLM agents. In a controlled 3-agent experiment using DeepSeek-chat with three distinct evaluator preference profiles (structured, balanced, evidence-based), we measure the Cross-Agent Contagion Matrix Gamma_3 and find that preferences consistently propagate between agents (gamma in [0.157, 0.352]). A neutral-prompt control experiment reveals a counter-intuitive result: shared architectural priors dominate explicit preference prompts as the driver of contagion (rho_neutral = 1.498 vs. rho_mixed = 1.299; prompt contribution: -63.5%). We identify three propagation regimes governed by the spectral radius rho(Gamma_N) and demonstrate that the same agents suppress preference contagion in chain topology (beta_3 = 0.0126 +/- 0.0038, 95% CI [0.0089, 0.0163], n=4 seeds) but cascade in fully-connected topology (Delta H_avg = -0.020) -- a topology-dependent regime transition validated both for homogeneous and cross-model agent pools (rho^cross = 1.296 +/- 0.016, n=4). We show that increasing evaluator committee size from k=1 to k=3 reduces effective contagion by 68.9% +/- 14.1% (n=4 seeds), providing an actionable mitigation strategy. We release the open-source Contagion Network experimental framework.

Improved Convergence Analysis of Topology Dependence in Decentralized SGD

Decentralized SGD is a fundamental algorithm in decentralized learning, although the influence of an underlying network topology on its convergence behavior is not yet fully understood. Existing convergence analyses have shown that topologies with a small spectral gap significantly deteriorate the convergence rate of Decentralized SGD in both homogeneous and heterogeneous cases. However, many prior papers have reported that indeed the choice of the topology has a significant experimental impact in the heterogeneous case, but has little experimental impact on training behavior in the homogeneous case. In this paper, we present a tighter convergence analysis of Decentralized SGD, offering a more precise understanding of how topologies affect the convergence rate than the prior analysis. Specifically, unlike existing convergence analyses that used only the spectral gap as a property of the topology, our novel analysis shows that all eigenvalues of the mixing matrix affect the convergence rate. Throughout the experiments, we carefully evaluated the convergence behavior of Decentralized SGD and demonstrated that our novel convergence analysis can more accurately describe the effect of topology on the convergence rate.

Exploring the Topology and Memory of Consensus: How LLM Agents Agree, Fragment, or Settle When Forming Conventions

How much should an LLM agent remember, and how should multi-agent systems be connected when trying to reach consensus? We show these two design choices interact in a way that flips the sign of memory's effect on coordination. Across 432 simulation runs of a networked Naming Game on eight fixed 16-agent topologies, we vary memory depth and network structure. Longer memory slows the time to reach steady state in decentralized networks but accelerates it in centralized ones; the same parameter pushes the system in opposite directions depending on topology. Critically, "faster settling" in centralized networks means locking in to a fragmented plateau more quickly, not reaching system-wide consensus, which can be used to generate diverging opinions. We further document a memory-mediated speed-unity trade-off: centralized networks consistently preserve more competing conventions than decentralized networks, but their settling speed depends sharply on memory. At the agent level, within-network analyses show that high-betweenness bridges suffer a brokerage penalty while agents in locally clustered neighborhoods achieve higher coordination success. Finally, in search of analytically tractable generative mechanisms, we find that agents' choices are well captured by Fictitious Play, indicating belief-based rather than reward-based adaptation. The practical implication: memory depth and communication topology should be co-designed, not optimized in isolation.