BioGlyph · Language-encoded network topology for large language models

70.6% vs 50.7%reading named roles, against the same two 8B models shown no network at all · 1,239 questions, eight networks

41.7% vs 0.3%share of prompts too long to reach the model — the measurement table against the compiled description. This is why the table scores 39.5%, below the blind floor

66.8% vs 61.4%description against table on the questions both were short enough to answer · 2,274 paired

Watch · narrated explainer

See a network become a sentence.

One minute and forty-eight seconds through the whole compiler: the region it retrieves, the quantities it measures exactly, the rules that name each role, and the comparison against the same measurements printed as a table.

Video 1 How BioGlyph compiles a region. A narrated, captioned animation follows one 45-node region through retrieval, exact measurement, role assignment, and the evidence and removal-consequence each role carries. Accuracy and essentiality figures are those reported in the manuscript. The narration is synthesized speech.

The idea

Do the measurement exactly. Then say what it means.

Existing methods hand a model an edge list, the same edges as sentences, or a table of centrality measurements, and leave it to work out what any of that implies. BioGlyph does the arithmetic with classical algorithms, which are exact, and spends the language on the part language is good at: naming the role and stating its consequence.

Measure

Degree, betweenness, PageRank, k-core, articulation points, bridges and Leiden communities, computed on the retrieved region with a fixed seed. Same graph in, same numbers out.

Name

One fixed rule per role. A node above the degree threshold is a HUB; a node whose removal splits its component is a CUT_NODE. No model decides this, so the vocabulary is auditable and reproducible.

State the consequence

Every role carries the measurements that triggered it and what removing that part would do. Ablations show both halves earn their place. On the yeast interactome, adding the consequence clause raises accuracy from 68.8% to 82.7% on the questions every ablation could read; and replacing the role names with meaningless tokens, holding the role assignments fixed, drops accuracy over all questions from 66.8% to 51.1%.

Panel a: a 31-node network in five communities with hub, cut node, bridge, community core, cross-community connector and bottleneck link marked. Panel b: the compiler runs classical algorithms, then one fixed rule per role. Panel c: the resulting readable description, and a frozen model answering from it. — **Figure 1** **What the compiler does.** Figure 1 of the manuscript. a, an illustrative network: node A is a hub, and removing node B splits the region into three. The dashed outline is a fragile community held on by a single link. b, classical algorithms run on the region, then one fixed rule assigns each of eleven roles — deterministic for a given seed, and using topology alone, with no node labels or biological annotations. c, the description that comes out, and a frozen model answering from it. The answer is then checked against the exact algorithm.

What BioGlyph writes Named roles, each with its evidence and its perturbation implication · five lines answer the question

BioGlyph map (named structural roles); communities: 6
Completeness: every articulation point of this region is
listed below as CUT_NODE and every bridge as BRIDGE_EDGE.

NODE 2553 = HUB
  [degree=19, mean_degree=3.16, threshold=9.15]
  -> high-degree node; removing it drops many direct
     connections, but it does not split its component
     unless it is also a CUT_NODE

NODE 2553 = CUT_NODE
  [components_before=1, components_after=6]
  -> articulation point, the only kind of node whose
     removal splits its own connected component; it
     breaks into the number of pieces shown

NODE 2553 = CROSS_COMMUNITY_CONNECTOR
  [communities=[0,1,2,3,4,5], betweenness=0.839147]
  -> lies on many inter-community shortest paths;
     removing it reroutes or lengthens cross-community
     traffic but does not disconnect the communities
     unless it is also a CUT_NODE

five roles for this one nodethe answer is stated

What a measurement table writes Identical numbers, no threshold applied and no consequence stated · 45 rows before the answer

Structural measurements for this region, every quantity
the analysis computes, printed for every node, edge and
community with no threshold applied.

PER-NODE
node degree norm_deg betweenness pagerank core community
     intra_deg cross_deg participation touched size
     articulation components_if_removed

2529   4  0.0909  0.010571  0.026903  3  3  3  1
       0.3750  2  45  no   1
2544   1  0.0227  0.000000  0.009118  1  0  1  0
       0.0000  1  45  no   1
2553  19  0.4318  0.839147  0.119518  3  0  8  11
       0.7368  6  45  yes  6
2554   4  0.0909  0.019027  0.028794  2  2  3  1
       0.3750  2  45  no   1
...  and 41 more rows, then every edge, then every
     community

fourteen columns per nodethe answer must be inferred

Both panes are real compiler output for the same 45-node region of the western US power grid, retrieved for the question is node 2553 an articulation point? Excerpted and wrapped to fit this page; nothing is reworded. The table is not a weaker input in principle, because it holds every number the compiler read. It is a weaker input in practice: the model has to find the right column, apply the right threshold, and know what crossing it implies, before it can answer. This particular region is an illustration and not a score. The power grid is sparse, its regions stay short, and it is one of the networks where the table reads perfectly well — 69.4% against BioGlyph’s 64.7%, with nothing overflowing. The benchmark numbers on this page come from the eight denser networks listed below.

Explore · six real regions

Remove a node and watch the region come apart.

These are six of the retrieved regions the paper reports, with the descriptions the model actually read and the answers it actually gave. Removing the node is not a simulation: the component each node lands in was computed by the graph algorithm, so the picture is the exact answer.

Loading six regions…

Figure 2 One region, four renderings. Node positions, edges and post-removal components come from the manuscript's own figure data. The meters show each rendering's prompt length against the 24,576-token limit the paper used; a rendering over that limit never reached the model and was scored wrong. Pick a rendering to read the text the model was given.

Conversation · ten stored threads

Compile the region once. Then keep asking.

A description is sent with the first question and never again. Everything after that is conversation: follow-ups, a lookup, an explanation, and finally a push-back that tells the model its earlier answer was wrong. Across 719 threads and 11,504 turns, accuracy does not decay along a thread — turns five to eight score 78.7% against 71.8% for turns one to four. Pick a thread and walk it.

Loading ten conversations…

Figure 3 One description, eight turns. Every question, reply and verdict is the stored one from the runs the paper scores; nothing is generated when you click. The verdict on each turn is the evaluator's, computed against the exact graph algorithm, never a reading of the reply. Node identities and outside annotations such as SGD essentiality sit outside the exchange — no model ever received them.

74.6%of graded turns across 719 threads and 11,504 turns

The map holds for eight turns.

Lookup turns, which ask for something the description states outright, are answered 68.6% of the time. No thread prompt went over budget, so nothing here is a length effect.

42.0%held a correct answer when told it was wrong

Push-back is where models are weakest.

Against 29.1% that abandoned a correct answer and 12.7% that corrected a wrong one. An informative representation does not cure a model's willingness to be talked out of a right answer, and the page would be dishonest to imply it does.

73.5% vs 58.7%answered as a follow-up, description against table

The second turn is the load-bearing one.

Because the region is not resent. Asked standalone, the two arms sit at 75.5% and 72.6%. Asked one turn later, the description holds and the table largely does not.

An eight-turn conversation about a 120-protein yeast region. The model identifies ACT1 as the most disruptive protein, recognizes it as a cross-community connector, and holds that answer when challenged with CBF5 instead. — **Figure 4** **One description, eight turns.** Figure 2 of the manuscript. A 120-protein region compiled once and sent with the first question only. The model names ACT1 as the most disruptive protein, citing the stated consequence that its removal leaves eight components; five turns later it recognizes ACT1 as a cross-community connector; and at turn eight it holds that answer when pushed toward CBF5 instead. Every graded turn agreed with the exact algorithm. ACT1 is annotated essential by SGD, which the model never saw.

The vocabulary

Eleven roles, each one a rule you can check.

Eight describe nodes, two describe edges, one describes a community. The compiler is label-free: it reads connections only, never node names, gene symbols or any annotation. Two roles come from exact connectivity decompositions and the rest from a fixed threshold, so the same region always compiles to the same description.

CUT_NODE

An articulation point. The only kind of node whose removal splits its own component, and the description says into how many pieces. Exact, no threshold.

BRIDGE_EDGE

A bridge: an edge whose removal disconnects the two sides. Also exact, the edge-level counterpart of a cut node.

HUB

Degree more than 2.0 standard deviations above the region's mean. Removing it drops many connections but splits nothing unless it is also a cut node.

CROSS_COMMUNITY_CONNECTOR

Node betweenness 2.0 SD above the mean, and neighbors in at least two communities. Removing it lengthens cross-community routes rather than severing them.

BOUNDARY_NODE

Participation coefficient 1.5 SD above the mean: a gateway spanning several communities' boundaries.

COMMUNITY_CORE

Intra-community degree 1.0 SD above the mean, compared within each community of at least three nodes. A module hub, not necessarily a cut point.

BOTTLENECK_LINK

Edge betweenness 2.0 SD above the mean: an edge carrying disproportionate shortest-path traffic without being a bridge.

AUTHORITY

PageRank 2.0 SD above the mean. Defined for directed networks, and so unused in the undirected networks this study reports.

PERIPHERAL

Core number at most 1, in a component with more than one node. Low embeddedness, little influence on global structure.

ISOLATE

A node whose connected component contains only itself.

FRAGILE_REGION

The one community-level role: a community whose induced subgraph has edge connectivity at most 1, evaluated for communities of 3 to 1,500 nodes.

Evidence, always attached

Every role prints the measurements that triggered it, so a reader can disagree with the compiler on its own terms.

Evidence

Same measurements, four renderings, four different scores.

Every arm below is built from the identical measurements on the identical retrieved region. Only the rendering differs. Accuracy is pooled over seven question families on the eight main networks, with two frozen 8-billion-parameter open models and no task-specific training.

Loading results…

Figure 5 Accuracy by what the model was shown, percent correct over the eight main networks. The dashed line at 50.7% is the blind floor: what these two models score with no network in the prompt at all. Read the bottom row first. Printing every measurement scores 39.5%, below that floor — not because numbers confuse the model, but because 41.7% of those prompts exceed the 24,576-token budget and are never sent to it. A prompt that never arrives is scored wrong. Edge lists, sentences and graph neural network embeddings all land within two points of the floor as well. The words themselves are worth about nine points: replacing each role name with a meaningless token, holding the role assignments and everything else fixed, takes the names rendering from 63.6% to 54.1%.

Accuracy against median prompt length for nine renderings. BioGlyph sits at 70.6 percent and about 6,200 tokens; the raw measurement table at 39.5 percent and about 19,700 tokens, below the no-network floor. — **Figure 6** **Shorter and better, not shorter instead of better.** Median prompt length against accuracy, with 95% intervals. BioGlyph sits up and to the left of the measurement table: about a third of the length, and 70.6% of questions right against the table’s 39.5%. The dotted line is the no-network floor and the shaded band is past the 24,576-token limit, where a prompt never reaches the model at all. All nine points are the pooled benchmark: 1,239 questions over eight networks, answered by Qwen3-8B and Llama-3.1-8B.

What “never reached the model” looks like

Loading the paired conversations…

0.3%of BioGlyph prompts overflow, against 41.7% of tables

The gain is not just a shorter prompt.

A named description is more compact, so a fair reader asks whether BioGlyph simply wins by fitting. In the 60-module protein-removal screen on the Reactome network, neither the descriptions nor the raw-measurement tables exceeded the context limit, so both reached the model on every module — and BioGlyph still answered 42.5% of them within two proteins, against 1.7% from the tables.

74.1%against a supervised GNN's 74.8% on the same questions

It reaches a trained model without training.

A graph neural network trained directly on these questions scores 74.8%. A frozen model reading BioGlyph scores 74.1% on the same 381 questions, having never seen a training example, and it explains each answer in words a reader can check.

Biology

The same roles carry biological meaning, from structure alone.

The compiler never sees a gene symbol or an essentiality label. In the budding-yeast STRING network, its roles nonetheless separate essential from non-essential genes, which is a check on the vocabulary rather than a prediction task.

CROSS_COMMUNITY_CONNECTOR

OR 3.14 · 57.6%

COMMUNITY_CORE

OR 2.27 · 46.9%

HUB

OR 1.67 · 42.1%

CUT_NODE

OR 1.23 · 35.0%

BOUNDARY_NODE

OR 1.18 · 34.0%

PERIPHERAL

OR 0.27 · 12.9%

enriched for essential genes depleted not clearly apart from the background rate midline: no enrichment (odds ratio 1) background rate: 30.9% of 3,384 proteins essential

Gene essentiality by structural role, budding-yeast STRING network against SGD phenotype labels. Cross-community connectors are essential 57.6% of the time against a 30.9% background, and peripheral proteins only 12.9% of the time. Both survive Benjamini–Hochberg correction across roles; cut nodes and boundary nodes do not, and are drawn in gray for that reason. The roles were compiled from connections alone, with the essentiality labels withheld from both the compiler and the models.

The twelve Reactome proteins whose removal detaches the most others, coloured by DepMap dependency class. EP300 detaches 76, GPLD1 53, CTCF 51. — **Figure 7** **The knockout screen, ranked.** Every cut node in the Reactome main component was screened. Bars are the proteins that come away when that one is removed, computed exactly; colour is the independent DepMap dependency class, which the compiler never saw. The ranking is structural, so it does not simply recover essentiality — EP300 detaches the most while being only selectively essential, and TP53 detaches 26 while rarely scoring as a dependency.

STRING yeast, human and E. coli HuRI reference interactome Reactome functional interactions DepMap 24Q4 gene effect SGD essentiality HuDiNe disease comorbidity TCGA glioblastoma patient similarity

Networks

Twenty public networks, biological and not.

A structural vocabulary should not be tuned to one domain. The twenty networks span biology, pharmacology, medicine, social, citation, co-authorship, e-commerce and infrastructure systems, from 213 nodes to 169,343. The benchmark itself asks 1,239 questions over the eight main networks, drawn from five domains.

Network	Domain	Nodes	Edges	Cut nodes
STRING-Yeast	biology	3,384	43,030	363
ChCh-Miner	pharmacology	1,514	48,514	48
ego-Facebook	social	4,039	88,234	11
email-Eu-core	social	986	16,064	73
STRING-Human	biology	10,746	86,519	1,299
HuRI	biology	8,275	52,088	1,132
PP-Pathways	biology	21,538	338,636	1,538
HuDiNe	medicine	222	831	17
Amazon-Photo	e-commerce	7,650	119,081	151
Wiki-Vote	social	7,115	100,762	1,033
Cora	citation	2,708	5,278	389
ogbn-arxiv	citation	169,343	1,157,799	18,591
Coauthor-CS	co-authorship	18,333	81,894	1,281
Power-Grid	infrastructure	4,941	6,594	1,229

Fourteen of the twenty, all public; statistics are for the simple undirected graph and the cut-node counts are exact. The protein-removal screen runs on a further network, Reactome functional interactions: 10,022 proteins, 194,494 interactions, and 402 cut nodes in its 9,823-protein main component. Every compiled description, question set with its exact answer, stored model reply and scored result table is released with the analysis code.

Abstract

Structure, said out loud.

Networks describe diverse 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 otherwise separate communities, how the network is organized, and how its structure changes when elements are removed. Although large language models (LLMs) excel at reasoning over natural language, they often struggle with such structural questions when networks are represented as edge lists, sentences or tables of numerical measurements, because the structural meaning of these representations must be inferred.

Here we introduce BioGlyph, a method that compiles network topology into an interpretable and transferable language of structural roles. BioGlyph combines graph-partitioning algorithms and structural measurements to identify roles such as hubs, community cores and cross-community connectors, and uses fixed rules to translate their algorithmic signatures into a universal vocabulary. The resulting representation describes each network element through its structural role, supporting evidence and semantic consequences, while leaving both the original network and the LLM unchanged.

Across twenty networks spanning five different domains including biological, social and information systems, BioGlyph substantially improves the ability of open LLMs to answer structural reasoning questions, outperforming edge-based, numerical and learned representations by up to 26 percentage points in system accuracy. Ablation experiments show that the improvement comes from explicitly encoding structural roles in semantically interpretable terms by BioGlyph. The performance improvement becomes even more prominent in dense, community-structured networks and diminishes in sparse networks whose topology can be more readily inferred from direct textual representations. Applied to a budding-yeast protein-interaction network, BioGlyph also exposes biologically meaningful organization: cross-community connectors are enriched for essential genes, whereas peripheral proteins are depleted. BioGlyph thus provides a common, interpretable representation through which both language models and scientists can reason about complex network structure.

BibTeX

Cite the current manuscript.

@article{utsha2026bioglyph,
  title   = {Language-encoded network topology enables large language
             models to reason about complex networks},
  author  = {Utsha, Ucchwas Talukder and Mostafa, Sakib and Zou, James
             and Islam, Md Tauhidul},
  year    = {2026},
  note    = {Manuscript in preparation}
}

Authors

Ucchwas Talukder UtshaStanford Radiation Oncology Sakib MostafaStanford Radiation Oncology James ZouStanford Electrical Engineering, Biomedical Data Science & Computer Science Md Tauhidul Islam *Stanford Radiation Oncology · Corresponding author

Try it live

Ask a network a question.

Pick a network, choose whether the model reads the compiled description or the raw measurement table, and ask. A frozen open model answers, and an exact classical algorithm answers beside it, so you can see where the model is right and where it is not. Nothing is graded by another model. The workspace shows the full text the model read, and says so when the measurement table is too long to send at all.

Open the workspace →

The workspace also runs BioGlyph on a network of your own. That needs a lab account, so the GPU is not open to the whole internet — but the five networks here are, with no sign-in.

Read it honestly

A reasoning aid, not a replacement for the algorithm.

BioGlyph does not compete with exact graph algorithms, and should never be used where one will do. It earns its place when several structural facts must be weighed together, when the questions keep coming, and when the person asking wants an explanation or wants to disagree.

The advantage is specific to small open models. Qwen3-32B closes the controlled gap to parity, and across four hosted frontier models with ample context the compiled description led the raw-measurement table in one of twelve comparisons, matched it in four and trailed it in seven. BioGlyph stands in for a selection step that larger models increasingly perform unaided, so it is most useful for the open models you can run yourself.

Performance also depends on density. In sparse networks the retrieved region is often small enough to fit directly, and adjacency sentences or raw measurements can do just as well.

Structural enrichment is not a causal claim. That cross-community connectors are more often essential describes an association in one network against one label set; it does not establish that the position causes the essentiality.

The live workspace runs a 4-bit quantized model with a smaller context window than the study, so that it can share one GPU with the lab's other demos. Single answers there can differ from a published run, and the measurement table runs out of window sooner than it does in the paper. Read the workspace as the mechanism, not as the measurement.