Very little, if the right parts go first. Removing cell types of the male fruit fly's central nervous system in order of their output synapses halves the number of independent routes from sensory to descending and motor cell types after 4.1% of the 11,751 types are gone. Removing them at random takes 28.3% (95% CI 27.7% to 28.9%). Routes thin out long before anything disconnects, and the order that does the most damage differs between the brain and the nerve cord.
_{Dhruvin Sarkar. An independent, pre-registered analysis of public connectome data, not peer reviewed.}

Illustrated findings Six attacks Any cell type Technical report Pre-registration Poster

Abstract

HHMI Janelia and Google Research have released a complete wiring diagram of an adult male fruit fly's central nervous system, brain and nerve cord together.¹ We asked how much of it has to be removed before sensory input can no longer reach motor output, and whether the order of removal matters. Percolation on the FlyWire brain connectome has tracked its largest connected components;² here the measure is directed routing, the number of edge-disjoint paths from 368 sensory to 665 descending and motor cell types (10,647 when intact), in a graph of 11,751 types and 243,439 connections. Six removal orders were pre-registered and applied in adaptive batches.³ Removing types by output synapses halves routing after 4.1% are gone, against 28.3% at random, and routes thin out long before anything disconnects. Against 200 degree-preserving randomizations of the graph, the real wiring is significantly more fragile under all six orders (one-sided p = 0.005 each, Bonferroni-corrected threshold 0.0083).

Results

Important

These are structural results on a static, type-aggregated wiring diagram. Removing a cell type from a graph is not the same as silencing it in a fly: the graph carries no synaptic sign, no electrical synapses and no dynamics, and nothing here simulates neural activity.

Pre-specified checks

• Every targeted order degrades flow capacity and reachability faster than random removal (10 of 10 comparisons)
• Every targeted critical fraction lies below the lower bound of the random-removal 95% CI
• Fourteen behaviorally validated cell types rank above other types in sensory-motor betweenness (one-sided p = 0.045; p = 0.10 with the positive control MN9)
• For 205 of 4,449 informative bilateral types, removing both sides costs more than the sum of each side (one-sided p = 5.2 × 10⁻³⁷); 4,235 are exactly additive
• Structural cascades follow a power law (not established: plausible in the primary pooling, p = 0.202, rejected in the sensitivity pooling, p = 0.036; see where it falls short)
• The real graph is more fragile than 200 degree-preserving randomized graphs under all six orders (one-sided p = 0.005 each, threshold 0.0083; see the null model)

All headline values

	value
cell types / connections	11,751 / 243,439
sensory / descending and motor types	368 / 665
intact flow capacity / connected sensory-motor pairs	10,647 / 237,405 of 244,720
flow halves, weighted out-degree	4.1% of types removed
flow halves, random (30 trials)	28.3% (95% CI 27.7% to 28.9%)
types cut off at any half-flow point	at most 37
types cut off at 50.25% removed, sensory-motor betweenness / first random trial	5,306 / 1 of 5,846 survivors
largest single cascade	6,046 types
flow halves, strongest connections first / random connections	26.8% / 47.6% of connections
curated behavioral types, sensory-motor betweenness	one-sided p = 0.045, AUC 0.630
orders significantly more fragile than 200 degree-preserving randomizations	6 of 6 (one-sided, Bonferroni threshold 0.0083)

_{Source: results/fragility_scores.json, results/critical_thresholds.json, results/type_atlas.json, results/edge_attack.json, results/literature_validation.json, results/null_model_summary.json}

Figure 1. Every targeted order collapses routing long before random removal does. Cell types are removed in batches of 1% of those remaining, and each targeted score is recomputed on the reduced graph before the next batch, which is usually more damaging than a ranking fixed on the intact graph.⁴ Flow capacity counts edge-disjoint routes from the sensory to the descending and motor types; by max-flow min-cut duality it is also the smallest number of connections whose loss would separate them.⁵ Removing the types with the most output synapses first is the most damaging order: after 2.99% of types are gone, 59% of flow capacity is left. At 50.25% removed, random removal still keeps 22.7% of flow on average over 30 trials.

Values behind Figure 1

The fragility score is the area under the normalized curve over the first 50% of removals, divided by that range: 1 for a curve that never drops, 0 for one that falls to zero at once.⁶

order	AUC, flow	AUC, reachability	flow halves at (interpolated)	first batch below half
weighted out-degree	0.197	0.349	4.11%	4.92%
sensory-motor betweenness	0.233	0.256	9.61%	10.51%
betweenness	0.315	0.267	9.04%	9.60%
weighted in-degree	0.370	0.484	13.87%	14.07%
PageRank	0.441	0.461	18.75%	19.10%
random, 30 trials (95% CI)	0.570 (0.564 to 0.576)	0.586 (0.581 to 0.591)	28.32% (27.74% to 28.90%)	28.70% (28.11% to 29.29%)

The two metrics rank the orders differently. Weighted out-degree removes capacity fastest, while the betweenness orders disconnect sensory-motor pairs fastest, because they remove relays through which many pairs communicate.

_{Source: results/fragility_scores.json, results/critical_thresholds.md, results/percolation_curves.csv}

How early routing fails

Figure 2. Random removal needs 6.9 times as many cell types as removal by output synapses. The critical fraction is the share of types removed when flow capacity first falls below half of its intact value, interpolated between the last batch above half and the first below it. The same cutoff applies to every order. Across the 30 random trials it ranges from 25.5% to 31.3%, and every targeted value lies well below that range. A gap of this size between random and targeted removal resembles the pattern described for networks with heavy-tailed connectivity.³ Here the out-degree and out-strength tails are heavy, but a lognormal or truncated power law describes them better than a pure power law.⁷

Capacity thins before anything disconnects. At each order's own half-flow batch, at most 37 surviving types have lost every directed path from sensory input. Disconnection comes later and differs sharply between orders. Under sensory-motor betweenness no surviving type is cut off up to 10.5% removed and only 18 by 20.7%; then a single batch, from 30.5% to 31.2% removed, cuts off 6,046 types at once, when flow capacity has already fallen to 3.3% of intact. Measures based on the largest connected component, which dominate the attack-tolerance literature, would register little of the first phase.

Disconnection across the type population

Surviving cell types with no directed path from any surviving sensory type, replaying each order (targeted runs and random trial 0):

order	at its own half-flow batch (removed)	at 50.25% removed, of 5,846 survivors
weighted out-degree	23 (4.92%)	662
weighted in-degree	37 (14.07%)	257
betweenness	2 (9.60%)	520
PageRank	4 (19.10%)	35
sensory-motor betweenness	0 (10.51%)	5,306
random, trial 0	0 (28.36%)	1

_{Source: results/type_atlas.json (replay), results/percolation_curves.csv, results/avalanche_analysis.md}

Where the routing runs

Figure 3. The gnathal ganglia carry the most routing of any neuropil. Each cell type is anchored to the neuropil holding most of its synapses, and all types anchored in one neuropil are removed together, against 200 random sets of the same size. Removing the 1,237 types anchored in the gnathal ganglia (GNG) costs 34.7% of flow capacity, against 20.6% for random sets. Neuropils that hold many sensory or motor types (the GNG, the leg neuromeres, the saddle, the antennal lobes) lead, as expected when removal deletes sources and sinks, and several mushroom body lobes lose no flow at all. This analysis is exploratory: with 200 draws the smallest attainable p is 1/201, and no neuropil can pass a Bonferroni correction across 91 tests.

Values behind Figure 3

neuropil	types	sensory	descending or motor	flow lost	same-size random	p
GNG	1,237	79	294	34.7%	20.6%	0.005
LegNp(T3)(R)	389	27	10	15.4%	6.7%	0.005
ANm	584	28	77	11.4%	10.0%	0.214
SAD	319	34	33	10.6%	5.5%	0.005
LegNp(T2)(L)	456	7	10	9.9%	7.8%	0.070
LegNp(T2)(R)	131	16	8	9.8%	2.2%	0.005
Ov(L)	115	24	1	9.2%	2.0%	0.005
AL(R)	226	50	1	8.9%	3.8%	0.005
LegNp(T3)(L)	366	11	8	7.8%	6.3%	0.129
IntTct	234	8	11	7.6%	4.1%	0.015

All 91 neuropils are in results/regional_impact.csv, which GitHub shows as a searchable table.

_{Source: results/regional_impact.md}

Which classes carry it

Figure 4. Ascending neurons carry far more routing than their number predicts. For the 13 superclasses with at least 20 types, every type of the class is removed at once. Classes that contain the sensory or motor terminals lose far more than random sets of the same size, which largely restates that they hold the sources and sinks. The informative rows are the others. The 563 ascending neuron types, which are neither sources nor sinks, cost 34.7% of flow against 9.7% for random sets (p = 0.005), consistent with ascending pathways from the nerve cord to the brain carrying a large share of the routes. The 6,605 central brain intrinsic types cost less than random sets of the same size (49.3% against 82.4%), and the optic lobe and visual classes each cost less than 1%, partly because the eleven visual sensory types contribute few sources however many neurons they contain.

Values behind Figure 4

superclass	types	neurons	flow lost	same-size random	p
descending	480	1,310	66.4%	8.2%	0.005
nerve cord sensory	169	5,598	50.1%	2.9%	0.005
central brain intrinsic	6,605	31,280	49.3%	82.4%	1.000
nerve cord intrinsic	2,777	12,943	47.0%	42.9%	0.040
ascending	563	1,865	34.7%	9.7%	0.005
central brain sensory	158	4,756	32.5%	2.7%	0.005
nerve cord motor	142	699	16.6%	2.4%	0.005
sensory ascending	26	536	13.6%	0.4%	0.005
optic lobe intrinsic	271	89,358	0.6%	4.7%	1.000
central brain motor	43	106	0.4%	0.7%	0.776
visual projection	346	9,202	0.4%	5.9%	1.000
visual centrifugal	108	562	0.1%	1.8%	1.000
nerve cord efferent	27	78	0.0%	0.4%	1.000

p = (1 + k) / 201, where k is the number of same-size random sets that lose at least as much flow. Exploratory and uncorrected.

_{Source: results/structure_profile.md, results/superclass_impact.csv}

Brain and nerve cord

Figure 5. What is critical depends on the circuit. Each type was assigned to the brain or the nerve cord by where most of its synapses are, and each subgraph received its own sensory and motor sets and the full protocol. Under random removal the two do not differ significantly (Welch t = −1.54, p = 0.13). Under targeted removal they behave differently: sensory-motor betweenness is the most damaging order in the brain (AUC 0.151) and comparatively mild in the nerve cord (0.363), where weighted in-degree (0.228) and PageRank (0.251) lead. In the brain, PageRank removal (0.664) is less damaging than random removal. No direction was hypothesized, the subgraphs differ in size and density, and the targeted runs are single runs, so these describe two graphs rather than estimating an effect.

Values behind Figure 5

	brain-dominant	nerve cord-dominant
cell types / connections	8,123 / 157,374	3,628 / 66,700
sensory / descending and motor types	182 / 498	186 / 167
intact flow capacity	3,765	3,066
AUC flow, random (95% CI)	0.572 (0.564 to 0.579)	0.579 (0.573 to 0.586)
AUC flow, weighted out-degree	0.257	0.276
AUC flow, weighted in-degree	0.504	0.228
AUC flow, betweenness	0.544	0.477
AUC flow, PageRank	0.664	0.251
AUC flow, sensory-motor betweenness	0.151	0.363
flow halves, random / weighted out-degree	28.4% / 6.3%	28.8% / 9.3%
flow halves, weighted in-degree / sensory-motor betweenness	25.3% / 5.9%	6.6% / 12.6%

_{Source: results/brain_vnc_comparison.md}

Connections, not only cell types

Figure 6. Synapse count is not routing capacity. Flow capacity gives every connection one unit, so removing connections by synapse count asks whether the heaviest connections also carry the routes.⁸ Removing the strongest first halves flow after 26.8% of the 243,439 connections; random orders need 47.6% on average (47.2% to 48.0% over 5 orders); removing the weakest first never halves it within 50%. Yet weakest-first removal disconnects more sensory-motor pairs than random removal, so some pairs depend on a thin connection as their only route. A heavy connection can be redundant, and a thin one can be the only way across.

Values behind Figure 6

order	connections removed when flow halves	flow left at 49.99% removed	connected pairs left
strongest first	26.8%	18.4%	51.0%
random, 5 orders	47.6% (47.2% to 48.0%)	47.2% (trial 0)	99.2% (trial 0)
weakest first	not reached	60.1%	94.5%

This analysis was added after the pre-registration and is exploratory.

_{Source: results/edge_attack.md, results/edge_attack.csv}

A hidden bottleneck

Figure 7. Lying on many shortest routes is not the same as being indispensable. The criteria were fixed in advance: the bottom half of all types by degree and by PageRank, and the top 1% by sensory-motor betweenness. Four types qualify. The most extreme, ALIN7, is a two-neuron central brain type fed by olfactory and mechanosensory neurons that ranks 21st of 11,751. Removing it disconnects no pair and costs 9 routes, but lengthens the shortest route for 849 pairs: parallel routes exist, and they are longer. Whether flies depend on any of these types has not been tested.

Values behind Figure 7

type	superclass	degree (percentile)	PageRank percentile	sensory-motor betweenness (percentile)
ALIN7	central brain intrinsic	34 (45.7)	9.8	1,881 (99.83)
ALON3	central brain intrinsic	29 (30.0)	36.1	1,558 (99.72)
GNG354	central brain intrinsic	32 (39.5)	15.5	952 (99.28)
ANXXX264	ascending	34 (45.7)	38.8	865 (99.20)

ALIN7	value
neurons / input and output partner types	2 / 19 and 15 (median degree over all types 36)
share of sensory-to-motor shortest routes through it	0.79% of 237,405 connected pairs
flow capacity, intact / without it	10,647 / 10,638
pairs disconnected / pairs with a longer shortest route	0 / 849

Percentiles are mid-rank. ANXXX264 is one of the two types outside the sensory and motor sets whose single removal disconnects any pair.

_{Source: results/hidden_bottleneck.md, results/hidden_bottleneck_candidates.csv}

Further results

Single types are almost never indispensable. Removed alone, the most costly type is the sensory type SApp (310 of 10,647 routes). No type outside the sensory and motor sets costs more than 31 (lLN2T_b), and only two, AMMC029 and ANXXX264, disconnect any sensory-motor pair (single_removal_impacts.csv).

The two sides rarely back each other up. In a graph with one node per type and hemisphere, removing both sides of a type costs more than the mean of removing one side (4,449 informative types, one-sided Wilcoxon signed-rank p < 10⁻³²³, below the smallest positive double; log₁₀ p = −728.2 by the normal approximation) and more than the sum of the two single-side removals (p = 5.2 × 10⁻³⁷). 205 types are superadditive, 4,235 additive and 9 subadditive, and for 12 types the other side is complete structural insurance: either side alone can go without any loss. The largest gains are in sensory types (eight of the nine types at +3 routes or more), where the gain reflects substitution at the entry points into shared downstream capacity (bilateral_symmetry.md).

Pairs of sensory types share capacity. Of 31,125 pairs from a pool of 250 high-impact types, 585 lose more together than the sum of their single losses, at most +12 routes (SNppxx with SNta29), and every such pair is two sensory types. As in the bilateral analysis, this reflects substitution at the entry points into shared downstream capacity, not parallel pathways deeper in the circuit. The pool fixed in advance was dominated by sensory types, so it does not reach the interneuron pairs the search was meant to find (synthetic_lethal_pairs.md).

Agreement with behavioral experiments is modest. Fourteen cell types with published activation or silencing phenotypes, fixed before scoring, rank above other types in sensory-motor betweenness. The result is close to the threshold and weakens when the positive control is added.

Curated cell types and tests

type	behavior	sensory-motor betweenness percentile	betweenness percentile
aSP22	courtship action sequence	95.9	99.6
LPLC2	looming-evoked escape	92.3	94.4
DNp10	landing	91.1	97.9
DNp07	landing	86.8	95.3
DNa02	ipsilateral turning	85.7	98.4
LC4	looming-evoked escape	79.8	93.7
DNp01	escape takeoff	78.4	43.0
MDN	backward walking	75.1	98.9
PFL3	goal-directed steering	54.2	99.9
pIP10	courtship song	53.1	91.4
DNp09	object-directed walking	47.2	83.7
PPL101	aversive punishment signal	22.6	46.0
EPG	menotaxis	9.8	99.1
MBON11	aversive memory expression	9.8	22.3

set	score	one-sided p	AUC	median percentile
primary (14)	sensory-motor betweenness	0.045	0.630	76.8
primary (14)	single-removal flow loss	0.97	0.376	32.3
primary (14)	global betweenness	8.7 × 10⁻⁶	0.832	94.9
with the positive control MN9 (15)	sensory-motor betweenness	0.10	0.595	75.1

Mann-Whitney U tests against all other types. Percentiles are mid-rank, so 9.8 is the shared value of types that score zero.

_{Source: results/literature_validation.md}

Against published thresholds. The 4.1% threshold lies in the range reported for engineered hub-dominated networks under degree or load attack, such as the Internet at about 3% and the North American power grid, which loses up to 60% of connectivity when 4% of substations are removed, and well below the roughly 40% reported for human functional brain networks. The breakdown criteria differ, so this comparison is qualitative (network_comparison.md).

The null model

The pre-registered hypothesis, restated before any randomized graph was scored, is directional: for each removal order, the real graph's flow-capacity AUC is lower, that is more fragile, than that of degree-preserving randomized graphs under the same order. Each of 200 randomized graphs is the real type graph after 10 × |E| edge swaps that keep every type's in-degree and out-degree,⁹ with each type's outgoing synapse counts shuffled onto its new edges so that out-strength is kept too. Every randomized graph receives the full protocol, including 30 random-removal trials, and each order is tested with the one-sided empirical p-value below at a Bonferroni-corrected threshold of 0.05 / 6 = 0.0083. With 200 graphs the smallest attainable p is 1/201 = 0.005. The plan and the full results, including the secondary test on reachable pairs, are in null_model_validation.md.

Result. Under all six orders the real graph's flow-capacity AUC is significantly lower than that of its 200 randomizations (p = 0.005 each), so its fragility does not follow from the degree sequence alone. The test does not say which further features of the wiring produce it. Where no randomized graph scored at or below the real one, p is the floor of 1/201, and the z-scores in the table show how far outside the randomized range the real value lies.

order	real AUC	randomized mean ± SD	at or below real	z	p	result
random	0.570	0.575 ± 0.0005	0 / 200	−11.5	0.005	significant
weighted out-degree	0.197	0.202 ± 0.0014	0 / 200	−3.6	0.005	significant
weighted in-degree	0.370	0.593 ± 0.0099	0 / 200	−22.7	0.005	significant
betweenness	0.315	0.345 ± 0.0034	0 / 200	−8.9	0.005	significant
PageRank	0.441	0.590 ± 0.0080	0 / 200	−18.7	0.005	significant
sensory-motor betweenness	0.233	0.353 ± 0.0118	0 / 200	−10.1	0.005	significant

The secondary test on reachable pairs is significant under four of the six orders.

_{Source: results/null_model_summary.json, results/null_model_scores.csv}

Where it falls short

Caution

One pre-specified check is not met. Structural cascades were to be tested for a power law, and one is not established: the fit is plausible in the pre-registered pooling (bootstrap p = 0.202) but rejected when all 30 random trials are pooled (p = 0.036), and a lognormal cannot be distinguished in either. It is reported as it stands.

Figure 8. The cascade sizes do not settle the power-law question. After each batch, the cascade size is the number of surviving types that have just lost every path from sensory input. A discrete power law was fitted by maximum likelihood with the smallest fitted size chosen by the Kolmogorov-Smirnov distance, and tested with a semi-parametric bootstrap of 1,000 synthetic sets.⁷ The tail is dominated by a few very large events, including the single batch of 6,046 types under sensory-motor betweenness.

• Structure, not function: removing a type from the graph is not silencing it in an animal. There is no synaptic sign, no electrical synapse, no neuromodulation and no activity.
• Cell-type aggregation: a type of one neuron counts the same as a type of thousands. The eleven visual sensory types hold 6,098 neurons but contribute few sources.
• The 1% input threshold: it caps in-degree at 100 partner types and decides which weak routes exist. It was fixed in advance and no alternative was tested.
• Unit capacities: flow counts routes, not synapses. A weighted capacity would give different values.
• What the null model keeps: the randomized graphs keep every type's in-degree, out-degree and output synapse total, not its input synapse total or any structure beyond degrees. The test can show that degrees alone do not explain the fragility; it cannot show which feature of the wiring does.
• Terminal definitions: the sensory and motor sets follow neuPrint superclass annotations, and removing a region or class that holds terminals deletes sources or sinks by construction.
• Single runs: each targeted order is deterministic apart from tie-breaking and was run once.
• Exploratory analyses: the full single-type removal table, disconnection across the type population, regional and superclass removal, the structural profile, the edge attack and the published-threshold comparison were added after the pre-registration, and the p-values among them are uncorrected.
• One animal: a single male fly, at one annotation release. Individual variability and reconstruction errors are not captured.
• Review: none of this has been peer reviewed.

Cascade fits

	primary: one run per order	sensitivity: all 30 random trials
batches / zero-size / fitted	414 / 185 / 229	2,415 / 2,073 / 342
exponent α	2.011 ± 0.120	1.872 ± 0.078
smallest fitted size (sizes in tail)	8 (71)	4 (125)
KS distance	0.0607	0.0595
bootstrap p (1,000 sets)	0.202, plausible	0.036, rejected
against exponential, R (p)	+2.628 (0.009)	+2.411 (0.016)
against lognormal, R (p)	−1.007 (0.314)	−0.316 (0.752)
against truncated power law, R (p)	+0.002 (0.997)	−0.328 (0.894)

R > 0 favors the power law. The largest cascade per order in the primary runs: sensory-motor betweenness 6,046, betweenness 182, weighted out-degree 41, weighted in-degree 27, PageRank 8, random 1.

_{Source: results/avalanche_analysis.md, results/avalanche_analysis.json}

Explore the site

The live site is an illustrated version of everything above, with every removal order replayable. Each image opens the view it shows.

How fragility is measured: a small network in which you remove types yourself and watch the edge-disjoint routes find their way around.

_{Removing the busiest type, one at a time, from the small network that introduces flow capacity.}

Six attacks: all six removal orders advancing together on maps of the nervous system, one square per cell type, with removed and cut-off types drawn as they go.

_{The race between the six removal orders, from the intact graph to half of all types removed, then the fastest, weighted out-degree, picked out.}

Any cell type: every one of the 11,751 types, with its place in the body, its scores, what removing it alone costs, and when each order removes it or cuts it off.

_{Looking up the hidden bottleneck ALIN7.}

• Findings: one block per result, each with an interactive figure: thresholds, disconnection, regions, superclasses, connections, brain and nerve cord, avalanches, structure, pairs, bilateral redundancy and the hidden bottleneck.
• Methods and limits: the data, graph construction, sensory and motor sets, measures, removal protocol, validation, limitations and how to reproduce every number.

_{The opening, the key results, the null model and a cell type profile at phone width.}

Methods

1. Data. The male CNS connectome, male-cns:v1.0, queried through neuPrint.¹⁰ The database holds 176,422 neuron records, of which 164,506 carry one of 11,751 cell types.

2. Type graph. Neuron-to-neuron synapse counts are summed into type-to-type counts $w(u \to v)$. An edge is kept when it supplies at least 1% of the target type's input, and self-loops are dropped, which leaves 243,439 directed edges:

   \frac{w(u \to v)}{\sum_{u'} w(u' \to v)} \ge 0.01
   

3. Terminals. The source set $S$ holds the 368 types whose majority superclass is sensory; the sink set $M$ holds the 665 descending neuron and motor types.

4. Pre-registration. The hypotheses, tests, test directions and every protocol parameter were committed in 0e72491, after the graph was built and before any removal was run. The order can be checked in the repository history.

5. Flow capacity. A supersource feeds every $s \in S$ and every $m \in M$ drains to a supersink; graph edges get unit capacity. The maximum flow $F(G)$ equals the number of edge-disjoint paths from $S$ to $M$.⁵ The secondary metric $R(G)$ counts sensory-motor pairs joined by a directed path.

6. Removal. Six orders: random, weighted out-degree and in-degree (synapse sums), betweenness, PageRank, and sensory-motor betweenness, which counts only shortest paths from $S$ to $M$. With $N$ = 11,751 types and $n_k$ removed, batch $k$ removes the

   b_k = \left\lceil 0.01\,(N - n_k) \right\rceil
   

   highest-scoring types, and scores are recomputed before the next batch. Random removal is run 30 times.

7. Fragility and thresholds. The fragility score is the trapezoidal area under $F(G_k)/F(G_0)$ over the first 50% of removals, divided by that range.⁶ The critical fraction interpolates between the last batch at or above half of intact flow and the first below it:

   f_c = x_{i-1} + (x_i - x_{i-1}) \, \frac{F_{i-1} - F_0/2}{F_{i-1} - F_i}
   

8. Null model. 200 degree-preserving randomized graphs,⁹ each given the full protocol. For each order $k$ the one-sided empirical p-value is

   p_k = \frac{1 + \#\{\, i : \mathrm{AUC}^{\mathrm{null}}_{i,k} \le \mathrm{AUC}^{\mathrm{real}}_k \,\}}{1 + 200}
   

   tested at 0.05 / 6.

9. Follow-up analyses. Structural avalanches, fitted by maximum likelihood with a bootstrap goodness-of-fit test,⁷ brain and nerve cord subgraphs, synthetic-lethal pairs, bilateral redundancy, the hidden bottleneck and literature validation were pre-registered. The full single-type removal table, disconnection across the type population, regional and superclass removal, the structural profile, the edge attack and the published-threshold comparison were added afterwards and are exploratory.

Protocol settings

setting	value
edge threshold	at least 1% of the target type's input synapses; self-loops dropped
batch size	1% of the remaining types, rounded up; 69 batches to 50% removed
scores	recomputed on the reduced graph before every batch; ties broken in seeded random order
removal window	until at least 50% of types are removed; fragility is the AUC over that range
critical fraction	first fall below 50% of intact flow, interpolated between batches
random removal	30 trials, mean with a Student-t 95% CI
null model	200 graphs, 10 × |E| degree-preserving swaps each, out-strength kept
null test	one-sided empirical p per order, Bonferroni threshold 0.05 / 6 = 0.0083
cascade fit	discrete power law, bootstrap with 1,000 synthetic sets, plausible at p ≥ 0.1
seeds	base 20260915; null graph i: base + 100000 + i; trial t of order j, counting orders from 0: base + 1000 j + t
exploratory analyses	200 same-size random sets for regions and superclasses; edge attack in 1% batches of connections, 5 random orders

The edge threshold, batch rule, removal window, critical fraction, random trials, null model and its test, the cascade fit and the null-graph seeds were fixed in the pre-registration and not changed.

Software

package	version
Python	3.12.12
neuprint-python	0.6.3
igraph	1.0.0
NumPy / SciPy / pandas	2.5.3 / 1.18.1 / 3.0.5
powerlaw	2.0.0
networkx	3.6.1
pyarrow	25.0.1
matplotlib	3.11.2
pandoc / typst	3.11 / 0.15.1

The poster

One-page summary, 3508 × 4960 pixels. Open the full-size poster

Data and outputs

Every number on this page comes from a file in this repository. These are the ones worth opening directly, with nothing installed and nothing run.

file	what it holds
results/preregistration.md	the analysis plan, committed before any removal
results/percolation_curves.csv	flow capacity, connected pairs and cascade size after every batch of every run
results/critical_thresholds.json	the critical fraction of each order, with all 30 random trials
results/single_removal_impacts.csv	what removing each of the 11,751 types alone costs
results/regional_impact.csv	all 91 neuropils against their same-size random sets
results/type_atlas.json	neuropil outlines and, for every order, when types are removed or cut off
results/bilateral_symmetry.csv	left, right and both-side removal for every bilateral type
paper/report.md	the technical report, also as PDF

Reproduce

Requirements: Python 3.12, Node 22, GNU Make, and network access to neuPrint and the public flyem-male-cns bucket. The paper target also needs pandoc with typst.

python -m venv .venv && . .venv/bin/activate   # .venv\Scripts\activate on Windows
pip install -r requirements.txt
make reproduce WORKERS=8   # data, analyze, validate, context, hero, export, paper, test and verify
make web                   # web/dist

The stages can also be run on their own: make data (schema, sensory and motor sets, type graphs), make analyze (percolation, thresholds and every follow-up analysis), make validate (null model and literature validation), make context (published thresholds), make hero (regional impact, hero image, type atlas), make export (site data), make paper, make poster, make test (unit tests) and make verify (checks every committed result against its invariants). make readme redraws the figures on this page from results/, setting their text as outlines in the site's typefaces, Source Serif 4 and Archivo (DejaVu where those font files are absent), and make captures records the site animations from a running development server and a Chrome started with --remote-debugging-port=9222.

Raw neuPrint data are cached under data/ and are not committed. The public dataset can be queried anonymously; set NEUPRINT_APPLICATION_CREDENTIALS to use a token. All randomness is seeded from 20260915, and every percolation run is cached as its own file, so an interrupted run resumes where it stopped.

On an 8-core laptop the 35 percolation runs on the real graph take about twenty minutes. The null model is the slow step: each of its 200 graphs repeats all 35 runs, about 200 times the main analysis. Use NULLS to run fewer while testing.

Pipeline modules and outputs

step	module	output
neuPrint schema	pipeline/schema_discovery.py	results/schema.md
sensory and motor sets	pipeline/identify_sensory_motor_sets.py	368 sensory, 665 descending and motor types: results/sensory_motor_sets.md
type graphs	pipeline/build_type_graph.py	11,751 types, 243,439 edges; hemisphere-resolved graph
metrics	pipeline/connectivity_metrics.py	flow capacity, reachability, cut-off types
removal orders	pipeline/removal_strategies.py, pipeline/run_percolation.py	results/percolation_curves.csv, results/fragility_scores.json
thresholds	pipeline/critical_thresholds.py	results/critical_thresholds.md
single removal	pipeline/single_removal.py	results/single_removal_impacts.csv
avalanches	pipeline/avalanche_analysis.py	results/avalanche_analysis.md
brain and nerve cord	pipeline/brain_vnc_comparison.py	results/brain_vnc_comparison.md
synthetic-lethal pairs	pipeline/synthetic_lethal_pairs.py	results/synthetic_lethal_pairs.md
bilateral redundancy	pipeline/bilateral_symmetry.py	results/bilateral_symmetry.md
hidden bottleneck	pipeline/hidden_bottleneck.py	results/hidden_bottleneck.md
structure and superclasses	pipeline/structure_profile.py	results/structure_profile.md
edge attack	pipeline/edge_attack.py	results/edge_attack.md
null model	pipeline/null_model.py	results/null_model_validation.md
literature validation	pipeline/literature_validation.py	results/literature_validation.md
published thresholds	pipeline/network_comparison.py	results/network_comparison.md
regional impact and hero image	pipeline/regional_impact.py, pipeline/render_hero.py	results/regional_impact.md, assets/hero.png
type atlas	pipeline/type_atlas.py	results/type_atlas.json
README figures	pipeline/readme_assets.py	plates, figures and methods diagram as SVG in assets/readme/
site captures	pipeline/site_captures.py	GIFs and the phone strip in assets/readme/
poster	pipeline/poster.py	assets/readme/fault-lines-poster.png
site data	export/build_static_json.py	web/public/data/
site	web/ (React, Vite)	GitHub Pages via .github/workflows/pages.yml

verify/ holds one check script per result, and tests/ holds the unit tests. Both run in continuous integration on every push.

Credits and citation

The data are the male adult Drosophila CNS connectome from HHMI Janelia FlyEM and Google Research, released under CC-BY 4.0. Please cite the original work:

Berg S, Beckett IR, Costa M, et al. (2026). Sexual dimorphism in the complete Drosophila male central nervous system connectome. Cell 189(18):5504-5526.e15. doi:10.1016/j.cell.2026.08.015

The data were accessed through neuPrint, and neuropil meshes were read from the public flyem-male-cns bucket. Citation metadata for this repository is in CITATION.cff, which GitHub's "Cite this repository" button reads.

Code is released under the MIT License.

Citing this work

@software{sarkar2026faultlines,
  author = {Sarkar, Dhruvin},
  title  = {Fault Lines: attack tolerance and structural robustness of the complete {Drosophila} male {CNS} connectome},
  year   = {2026},
  url    = {https://github.com/dhruvin-sarkar/fault-lines},
  note   = {Independent analysis of public connectome data, not peer reviewed}
}

Footnotes

1. Berg S, Beckett IR, Costa M, et al. (2026). Sexual dimorphism in the complete Drosophila male central nervous system connectome. Cell 189(18):5504-5526.e15. doi:10.1016/j.cell.2026.08.015 ↩

2. Lin A, Yang R, Dorkenwald S, et al. (2024). Network statistics of the whole-brain connectome of Drosophila. Nature 634:153-165. doi:10.1038/s41586-024-07968-y ↩

3. Albert R, Jeong H, Barabási A-L (2000). Error and attack tolerance of complex networks. Nature 406:378-382. doi:10.1038/35019019 ↩ ↩²

4. Holme P, Kim BJ, Yoon CN, Han SK (2002). Attack vulnerability of complex networks. Physical Review E 65:056109. doi:10.1103/PhysRevE.65.056109 ↩

5. Ford LR, Fulkerson DR (1956). Maximal flow through a network. Canadian Journal of Mathematics 8:399-404. doi:10.4153/CJM-1956-045-5 ↩ ↩²

6. Schneider CM, Moreira AA, Andrade JS, Havlin S, Herrmann HJ (2011). Mitigation of malicious attacks on networks. Proceedings of the National Academy of Sciences 108(10):3838-3841. doi:10.1073/pnas.1009440108 ↩ ↩²

7. Clauset A, Shalizi CR, Newman MEJ (2009). Power-law distributions in empirical data. SIAM Review 51(4):661-703. doi:10.1137/070710111 ↩ ↩² ↩³

8. Kaiser M, Hilgetag CC (2004). Edge vulnerability in neural and metabolic networks. Biological Cybernetics 90:311-317. doi:10.1007/s00422-004-0479-1 ↩

9. Maslov S, Sneppen K (2002). Specificity and stability in topology of protein networks. Science 296(5569):910-913. doi:10.1126/science.1065103 ↩ ↩²

10. Plaza SM, Clements J, Dolafi T, et al. (2022). neuPrint: an open access tool for EM connectomics. Frontiers in Neuroinformatics 16:896292. doi:10.3389/fninf.2022.896292 ↩