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from __future__ import annotations
import pandas as pd
from IPython.display import Markdown, display
from eu_trade_network import config, data_loader, graph, metrics, resilience, viz
N_RANDOM_RUNS = 2004 · Resilience
RQ3 — how much of the network survives losing its hubs? Economies are removed one at a time, targeted and at random, tracking both connectivity and retained trade value.
The removal protocol is described on the Data & method page.
The simulation runs twice, and the pairing is the point. The full graph is complete, so it cannot fragment topologically — there the value curve carries the whole story. The disparity-filter backbone keeps only statistically significant links, and that is where asking whether the network can break apart actually means something.
Graph + backbone
Rebuild the directed weighted graph for config.YEAR and extract the disparity-filter backbone.
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edgelist = data_loader.build_edgelist()
G = graph.build_graph(edgelist)
backbone = metrics.disparity_filter(G, alpha=config.DISPARITY_ALPHA)
summary = graph.graph_summary(G)
n_nodes = int(summary["n_nodes"])
print(
f"Full graph: {n_nodes} economies, {int(summary['n_edges'])} edges, "
f"density = {summary['density']:.2f}, "
f"total trade = {summary['total_value_kusd'] / 1e6:,.0f} bn USD"
)
print(
f"Backbone (alpha = {config.DISPARITY_ALPHA}): {backbone.number_of_nodes()} economies, "
f"{backbone.number_of_edges()} significant edges"
)Who goes first?
The two targeted hit lists. Out-strength ranks by export volume; weighted betweenness ranks by how often an economy sits on the cheapest trade path between two others.
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top_n = 8
by_strength = resilience.simulate_removal(G, "strength")
by_betweenness = resilience.simulate_removal(G, "betweenness")
hit_lists = pd.DataFrame(
{
"rank": range(1, top_n + 1),
"by out-strength": by_strength["removed_node"].tolist()[1 : top_n + 1],
"by betweenness": by_betweenness["removed_node"].tolist()[1 : top_n + 1],
}
).set_index("rank")
hit_listsFull network — connectivity never breaks, value does
On a complete digraph the largest component always holds every survivor, so the left panel is flat at 100% by construction. That is the finding: this network has no articulation point. The right panel shows what is actually at stake.
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curves_full = resilience.run_random_vs_targeted(G, n_random_runs=N_RANDOM_RUNS)
fig_full = viz.plot_resilience(
curves_full,
title=f"Full trade network ({n_nodes} economies, density = 1) — hub attack vs random failure",
)
out = viz.save_fig(fig_full, "04_resilience_full_graph.png", headline=False)
print(f"Saved {out}")
fig_full.show()Significant-trade backbone — where fragmentation happens
Repeat the simulation on the disparity-filter backbone, i.e. the sub-network of links that carry a significantly larger share of a country’s trade than a random allocation would give them. This is the headline figure for RQ3.
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curves_bb = resilience.run_random_vs_targeted(backbone, n_random_runs=N_RANDOM_RUNS)
fig_bb = viz.plot_resilience(
curves_bb,
title=(
f"Significant-trade backbone (alpha = {config.DISPARITY_ALPHA}) — "
"hub attack vs random failure"
),
)
out = viz.save_fig(fig_bb, "04_resilience.png", headline=True)
print(f"Saved {out}")
fig_bb.show()Critical fraction
critical_threshold reports the first removal fraction at which the largest component holds less than half of the surviving economies; value_threshold does the same for retained trade value. A critical fraction of 100% means “never fragments” — the curve only crosses when the graph is emptied.
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rows = []
for network, curves in (("full graph", curves_full), ("backbone", curves_bb)):
for strategy, frame in curves.groupby("strategy", sort=False):
crit = resilience.critical_threshold(frame)
half = resilience.value_threshold(frame)
rows.append(
{
"network": network,
"strategy": str(strategy),
"critical_fraction": crit,
"economies_to_fragment": round(crit * n_nodes),
"half_value_fraction": half,
"economies_to_halve_value": round(half * n_nodes),
}
)
thresholds = pd.DataFrame(rows)
thresholds.style.format({"critical_fraction": "{:.1%}", "half_value_fraction": "{:.1%}"}).hide(
axis="index"
)What this means (RQ3)
The paragraphs below are generated from the run above, so the numbers always match the figures.
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def _pick(network: str, strategy: str, column: str) -> float:
row = thresholds.loc[(thresholds["network"] == network) & (thresholds["strategy"] == strategy)]
return float(row[column].to_numpy()[0])
crit_strength = _pick("backbone", resilience.STRENGTH_STRATEGY, "critical_fraction")
crit_between = _pick("backbone", resilience.BETWEENNESS_STRATEGY, "critical_fraction")
crit_random = _pick("backbone", resilience.RANDOM_STRATEGY, "critical_fraction")
half_targeted = _pick("full graph", resilience.STRENGTH_STRATEGY, "half_value_fraction")
half_random = _pick("full graph", resilience.RANDOM_STRATEGY, "half_value_fraction")
n_half = round(half_targeted * n_nodes)
top_exporters = by_strength["removed_node"].tolist()[1 : n_half + 1]
lost_first = 1.0 - float(by_strength["trade_value_retained"].to_numpy()[1])
lost_deu = 1.0 - float(by_betweenness["trade_value_retained"].to_numpy()[1])
aut_rank = by_strength["removed_node"].tolist().index("AUT")
aut_curve = resilience.simulate_removal(G, ["AUT"])
aut_share = 1.0 - float(aut_curve["trade_value_retained"].to_numpy()[1])
paragraphs = [
f"**Critical fraction.** On the significant-trade backbone the network breaks apart once "
f"{crit_between:.0%} of economies ({round(crit_between * n_nodes)} of {n_nodes}) are removed "
f"in betweenness order, or {crit_strength:.0%} ({round(crit_strength * n_nodes)}) in "
f"export-volume order — *broken* meaning the largest surviving component no longer holds "
f"half the remaining economies. Random failure has to take out {crit_random:.0%} "
f"({round(crit_random * n_nodes)}) before the same thing happens, so the backbone is about "
f"**{crit_random / crit_between:.1f}× more tolerant of accidents than of a deliberate hit "
f"list**. Bridge economies bite sooner than big exporters: targeting betweenness fragments "
f"the backbone {(crit_strength - crit_between) * n_nodes:.0f} economies earlier than "
f"targeting export volume.",
"**Connectivity is not the weak point.** The full network is complete (density = 1): every "
"economy trades directly with every other, so nothing short of emptying it leaves anyone "
"stranded. There is no bridge to cut, and no trade agreement can add redundancy that is not "
"already there. Resilience here is not about whether the links exist — it is about how "
"lopsidedly the value sits on them.",
f"**Value is the weak point.** Losing the single largest exporter ({top_exporters[0]}) "
f"already strands {lost_first:.0%} of this {n_nodes}-economy network's merchandise trade "
f"value; losing Germany alone strands {lost_deu:.0%}. **Half of all trade value is gone once "
f"{n_half} economies ({', '.join(top_exporters)}) are removed** — {half_targeted:.0%} of the "
f"nodes. Random failure needs {round(half_random * n_nodes)} economies ({half_random:.0%}) "
f"for the same damage, making a targeted shock roughly "
f"{half_random / half_targeted:.1f}× more efficient than an untargeted one.",
"**Policy reading.**",
"1. **Stress-test the backbone, not the full graph** — shocks travel along the significant "
"corridors, and that is the object that actually fragments.\n"
"2. **Diversification, not redundancy, is the lever** — the links already exist; the volume "
"on them is what is concentrated, so exposure falls only by shifting trade away from the top "
"handful of partners.\n"
"3. **Watch bridge economies as well as big exporters** — on the backbone, betweenness "
"targeting fragments the network faster than volume targeting, which is exactly the failure "
"mode a supply-chain contingency plan should model.\n"
f"4. **Austria** — a mid-sized open economy: {aut_rank}th of {n_nodes} by export volume and "
f"{aut_share:.1%} of the network's trade value, with zero betweenness on the full graph "
f"(NB02) because its partners already trade directly. Austria is therefore not a chokepoint "
f"— removing it changes nothing structurally — but it sits downstream of the economies that "
f"are. Its resilience question is dependency on Germany and the other top hubs, not its own "
f"criticality.",
]
display(Markdown("\n\n".join(paragraphs)))