modelling Level 4

The Integrated Trade Network

The previous four models examine pieces: gravity determines volumes, corridors carry them, ports gate them, modal choice routes them. This model assembles those pieces into a directed network graph and applies the same graph-theoretic tools used for the pipeline system to the trade system — revealing a structural architecture with one dominant vulnerability: Windsor-Detroit's betweenness centrality of 0.82.

Prerequisites: Directed graph, betweenness centrality, max flow min cut, network resilience, O D matrix

9 Mar 2026 Updated 12 Mar 2026 15 min read

1. From Pieces to Network

The four preceding essays in this cluster each examine a component of Canada’s goods trade system in isolation. T1 derives the gravity model and quantifies the volumes that geography and economic mass predict. T2 maps the corridor systems that carry those volumes and examines the flow assignment mathematics that determines routing. T3 analyses port economics — throughput functions, queuing theory, hinterland competition. T4 examines modal choice and the cost functions that determine whether freight moves by truck, rail, or ship.

Each analysis is valuable on its own terms. But pieces, however well understood individually, do not compose automatically into a system-level picture. To understand which nodes matter most, which links constrain total flow, and which disruptions have outsized systemic effects, we need to assemble the pieces into a single directed network and apply the tools of network analysis.

This is exactly what Cluster P did for Alberta’s pipeline infrastructure. P5 assembled crude oil, natural gas, NGL, and refined product flows into a directed graph and computed betweenness centrality and max-flow min-cut to identify Hardisty as the network’s dominant structural vulnerability — the node through which virtually all Alberta hydrocarbon exports pass, whose disruption would simultaneously affect all export directions.

This essay applies the same framework to Canada’s goods trade network. The nodes are different — ports, rail hubs, and border crossings rather than pump stations and tank farms. The edge weights represent corridor capacity rather than pipe throughput. But the mathematics is identical, and the result — a high-centrality node whose disruption has asymmetric systemic consequences — is structurally similar to what the pipeline analysis found.

2. The Network Defined

Nodes

Canada’s freight trade network can be represented with twelve key nodes, chosen to capture the major geographic decision points where freight routes diverge, where modes transfer, and where international borders are crossed:

Vancouver Port — Pacific Gateway primary container terminal
Prince Rupert Port — Pacific Gateway secondary, fastest-growing
Edmonton — Prairie freight hub; junction of northern and southern rail corridors
Calgary — Prairie distribution point; CN/CP interchange
Winnipeg — Mid-continent gateway; junction of east-west and north-south rail
Toronto — Ontario distribution hub; largest concentration of manufacturing freight origins
Montreal — Eastern Canada hub; inland ocean port
Halifax Port — Atlantic Gateway
Windsor — US border crossing; automotive corridor gateway to US Midwest
Sarnia — Secondary Great Lakes crossing; Bluewater Bridge complex
Niagara — Third major Ontario-US crossing; Rainbow, Peace, and Queenston bridges
US Markets — Composite sink node representing all US destinations

The choice to treat “US Markets” as a single composite sink node is a modelling simplification. In reality, US destinations span the continent, with different import crossing points serving different US regions. For the purpose of identifying Canadian network structure, this simplification is appropriate: we are interested in the Canadian freight network’s internal geometry, not the distribution within the US.

Edges and capacities

Directed edges represent major freight corridors with estimated annual capacity in thousands of TEU-equivalents (a normalised unit that allows comparison across commodity types). The capacity figures are approximate, derived from rail waybill data, port statistics, border crossing records, and published infrastructure capacity assessments.

Corridor	Capacity (000 TEU-equiv/yr)
Vancouver → Edmonton (CN/CP rail)	2,500
Prince Rupert → Edmonton (CN rail)	1,000
Edmonton → Calgary	1,800
Calgary → Winnipeg	1,200
Winnipeg → Toronto	1,500
Toronto → Windsor	800
Windsor → US Markets	600
Toronto → Niagara	400
Niagara → US Markets	400
Toronto → Montreal	700
Toronto → Sarnia	350
Sarnia → US Markets	350
Montreal → Halifax	200
Halifax → US Markets	100
Montreal → US Markets (direct)	150

3. Max-Flow Min-Cut

The theorem

The max-flow min-cut theorem, proved independently by Ford and Fulkerson (1956) and Elias, Feinstein, and Shannon (1956), states that in any network with a source node $s$ and a sink node $t$, the maximum flow that can be pushed from $s$ to $t$ equals the capacity of the minimum cut separating $s$ from $t$.

Formally, a cut $(S, T)$ is a partition of the node set $V$ into two disjoint subsets $S$ (containing the source) and $T$ (containing the sink). The capacity of the cut is the sum of capacities of edges directed from $S$ to $T$:

\[c(S,T) = \sum_{(u,v): u \in S, v \in T} c(u,v)\]

The minimum cut is the cut with the smallest capacity. The max-flow min-cut theorem states:

\[\max \text{ flow}(s \to t) = \min \text{ cut capacity}(s, t)\]

This theorem has a direct policy interpretation: the maximum throughput of any network is constrained by its weakest link set — the set of edges that, if removed, would disconnect the source from the sink and whose total capacity is minimised.

Application to the Canadian trade network

In Canada’s trade network, sources are Pacific Gateway ports (Vancouver and Prince Rupert) and Atlantic Gateway ports (Montreal and Halifax), plus Prairie production nodes (Edmonton, Calgary). The sink is “US Markets.” The maximum flow the network can sustain from Canadian sources to US destinations is determined by the minimum cut.

Examining the network structure, the minimum cut is dominated by the Windsor-Detroit crossing. Windsor’s outbound capacity to US Markets is 600,000 TEU-equivalents per year — lower than the combined capacity of the links feeding it from Toronto. This means Windsor is a binding constraint: even if upstream links (Winnipeg-Toronto, Toronto-Windsor) have spare capacity, flow through Windsor cannot exceed 600K TEU-equiv. The minimum cut capacity identifies Windsor as the binding constraint on the entire Canada-to-US-Midwest flow.

This has a direct infrastructure policy implication. Adding capacity at Vancouver — a new terminal, improved rail service — does not increase the maximum flow to the US Midwest. The maximum flow is determined by Windsor, not by the Pacific Gateway. Infrastructure investment improves the overall system only when it addresses the actual minimum cut, not upstream links that already exceed the minimum cut capacity.

The Gordie Howe International Bridge addresses exactly this. By adding six lanes of crossing capacity, it increases Windsor’s outbound capacity from approximately 600K to over 1,200K TEU-equivalents — effectively doubling the minimum cut and correspondingly increasing the maximum possible flow through the Canada-US Midwest corridor.

4. Betweenness Centrality

The definition

Betweenness centrality measures how frequently a node appears on shortest paths between all other pairs of nodes in the network. For a node $v$:

\[B(v) = \sum_{s \neq v \neq t} \frac{\sigma(s,t \mid v)}{\sigma(s,t)}\]

where $\sigma(s,t)$ is the total number of shortest paths from source $s$ to target $t$, and $\sigma(s,t \mid v)$ is the number of those shortest paths that pass through $v$. Normalised betweenness divides by the maximum possible value, giving a score between 0 and 1. A node with normalised betweenness of 1.0 lies on every shortest path in the network; a node with 0 lies on none.

High betweenness centrality identifies nodes that are critical intermediaries: their removal or disruption affects not just their own connections but the shortest-path structure between many other pairs of nodes. In freight networks, high-betweenness nodes are the strategic vulnerabilities — the places where disruption has amplified systemic effects.

Estimated centrality values

For Canada’s trade network, estimated normalised betweenness centrality values (computed approximately from the network structure described above) are:

Node	Betweenness (0–1)
Windsor	0.82
Toronto	0.71
Winnipeg	0.58
Montreal	0.45
Halifax	0.25
Vancouver	0.38
Calgary	0.32
Edmonton	0.28
Prince Rupert	0.18
Sarnia	0.20
Niagara	0.22

Windsor’s centrality of 0.82 reflects its position as the primary gateway for freight moving from Ontario — Canada’s manufacturing and distribution heartland — to the US Midwest, which is Canada’s largest single export market region. Almost every optimal path from Canadian interior origins to US Midwest destinations passes through Windsor. No other single node approaches this level of path concentration.

5. Network Betweenness: Visualised

Windsor’s betweenness of 0.82 is substantially higher than Toronto’s 0.71 — which itself is high — because Windsor is where virtually all optimal paths from Toronto to US Midwest destinations must exit. Toronto distributes and accumulates freight; Windsor gates it to the US.

6. The Full Network Map

The network visualised geographically. Windsor (southwest Ontario) is the geographic funnel through which Ontario-origin freight exits to the US Midwest. Winnipeg is the Prairie gateway — all rail traffic east from the Prairies flows through or near it. Pacific Gateway ports handle Asian trade; Atlantic ports handle European flows.

7. Max-Flow by Corridor

Windsor is the only corridor where the min-cut constraint (600K) falls below theoretical feed capacity (700K). All other corridors are not currently bottlenecked at the crossing point itself — their constraints lie upstream or in terminal handling. The Gordie Howe bridge doubles Windsor’s min-cut capacity when complete.

8. The Windsor Problem: Disruption Economics

Automotive parts account for roughly 51% of the per-day disruption cost, reflecting Windsor’s dominance as an automotive corridor. A six-day blockade cost an estimated CAD$2.1 billion, concentrated in automotive just-in-time supply chains with no buffer inventory.

9. Integrated Flow: The Sankey View

The Sankey diagram makes the network’s structure immediately legible: Pacific ports feed the Prairie hub and Asia; the Eastern hub (Toronto-Montreal region) distributes to Windsor, Niagara-Sarnia, and Atlantic gateways; Windsor carries by far the largest single flow to the US Midwest. The width of each link is proportional to flow value.

10. Comparison to Cluster P: The Parallel Structure

The structural parallel between Canada’s trade network and Alberta’s pipeline network — examined in P5 — is direct and instructive, and it is worth making explicit.

In the pipeline network, Hardisty is the high-betweenness node. Every barrel of oil sands production must pass through or near Hardisty before entering the export pipeline system. Hardisty’s centrality reflects the geology of the oil sands: production is concentrated in the Athabasca region north of Fort McMurray, and all export corridors begin at the Hardisty hub. Disruption at Hardisty affects all export directions simultaneously.

In the trade network, Windsor is the high-betweenness node. The majority of Ontario-origin goods trade with the United States must pass through the Windsor-Detroit crossing. Windsor’s centrality reflects the geography of the Canada-US border: the Detroit River is narrow, the US manufacturing heartland is directly across it, and decades of automotive supply chain investment have created a corridor so economically integrated that alternative routes are structurally uncompetitive for the dominant commodity flows.

Both are geographic bottlenecks. Both have betweenness centrality substantially above all other nodes in their respective networks. Both have experienced high-profile disruption events: Freedom Convoy at Windsor (2022), pipeline price collapse at Hardisty during the 2018 AECO crisis. And both are being addressed through infrastructure investment designed to add redundancy without displacing the existing dominant node: Gordie Howe adds a second Windsor crossing; Trans Mountain Expansion added a second Pacific corridor.

Betweenness centrality is the mathematical concept that names both vulnerabilities. It is not a metaphor or an analogy — it is the same calculation applied to two different networks, producing the same structural finding: a single node of extremely high centrality, whose disruption has consequences disproportionate to its geographic size or apparent significance. The pipeline system’s Hardisty and the trade network’s Windsor are, in this formal sense, the same kind of problem.

References

Brandes, Ulrik. 2001. “A Faster Algorithm for Betweenness Centrality.” Journal of Mathematical Sociology 25 (2): 163–177. https://doi.org/10.1080/0022250X.2001.9990249

Canada Border Services Agency. 2024. Trade Facilitation, Compliance and Incentives. Ottawa: Government of Canada. https://www.cbsa-asfc.gc.ca/trade-commerce/facil-eng.html

CBC News. 2022. “Convoy Blockades Halted Almost $4B in Trade, Inquiry Hears.” CBC News, November 17, 2022. https://www.cbc.ca/news/politics/convoy-economics-1.6653986

Elias, Peter, Amiel Feinstein, and Claude E. Shannon. 1956. “A Note on the Maximum Flow Through a Network.” IRE Transactions on Information Theory 2 (4): 117–119. https://doi.org/10.1109/TIT.1956.1056816

Ford, Lester R., and Delbert R. Fulkerson. 1956. “Maximal Flow Through a Network.” Canadian Journal of Mathematics 8: 399–404. https://doi.org/10.4153/CJM-1956-045-5

Gordie Howe International Bridge. 2025. Project Overview. Windsor-Detroit Bridge Authority. https://gordiehoweinternationalbridge.com/project/overview/

Statistics Canada. 2024. “Canadian International Merchandise Trade: Annual Review 2023.” The Daily, May 9, 2024. Ottawa: Statistics Canada. https://www150.statcan.gc.ca/n1/daily-quotidien/240509/dq240509a-eng.htm

Statistics Canada. 2024. Railway Industry Summary Statistics on Freight and Passenger Transportation. Table 23-10-0057-01. Ottawa: Statistics Canada. https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=2310005701

Transport Canada. 2024. Transportation in Canada 2023. Ottawa: Transport Canada. https://tc.canada.ca/en/corporate-services/transparency/corporate-management-reporting/transportation-canada-annual-reports/transportation-canada-2023