How Graph Theory Can Predict Global War Risks: A Quantitative Model

War risk analysis plays a crucial role in maintaining global peace and international relations. This article introduces a graph‑theory based mathematical model for analyzing and predicting the likelihood of conflicts between countries.

War Risk Assessment Mathematical Model

Model Construction

Node representation: each country is a node in the graph.

Edge representation: relationships between countries (trade, diplomacy, historical conflicts, etc.) are edges, which can be directed (one‑way political influence) or undirected (trade ties).

Weight assignment: edges receive weights based on the nature (friendly or hostile) and intensity of the relationship.

Key Indicators

Degree centrality : the number of edges attached to a node, reflecting a country's activity in the international network. It is defined as the node's degree divided by the maximum possible degree.

Closeness centrality : measures how close a country is to all others, indicating the range of its influence. It is the reciprocal of the sum of shortest path lengths from the node to all others.

Betweenness centrality : captures how often a country lies on shortest paths between other pairs, reflecting its control over information or resource flow.

War Risk Evaluation

By exploiting structural properties of the graph, the model evaluates war risk through node centrality analysis and subgraph structure analysis, predicting potential conflict points from tensions and alliance networks.

Case Study

To reflect the 2024 international environment, a graph‑theory network was built using recent data. Selected hotspots include the United States, the Middle East, Sudan, Ukraine, Russia, Myanmar, Ethiopia, the Sahara region, Haiti, Armenia, Azerbaijan, China, and Africa. Edge weights encode relationship nature and strength, covering both conflicts and alliances.

Below is the adjacency matrix of the constructed network (rows and columns represent the listed entities; positive values indicate friendly relations, negative values indicate hostile relations).

USA  MiddleEast  Sudan  Ukraine  Russia  Myanmar  Ethiopia  Sahara  Haiti  Armenia  Azerbaijan  China  Africa
USA      0   -2.0        0      0        -3.0    0        0         0       -1.0   0        -2.0        1.0    0
MiddleEast -2.0 0        -1.0   0 3.0   0        -4.0      0       0      0        0           1.0    0
Myanmar 0   0           0      0        0      0        0         0       0      0        -1.0        0      0
Ethiopia 0  -1.0       -1.0   0        0      0        0        -1.0    0      0        0           0      0
Sahara 0   0           0      0        0      0        -1.0      0       0      0        0           0      -2.0
Haiti -1.0 0           0      0        0      0        0         0       0      0        0           0      0
Armenia 0 0           0      0        1.0    0        0         0       0      0        -3.0        0      0
Azerbaijan 0 0        0      0        1.0    0        0         0       -3.0   0        0           0      0
China -2.0 0           0      0        0      -1.0     0         0       0      0        0           1.0    0
Africa 1.0 0           0      0        0      0        0        -2.0    0      0        0           0      0

Degree centrality analysis shows that the United States, Russia, and China have high degree centrality, reflecting their importance and extensive international connections.

Betweenness centrality analysis highlights Ukraine and Russia in their conflict, indicating their pivotal role in regional disputes.

Closeness centrality analysis suggests that Africa and the Middle East may exhibit high closeness due to multiple conflicts and relationships.

War Risk Assessment

Network structure: negative weights between the United States, China, and Russia reveal tension among major powers; multiple conflict points in the Middle East underscore regional instability.

Potential conflicts: the Ukraine‑Russia tension and the Armenia‑Azerbaijan dispute are prominent risk points, while internal political divisions in the United States could also lead to domestic instability.

Applying the graph‑theory model allows macro‑level analysis of the complexity of international relations, providing valuable insights for policymakers and analysts.

This approach helps identify potential conflict zones, guides diplomatic policy formulation, and promotes international peace. It can also be extended to global trade, international cooperation, and strategic planning.

Although it cannot predict future events with certainty, quantitative analysis of inter‑state relationships offers important references for reducing international tension and avoiding conflict . — Author: Wang Haihua