Understanding Russian War Strategy Through Weak Ties in Graph Theory
Over 6 months ago, Russia shocked the world when it invaded Ukraine, starting a war on multiple fronts for the Ukrainians. As the war rages on, some have used mathematical theories to understand what are the strategies that will most likely lead to success for both the Ukrainians and Russians. The article mentioned at the bottom of this post uses graph theory to determine what is the most effective strategy for the Russian army, such that Ukraine would theoretically do as much as it can to prevent the Russians from using this strategy. As the article touches on, many times the best way to plan your chess strategy is to understand what is the ideal move for your opponent.
The graph (as seen below) has cities in Ukraine as nodes connected by edges that represent roads interconnecting the aforementioned cities. There are seven “special” nodes which were Russian staging areas before the invasion; these, in more colloquial terms, represent the entry points for Russian forces. The goal of the Ukrainians is to prevent Russian control, most importantly to prevent control of the capital of Ukraine, Kyiv.
The simulation run in the article creates a graph where red edges represent the flow of Russian tanks (we can represent these as negative or enemy edges), and green edges represent Ukrainian-controlled roads (we can represent these as positive or friendly edges). In the simulation below that plots the Russians most effective attack plan, we can see fundamentally the Russians aim to make Ukrainian cities isolated, encircled and unable to reach outside help, creating a graph that is fundamentally unbalanced.
As many edges connecting cities have other smaller cities simply along the main routes, we can treat “intersecting cities” like Poltava, Kharkiv, Kyiv, Kremenchuk, and others as the most major nodes and then create large triangles between these major cities. In doing so, we can see the optimized Russian plan to target routes that block passage through these major cities, creating a map almost where Ukraine is split into two main areas, isolated and unable to receive reinforcements from other parts of Ukraine. In doing this we can see for example, a major country triangle, such as that of Kyiv, Kharkiv, and Dnipro, is unbalanced, where cities that lie in any of the routes inside of this triangle are now isolated from Ukrainian reinforcements and troops. We can even see the Russian’s use of unbalanced triads on a smaller triangle, for example, between Zaporizhzhia, Berdyansk, and Donetsk, where there are two positive edges and one negative edge.
While this is just a simulation trying to predict the moves of Russians, it helps shed light on some of the possible contributions we can all have towards ending this war of tyranny and conquest brought on by Putin. Sometimes I think we all can feel a little useless or unable to help confront the monstrosities brought upon by this unwanted war, but through bringing our own expertises to the table to help confront the issue in one way or another, we can all help, even if it is just something as small as a simulation of troop movements.
https://medium.com/@rohitpandey576/data-science-in-battle-applying-graph-theory-to-the-ukraine-war-6cda499c86fc