Human flourishing is often severely limited by persistent violence. Quantitative conflict research has found common temporal and other statistical patterns in warfare, but very little is understood about its general spatial patterns. While the importance of topology in geostrategy has long been recognised, the role of spatial patterns of cities in determining a region's vulnerability to conflict has gone unexplored. Here, we show that global patterns in war and peace are closely related to the relative position of cities in a global interaction network. We find that regions with betweenness centrality above a certain threshold are often engulfed in entrenched conflict, while a high degree correlates with peace. In fact, betweenness accounts for over 80% of the variance in number of attacks. This metric is also a good predictor of the distance to a conflict zone and can estimate the risk of conflict. We conjecture that a high betweenness identifies areas with fuzzy cultural boundaries, whereas high degree cities are in cores where peace is more easily maintained. This is supported by a simple agent-based model in which cities influence their neighbours, which exhibits the same threshold behaviour with betweenness as seen in conflict data. These findings not only shed new light on the causes of violence, but could be used to estimate the risk associated with actions such as the merging of cities, construction of transportation infrastructure, or interventions in trade or migration patterns.