*2.5. Spatial Analysis*

To demonstrate the regional interactions in the social responses, the origins and destinations of the starving migrants were regarded as nodes, and the migration flows were regarded as the links. A spatial network of the famine-related migration in 1877–1878 was built (Figure 4). Similarly, taking the provinces where silver and grain transferred out and in as the nodes, the inter-provincial transfers as the links, and the number of transfers as the weight, a weighted network of money and grain allocation in 1877–1878 was built (Figure 5). In the networks, the degree refers to the number of direct links connected with each node. It can reflect the number or range of connections between different areas. Using ArcGIS, the lengths (distances) of migration and allocation flows can be calculated.

Besides, regarding the sites where the social unrest events took place as the core, point density analysis was conducted in ArcGIS. In the analysis, a particular sample point is set as the center, then a neighborhood is defined around each center with a certain value of search radius. After that, points of different weight values that fall within the neighborhood are identified. Points are weighted higher if they are closer to the centers. The weights gradually reduce until they drop to zero at the edge of the neighborhood. The density value is the sum of the values of the sample points divided by the area of the neighborhood [45,46]. In this paper, the unrest occurrence sites are the centers, and the search radius is 100 km. The unrest density value is divided into eight levels according to the number of unrest events per 10,000 square kilometers. The frequency of occurrence and the spillover effects of social unrest were analyzed.

**Figure 4.** (**a**) Origins, destinations and sizes of the famine-related migration in 1877. (**b**) Origins, destinations and sizes of the famine-related migration in 1878. Straight line: migration flows with exact locations of destinations; Dotted line: migration flows with approximate locations of destinations; Degree: the number of direct links connected with a node.

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**Figure 5.** (**a**) Spatial characteristics of grain and monetary allocations in 1877. (**b**) Spatial characteristics of grain and monetary allocations in 1878. Degree: the number of direct links connected with a node; Weight: the number of inter-provincial transfers.
