What is the name of this graph/plot?
I think it is Chord Diagram. you can see this for more information.
"A chord diagram is a graphical method of displaying the inter-relationships between data in a matrix. The data are arranged radially around a circle with the relationships between the data points typically drawn as arcs connecting the data." based on the Wikipedia
This is a Circos plot, often used for visualizing genomic data, but works equally well for migration and some other applications.