Kidney paired donation is a partial solution to biological incompatibility preventing kidney transplants. A kidney paired donation program (KPDP) consists of altruistic or non-directed donors (NDDs) and pairs, each of which comprises a candidate in need of a kidney transplant and her/his willing but incompatible donor. Potential transplants from NDDs or donors in pairs to compatible candidates in other pairs are determined by computer assessment. A KPDP can be viewed as a directed graph with NDDs and pairs as vertices and potential transplants as edges. Transplants are carried out in the form of directed cycles among pairs and directed paths initiated by NDDs.
In file "Graph", "vertexType.csv" and "adjacencyMatrix.csv" are the vertex vector and the adjacency matrix of a combined KPDP database, respectively. The ith entry of the vertex vector indicates whether vertex i is a NDD. The (i,j) entry of the adjaency matrix indicates whether a directed edge points from vertex i to vertex j.
For example, a directed graph derived from a KPDP consists of vertices: 12, 45, 176, 210, 271, 471, 542, 544, 562, 789, 884, 885.
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| An example of a directed graph derived from a KPDP: circles stands for vertices and arrows stands for directed edges. Red vertices are NDDs and blue vertices are pairs. |
Its vertex vector is:
NAME,VALUE
12, 1
45, 1
176, 0
210, 0
271, 0
471, 0
542, 0
544, 0
562, 0
789, 0
884, 0
885, 0.
And its adjacency matrix is:
ROW/COLNAME ,12, 45, 176, 210, 271, 471, 542, 544, 562, 789, 884, 885
12 ,0 , 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0
45 ,0 , 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0
176 ,0 , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
210 ,0 , 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0
271 ,0 , 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0
471 ,0 , 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0
542 ,0 , 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0
544 ,0 , 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0
562 ,0 , 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0
789 ,0 , 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0
884 ,0 , 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0
885 ,0 , 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0.
The combined database includes pairs and NDDs from the Alliance for Paired Donation (APD) and the University of Michigan (UM) KPD programs. There are 585 pairs and 56 NDDs in the APD data and 281 pairs and 7 NDDs in the University of Michigan KPD program. In both data sources, blood type, anti-HLA antibodies of each candidate and blood type and HLA antigens of each donor are recorded. Those characteristics are used to generate edges in the adjacency matrix.