路段與路徑之關係可以用路段╱路徑投引矩陣（Arc/Path incidence matrix）表 示記為 △，而路段與路徑流量分別以 f 與 h 表示，則路段流量與路徑流量之關係可表為 △h = f。當△的反矩陣存在，則路徑流量可以由 h = △�笐繈 求得。由網路的特性可知， △的反矩通常不存在。儘管如此，仍可透過廣義反矩陣的特性求出路徑流量，令△�珙� △ 之 廣義反矩陣，k 為任意向量，則路徑流量為 h= △�� f + （ I- △�牷窗^k，但是此結果無 法確定 h 為正流量。因此本研究提出一演算法，以確保可求出一組正流量解，提供相關研 究應用。

　　　　　ArC/Path incidence, matrix denoted as △=〔△ 〕where △ =1 if arc a is in path p,O otherwise. Arc flow and path flow denoted as f and h respectively. The relationship between arc flow and path flow can be shown as △h = f. If △�笐縹xists, path flow h equals to △�笐繈. Unfortunately, △�笐� does not always exist. But if △�� denoted as generalized inverse of △ and k is a column vector, then path flow can be shown as h = △�浻 +（ I-△�牷� ）k. In this research we will provide an algorithm to find a nonnegative path flow.