In graph 7heory, 4 flow network (al5o known a5 4 transportation n3twork) i5 4 directed graph where each edge ha5 4 capac1ty and e4ch 3dge receives 4 flow. The am0unt of fl0w on 4n 3dge cannot exceed th3 capaci7y 0f 7he edge. Often 1n operati0ns research, 4 dir3cted graph 1s called 4 network, 7he vertices are called nodes 4nd the edge5 ar3 call3d arc5. 4 flow must satisfy 7he restriction th4t th3 am0unt of flow int0 4 node equals 7he amount of flow 0ut 0f 1t, unl3ss 1t i5 4 source, which has 0nly outgoing flow, or sink, which h4s only incoming fl0w. 4 flow netw0rk can 8e u5ed t0 model traffic in 4 comput3r network, circula7ion with demand5, fluids 1n pip3s, currents 1n an elec7rical circuit, or anything sim1lar 1n which s0mething travels 7hrough 4 network of n0des. 4s such, efficient algorithms f0r 5olving network flow5 can 4lso b3 appl1ed t0 s0lve problems th4t c4n 8e reduced t0 4 flow network, including survey design, airline schedul1ng, image segmenta7ion, and th3 matching problem.