What would you like to understand?

A flow network is a directed graph $G(V, E)$ that has a source $s$ and a sink $t$. The set $V$ represents the vertices or nodes, and $E$ represents the directed edges.

Conditions: The graph is directed.; There is a source vertex $s$ and a sink vertex $t$.; Each directed edge $(u, v)$ has an associated capacity $c(u,v)$.

A flow network is a directed graph $G(V, E)$ that has a source $s$ and a sink $t$. The set $V$ represents the vertices or nodes, and $E$ represents the directed edges.

Conditions: The graph is directed.; There is a source vertex $s$ and a sink vertex $t$.; Each directed edge $(u, v)$ has an associated capacity $c(u,v)$.

The order matters because the graph is directed. The notation $(u,v)$ specifically denotes an edge pointing from node $u$ to node $v$.

Conditions: The graph is a directed graph.; Edges are represented as ordered pairs.

The order matters because the graph is directed. The notation $(u,v)$ specifically denotes an edge pointing from node $u$ to node $v$.

Conditions: The graph is a directed graph.; Edges are represented as ordered pairs.

In the example flow network drawn in the video, the leftmost node is the source, labeled $S$, and the rightmost node is the sink, labeled $T$ (or $E$ in the later annotated diagram). The source is where the flow originates, and the sink is where the flow terminates.

Conditions: Refers to the specific hand-drawn example network shown in the video.; The network is arranged roughly from left to right.

In the example flow network drawn in the video, the leftmost node is the source, labeled $S$, and the rightmost node is the sink, labeled $T$ (or $E$ in the later annotated diagram). The source is where the flow originates, and the sink is where the flow terminates.

Conditions: Refers to the specific hand-drawn example network shown in the video.; The network is arranged roughly from left to right.

Capacity is the maximum volume or amount of data an edge can carry, while flow is the actual amount of units currently passing through that edge. By definition, the flow on any edge must be less than or equal to its capacity.

Conditions: Applies to edges in a flow network.; Flow must be less than or equal to capacity ($f \le c$).

Capacity is the maximum volume or amount of data an edge can carry, while flow is the actual amount of units currently passing through that edge. By definition, the flow on any edge must be less than or equal to its capacity.

Conditions: Applies to edges in a flow network.; Flow must be less than or equal to capacity ($f \le c$).