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The notation $c(u,v)$ represents the capacity of the directed edge from vertex $u$ to vertex $v$. It defines the maximum volume or amount of data that the edge can carry.

Conditions: There is a directed edge from $u$ to $v$.; Capacity is a quantitative attribute assigned to that specific edge.

The notation $c(u,v)$ represents the capacity of the directed edge from vertex $u$ to vertex $v$. It defines the maximum volume or amount of data that the edge can carry.

Conditions: There is a directed edge from $u$ to $v$.; Capacity is a quantitative attribute assigned to that specific edge.

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 $c(u,v)$.

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 ($f \le c$).