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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.

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 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.