Relative to a given fixed tree of a network, we can define the following:

A. Link Current from an Independent Set:
- In a network, a link refers to a connection between two nodes.
- An independent set is a set of links in which no two links are connected to the same node.
- Link current refers to the current flowing through a particular link in the network.
- The link currents can be determined by applying Kirchhoff's current law (KCL) at the nodes connected by the links.
- By solving the set of equations obtained from KCL, we can find the link currents for the given independent set of links.
- The link currents are influenced by the voltages and resistances associated with the links.

B. Branch Current from an Independent Set:
- In a network, a branch refers to a path between two nodes.
- An independent set is a set of branches in which no two branches share a common node.
- Branch current refers to the current flowing through a particular branch in the network.
- The branch currents can be determined by applying Kirchhoff's current law (KCL) at the nodes connected by the branches.
- By solving the set of equations obtained from KCL, we can find the branch currents for the given independent set of branches.
- The branch currents are influenced by the voltages and resistances associated with the branches.

C. Link Voltage from an Independent Set:
- Link voltage refers to the voltage across a particular link in the network.
- The link voltages can be determined by applying Kirchhoff's voltage law (KVL) in a loop containing the link.
- By solving the set of equations obtained from KVL, we can find the link voltages for the given independent set of links.
- The link voltages are influenced by the currents and resistances associated with the links.

D. Branch Voltage from an Independent Set:
- Branch voltage refers to the voltage across a particular branch in the network.
- The branch voltages can be determined by applying Kirchhoff's voltage law (KVL) in a loop containing the branch.
- By solving the set of equations obtained from KVL, we can find the branch voltages for the given independent set of branches.
- The branch voltages are influenced by the currents and resistances associated with the branches.

In summary, the determination of link currents, branch currents, link voltages, and branch voltages in a network is based on the application of Kirchhoff's laws (KCL and KVL) and the consideration of the independent sets of links and branches. These parameters are essential for analyzing and understanding the behavior of electrical networks.