Network Topology Basics: Graphs, Trees, and Cut-sets Quiz Quiz

Explore key concepts in network topology with focused questions on graphs, trees, and cut-sets to strengthen your understanding of network analysis structures and terminology. Gain clarity on essential terms and their differences to excel in network theory and related engineering fields.

1. Identifying Graph Structures

   Which of the following best describes a 'tree' in the context of network topology graphs?

   1. A single node connected to itself
   2. A graph containing at least one loop
   3. A connected graph with no closed paths or cycles
   4. A disconnected group of vertices

   Explanation: A tree in network topology is defined as a connected graph without any cycles or closed paths, making it an acyclic connected structure. A graph containing a loop is not a tree because it has a closed path, violating the acyclic property. A disconnected group of vertices is not a tree, as connectivity is a requirement. A single node connected to itself describes a self-loop, which also forms a cycle, so it is not a tree.

2. Understanding Cut-sets

   In a connected network graph, what is a cut-set?

   1. A set of branches that do not affect connectivity when removed
   2. A set of nodes that form a cycle
   3. A set of branches whose removal increases the number of disconnected components
   4. A group of nodes at different voltage levels

   Explanation: A cut-set is a group of branches that, if removed, will break the network into two or more isolated parts, increasing the number of disconnected components. A set of nodes forming a cycle is simply a loop and not related to cut-sets. Branches that do not affect connectivity are not part of a cut-set, since a cut-set specifically impacts connectivity. Nodes at different voltage levels are not related to the structural definition of cut-sets.

3. Counting Tree Branches

   If a network graph contains 8 nodes, how many branches will its tree contain?

   1. 7
   2. 8
   3. 16
   4. 9

   Explanation: A tree of a connected graph with N nodes always has (N-1) branches; so for 8 nodes, it will have 7 branches. Eight branches would mean there is a cycle, which is not permissible in a tree. Sixteen branches are far too many and would suggest multiple cycles. Nine branches also forms a cycle in an 8-node graph, so it is incorrect.

4. Fundamental Loops in a Network

   What is a fundamental loop with respect to a tree of a network graph?

   1. A set of branches removed from the tree
   2. Any cycle present in the network
   3. A sequence of nodes with no repeated branches
   4. A unique loop formed by adding one link to the tree

   Explanation: A fundamental loop is the unique cycle created when a single link (also called a chord) is added to a tree. Any cycle present in a network might not necessarily be fundamental, as fundamental loops are specifically generated this way. A set of branches removed from a tree relates to cut-sets, not loops. A sequence of nodes with no repeated branches could describe a path, not a fundamental loop.

5. Defining a Graph

   Which of the following statements correctly defines a graph in the context of network topology?

   1. A straight line of nodes with no connections
   2. A pictorial representation of voltage levels
   3. A set of nodes with only one branch
   4. A collection of nodes connected by branches

   Explanation: A graph, within network topology, refers to a collection of nodes connected by branches (edges), forming the basis for analysis. A straight line of nodes with no connections lacks the necessary branches, so it does not qualify as a graph. A set of nodes with only one branch is too limited and cannot represent most networks. A pictorial representation of voltage levels describes a different concept entirely, unrelated to graph structure.