MPPSC 2020 Prelims Paper-I · Question 58 of 100

A (Graph) or B (Tree) — both are accepted (grace). A social network is a set of people (nodes) joined by relationships (edges), so its natural and most general representation is a GRAPH — that is why option A is correct. Option B, Tree, is also credited because a tree is itself a special kind of graph (a connected, acyclic graph); hierarchical social structures — an organisation's reporting chain, a family tree, a follower/sharing cascade — are trees, and a tree therefore also validly represents a social network. Because both are defensible, the commission accepted either answer.

• (c)Star — Star is a fixed network topology (every node wired to one central hub) borrowed from computer networking — a rigid special layout, not a general model of arbitrary social relationships, so it was not credited.
• (d)Ring — Ring is a fixed network topology (each node linked to two neighbours forming a closed loop); it cannot capture the many-to-many ties of a social network, so it was not credited.

In graph theory a graph G = (V, E) is a set of vertices V (nodes) and edges E (links). Social Network Analysis models people as vertices and their ties (friendship, follows) as edges. A tree is a special graph — connected and acyclic (n vertices, n-1 edges, no cycles). Star and Ring are standard physical network topologies.

The question really asks 'which structure models a social network'. Graph is the textbook answer; Tree is accepted because it is a sub-type of graph well suited to hierarchies. Star and Ring are computer-network topologies, so they are the intended distractors — which is why the grace covers exactly the two graph-family answers.

• A graph = vertices (nodes) + edges (links); the standard model in Social Network Analysis (people = nodes, ties = edges).
• A tree is a special graph: connected and acyclic (no cycles), good for hierarchies.
• Star and Ring are network topologies (central hub; closed loop) from computer networking.
• Grace question: the commission's key accepted both Graph and Tree.

• Assuming a single answer when the key accepted two (Graph and Tree)
• Confusing graph-theory structures (graph/tree) with physical network topologies (star/ring)

Computer-aptitude/IT sections ask 'a social network is represented as' or 'a tree is a ... graph'. Remember: graph = general model; tree = acyclic special case.

No directly related past PYQ was found.

• practice — not a real PYQ

  In graph-theory terms, a tree is best described as:

  • (a)A connected acyclic graph
  • (b)A graph with exactly one cycle
  • (c)A disconnected graph
  • (d)A complete graph

  Answer(a) A connected acyclic graph — a tree has no cycles and n-1 edges for n nodes.

• practice — not a real PYQ

  In Social Network Analysis, individuals and the relationships between them are modelled respectively as:

  • (a)Nodes and edges
  • (b)Edges and nodes
  • (c)Rows and columns
  • (d)Keys and values

  Answer(a) Nodes and edges — people are nodes, ties are edges.