CAT DILR Networks: 3 Solved Sets and the Mapping Method
A targeted DILR guide on the network and connections set family. Covers the 4-step mapping method, the edge list versus adjacency matrix decision, the directed versus undirected trap that compounds across every question, and three fully solved CAT-style network sets covering city routes, reporting hierarchies, and an 8-node communication matrix.
CAT DILR Networks: 3 Solved Sets and the Mapping Method
What does a DILR network set actually test? The honest answer is graph-theory instinct, not arithmetic. Most DILR set types reward constraint-elimination skills built across years of seating arrangement and tournament practice, but networks and connections DILR CAT sets reward a completely different mental tool: the ability to translate a paragraph of "A connects to B, B connects to C, D connects to A and E" into a clean visual graph or adjacency matrix that becomes the source of truth for every question. Aspirants who try to solve these without drawing the network spend twice as long and get half the accuracy.
This guide decodes the network and connections DILR set family for CAT 2026: the 4-step graph-reading approach, when to draw an edge list versus an adjacency matrix, the directed versus undirected distinction that compounds across every question, and 3 fully solved CAT-style sets. Use this alongside the DILR data interpretation guide and the DILR games and tournaments guide for the broader DILR set taxonomy.
Networks DILR sets test graph mapping, not constraint elimination. Solve in 4 steps: identify entities and edge type (directed or undirected), build edge list or adjacency matrix, derive secondary information through graph traversal, then answer questions from the data structure. Edge list works for under 8 nodes; adjacency matrix beats it for dense networks of 8 plus nodes. This guide includes 3 fully solved CAT-style sets.
What a network DILR set actually tests
The 4-step network mapping method
Edge list versus adjacency matrix decision
Directed versus undirected networks
Solved Set 1: Routes between cities
What a Network DILR Set Actually Tests
A network DILR set looks innocent on first read. The paragraph describes some entities (cities, people, departments, computers) and the relationships between them (routes, friendships, reporting lines, cables). Then it asks questions about connectivity, shortest paths, total connections, or reachability. The visual instinct is to treat it like a constraint puzzle. That instinct burns 15 minutes on a set that should take 8.
The set is actually a graph theory problem disguised as a paragraph. The entities are nodes, the relationships are edges, and almost every question is a graph property query: degree of a node, shortest distance between two nodes, number of components, reachability, or completeness. The candidate who recognises the underlying graph structure in the first 90 seconds and draws the right data structure (edge list or adjacency matrix) solves the questions by reading the structure, not by re-tracing the paragraph for every question.
Three signals identify a network set in the first 30 seconds: the paragraph names a fixed set of entities (5 to 12 typically), the paragraph describes pairwise relationships between them, and at least one question asks about connectivity, distance, or relationship count. If all three are present, switch to graph-mapping mode immediately. Do not try to solve it like a seating arrangement.
The 4-Step Network Mapping Method
Networks DILR sets become tractable when you treat them as graph-construction problems. The 4 steps below are universal across every network set the CAT has set since 2022 and every CAT-style mock the major coaching institutes have released.
Identify entities and edge type
List the entities (nodes) and decide whether the relationships are directed or undirected. Physical connections (cables, routes, friendships) are usually undirected. Hierarchical or one-way relationships (reporting lines, parent-child, one-way streets) are directed. This single decision changes every downstream calculation.
Build the right data structure
Choose edge list for sparse networks under 8 nodes; choose adjacency matrix for dense networks of 8 plus nodes or when questions ask about reachability and connection counts. Build it once, cleanly, before attempting any question.
Derive secondary information
Calculate degree of each node (number of connections), identify components (disconnected subgroups), spot articulation points (nodes whose removal disconnects the network), and note any obvious symmetries. This pre-work saves 30 to 40 seconds per subsequent question.
Answer from the data structure
Every question reads off the graph or matrix, not the original paragraph. The graph is now the source of truth. Re-reading the paragraph mid-set indicates that step 2 was incomplete; fix the data structure before continuing.
Edge List Versus Adjacency Matrix Decision
The two data structures serve different question types. Edge list is a sequential list of all the pairs that have a connection (A-B, B-C, C-D). It is fast to write and easy to scan for specific pair questions. Adjacency matrix is a grid where rows and columns represent nodes and a 1 in cell (i, j) indicates a connection from i to j. It takes longer to draw but answers count-based and reachability questions almost instantly.
| Question type | Best structure | Time per question |
|---|---|---|
| Does A connect to B? | Either | 3 to 5 seconds |
| How many neighbours does A have? | Matrix (sum the row) | 5 seconds |
| Shortest path from A to D | Visual graph drawing | 15 to 25 seconds |
| Total number of connections in network | Matrix (sum upper triangle) | 10 seconds |
| Are any two nodes in different components? | Matrix (check reachability) | 20 seconds |
| Which node is most connected? | Matrix (max row sum) | 15 seconds |
The structure choice is not aesthetic. A network with 6 nodes and 8 edges resolves faster on an edge list because the matrix would have 18 of its 30 cells empty and reading sparse matrices wastes scan time. A network with 10 nodes and 20 edges resolves faster on a matrix because tracing through an edge list 20 times for the 5 to 6 questions is slower than the one-time matrix setup.
For networks at the threshold (7 to 9 nodes), check the questions before choosing the structure. If most questions ask about specific pairs, use the edge list. If most questions ask about counts, degree distributions, or reachability, use the matrix. The 30 seconds spent on this decision saves 2 minutes across the set.
Directed Versus Undirected Networks
An undirected network has symmetric edges. If A connects to B, then B connects to A. The adjacency matrix is symmetric across its diagonal. Physical-connection sets (city routes, friendship circles, communication links, cable networks) are usually undirected. A directed network has asymmetric edges. If A reports to B, then B does not report to A. The adjacency matrix is not symmetric. Hierarchical sets (reporting lines, parent-child, one-way roads) are directed.
The mistake aspirants make most often: assuming a set is undirected because it sounds physical, when in fact the relationship is one-way. A common CAT trap is "A sent a message to B, B sent a message to C". This is directed (sending is one-way), not undirected (acquaintance is two-way). The adjacency matrix for this is fundamentally different, and every subsequent question answers differently.
Reading "A is connected to B" and assuming undirected when the paragraph context implies directional. Always check the verb. "Connects to" and "linked with" are usually undirected. "Reports to", "sends to", "follows", "leads to" are usually directed. When uncertain, draw both versions briefly and check which one makes the dataset consistent.
Solved Set 1: Routes Between Cities
Six cities and the road network
Step 1: Type identification
Undirected (two-way roads), 6 nodes, 7 edges. Sparse network, so edge list is sufficient.
Step 2: Edge list
Step 3: Derive degrees
Degree of A = 2 (B, D). Degree of B = 3 (A, C, E). Degree of C = 2 (B, F). Degree of D = 2 (A, E). Degree of E = 3 (B, D, F). Degree of F = 2 (C, E).
Sample question and answer
Q: What is the shortest path between A and F? Trace from A: A to B to C to F (3 edges) or A to B to E to F (3 edges) or A to D to E to F (3 edges). Shortest path = 3 edges. Q: Which city is most centrally connected? B and E both have degree 3, the highest. Q: If road A-D is removed, can A still reach D? A to B to E to D = 3 edges. Yes, A reaches D via B and E.
Solved Set 2: Departmental Reporting Lines
Five departments and their reporting hierarchy
Step 1: Type identification
Directed (one-way reporting), 5 nodes, 4 edges. Hierarchical tree structure.
Step 2: Edge list (directed, source then target)
Step 3: Derive levels
Level 0 (root): X. Level 1 (direct reports to X): W, Y. Level 2 (reports to W): Z. Level 3 (reports to Z): V.
Sample question and answer
Q: How many departments are below W in the hierarchy? Z reports to W and V reports to Z. So 2 departments (Z, V) are below W. Q: Which department has no one reporting to it? V and Y have no incoming reports. Q: If a memo from V reaches X, how many departments does it pass through? V to Z to W to X = 3 hops, passing through Z and W (2 intermediate departments).
Solved Set 3: Communication Network
Eight team members and their communication links
Step 1: Type identification
Undirected (two-way), 8 nodes, 10 edges. Dense enough to warrant adjacency matrix.
Step 2: Adjacency matrix (1 = connected, 0 = not)
Step 3: Derive degrees from row sums
P = 2, Q = 2, R = 3, S = 3, T = 3, U = 3, V = 2, W = 2. Total degree = 20, so edge count = 10 (matches).
Sample question and answer
Q: How many direct communication links does R have? Sum row R = 3 (with P, S, T). Q: Can P reach W? P to R to T to U to W (4 hops) or P to Q to S to U to W (4 hops). Yes. Q: Which member has the highest number of direct contacts? R, S, T, U all tie at 3 (each has the maximum row sum).
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Get My Network DILR Practice PackPutting the Method to Work
Networks DILR sets are one of the few CAT DILR set types where prior pattern recognition compresses solving time by 60 to 70 percent. Aspirants who have solved 10 to 15 network sets recognise the graph structure in 30 seconds, choose the right data structure in another 30, and answer the questions in 2 to 3 minutes per question. Aspirants who have not seen a network set before spend 4 to 6 minutes on initial reading alone.
The practice path that works: solve the 3 sets above untimed first, then re-solve them timed at 12 minutes per set, then attempt 10 to 12 new network sets across 4 weeks with the 4-step method enforced on every set. After that volume, network sets become a confident pick on exam day rather than a skip. The Venn diagrams CAT 2026 guide and the data sufficiency CAT 2026 guide cover adjacent DILR set types that share the same data-structure-first mindset.
- Recognise the network set in the first 90 seconds: fixed entities, pairwise relationships, connectivity questions.
- Identify directed versus undirected before drawing anything; the wrong assumption compounds across every question.
- Choose edge list for under 8 nodes; choose adjacency matrix for 8 plus nodes or count-heavy questions.
- Derive degree, components, and articulation points before attempting any question.
- Answer every question from the data structure, not the original paragraph.
- Practice 10 to 15 network sets across 4 weeks to compress recognition time and lock the 4-step method.
Networks DILR is graph theory in disguise. Draw the graph, and the questions answer themselves.
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What is a network or connections set in CAT DILR?
A network or connections set is a DILR question type where the dataset describes relationships between entities (cities connected by routes, people connected by communication links, departments connected by reporting lines). Each entity is a node and each relationship is an edge. Questions test the candidate's ability to map relationships as a graph and answer connectivity, shortest-path, or completeness questions. The set rewards graph-theory instincts over constraint-elimination skills.
How do you solve a networks DILR set?
Use the 4-step mapping method. Step 1: identify entities and edge type (directed or undirected). Step 2: build an edge list (under 8 nodes) or an adjacency matrix (8 plus nodes). Step 3: derive secondary information (degrees, components, articulation points). Step 4: answer every question from the data structure, not the paragraph. The graph becomes the source of truth.
When should I draw an edge list vs an adjacency matrix?
Edge list for sparse networks under 8 nodes where pair-specific questions dominate. Adjacency matrix for dense networks of 8 plus nodes or when questions ask about degree counts, total connections, or reachability. The matrix takes longer to set up but answers count-based questions in 5 seconds each, which beats re-tracing edge lists 5 times during the question round.
Are network sets common in CAT DILR?
Networks and connections sets appeared in CAT 2022 and CAT 2024 papers, and have been seen in 2 to 3 mocks per quality coaching institute every test cycle. They are not the most common DILR set type, but skipping them entirely can cost 3 to 4 marks in a single CAT paper. They are also one of the few set types where prior pattern recognition compresses solving time by 60 to 70 percent, making them high-ROI for focused preparation.
What is the difference between directed and undirected networks in CAT?
An undirected network has symmetric edges: if A connects to B, then B connects to A. Most physical-connection sets (cities, cables, friendships) are undirected. A directed network has asymmetric edges: if A reports to B, then B does not report to A. Most hierarchical sets (reporting lines, parent-child, one-way roads) are directed. Identifying the type at step 1 is critical because the adjacency matrix has different symmetry properties and misidentification compounds across every question.
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