Rules and Guidelines for Drawing a Network Diagram
A network diagram is a graphical representation of the activities and events of a project. It shows the sequence and precedence relationships among project activities.
While drawing a network diagram, especially an Activity-on-Arrow (AOA) network, certain rules and conventions should be followed to ensure that the network is logically correct, clear, and easy to analyse.
Network Diagram Rules in Operations Research
There are several rules that apply to the handling of events and activities in a project network, and so guidelines for Drawing Network Diagram are as follows:
1. Each Activity Should Be Represented by One Arrow
In an AOA network, each activity is represented by one and only one arrow. Therefore, the same activity should not be represented twice in the network.
This means that no single activity can be represented in the network twice. This differs from the case where a single activity is divided into segments. In this case, each segment could be depicted by a different arrow.
The arrow represents the activity, while its starting and ending events identify the activity.
Example:
1 → A → 2
Here, Activity A is represented by the arrow from Event 1 to Event 2.
Note: This rule applies specifically to the Activity-on-Arrow (AOA) representation.
2. Two Activities Should Not Have the Same Starting and Ending Events
Two different activities should not have the same starting event and ending event because activities in an AOA network are identified by their starting and ending event numbers.
For example, it is incorrect to represent both A and B as:
1 → A → 2
1 → B → 2
A dummy activity may be introduced when necessary to give the activities unique identification and, more importantly, to preserve the correct precedence relationship.
A dummy activity has zero duration and does not consume project resources. It is generally represented by a dashed arrow.
That is, the same beginning and end event cannot be used to identify two activities. In such cases, as shown in Figure, a dummy activity is introduced to solve the problem..
3. Maintain the Correct Precedence Relationship
The network must correctly represent the order in which activities are performed.
Before drawing an activity, ask:
What activity must be completed first in order for this activity to begin? That is, which activities must be completed before this activity can start?
Which activities can start after this activity is completed?
What activities must occur simultaneously with this activity?
What activities must follow this activity?
Which activities can proceed independently or in parallel?
These above question must be checked whenever any activity is added to a network to ensure that the precedence relationship in an arrow diagram is correct.
For example, if Activity B can start only after Activity A is completed, the network should show:
A → B
The network must represent the actual logical or technical dependency among project activities.
4. Avoid Loops in the Network
A project network should not contain a loop or cycle.
A loop would imply that activities have to be performed repeatedly in a cycle, which does not represent the normal logical structure of a project network.
Therefore, the network should progress continuously from the start event toward the finish event.
5. Draw the Network from Left to Right
As a standard convention, the network should be developed from left to right.
The start event is generally placed on the left and the finish event on the right.
The arrows should show the logical progression of the project from earlier activities toward later activities.
6. Avoid Crossing Arrows Where Possible
Arrows should preferably be arranged so that they do not cross one another.
Crossing arrows can make a network difficult to read and may create confusion about activity relationships.
However, avoiding crossings is primarily a drawing convention for clarity, rather than a basic mathematical rule of network analysis.
7. Prefer Straight and Clearly Arranged Arrows
Straight arrows are generally preferred because they make the network easier to read.
The network should be arranged neatly so that the relationship between activities and events can be understood easily.
The important point is not the artistic shape of the arrow but the logical relationship that the arrow represents.
8. The Length of an Arrow Does Not Represent Activity Duration
The physical length of an activity arrow has no significance in an AOA network.
For example, an activity requiring 2 days and another activity requiring 10 days do not have to be drawn with different arrow lengths.
The actual activity duration is written or assigned separately.
Thus:
Arrow length ≠ Activity duration
This is an important point for examinations. Standard network-construction rules explicitly state that the length of an arrow has no significance.
9. Arrow Direction Shows Logical Progression
The direction of an arrow is important.
It indicates the progression from the beginning event to the ending event and therefore helps represent the precedence relationship.
For an activity represented as:
i → j
Event i is the starting event and Event j is the ending event.
Therefore, it would be incorrect to say that the direction of an arrow is unimportant. Its geometrical shape or physical length is not important, but its direction in the network is important.
10. Number the Events in Logical Sequence
Each event should have a unique number.
The numbering should follow the logical progression of the network. In the standard numbering convention, the starting event is numbered first, and an event receiving a higher number occurs later in the logical sequence.
Thus, for an activity from Event i to Event j:
i < j
For example:
1 → 2 → 3 → 4
This type of numbering is useful for identifying activities and performing network calculations. Fulkerson's numbering procedure also starts with the initial event and assigns progressively higher numbers as the network is developed.
11. Use Dummy Activities Only When Necessary
A dummy activity should not be inserted unnecessarily.
It is used in an AOA network when necessary to:
- maintain the correct precedence relationship, or
- avoid two activities having the same starting and ending events.
A dummy activity has zero duration and consumes no resources.
Therefore, the final network should contain only those dummy activities that are actually required for the correct representation of project logic.
12. The Network Should Have One Start Event and One Finish Event
A standard project network should have:
- One start event, and
- One finish event.
The start event represents the beginning of the project, while the finish event represents the completion of the project.
This provides a clear starting and ending point for the entire project network.
13. Avoid Dangling Activities or Events
The network should be properly connected.
A dangling event is an event that becomes disconnected from the main network—for example, an event from which no further activity emerges even though it is not the final event.
Such unnecessary dangling portions should be avoided because every intermediate part of the network should contribute to the logical representation of the project.
Quick Revision: Rules for Drawing a Network Diagram
| Rule | Key Point |
|---|---|
| 1. One activity – one arrow | Represent each activity once. |
| 2. No identical start and end events | Two activities cannot have the same event pair. |
| 3. Use dummy when necessary | Dummy maintains logic or provides unique identification. |
| 4. Maintain precedence | Predecessor activities must be completed as required. |
| 5. Avoid loops | The network should not contain cycles. |
| 6. Left-to-right progression | Show logical project progression from left to right. |
| 7. Avoid crossing arrows | Prefer a clear, uncluttered layout. |
| 8. Use straight arrows | Helps improve readability. |
| 9. Arrow length has no significance | It does not represent activity duration. |
| 10. Arrow direction matters | It indicates logical progression. |
| 11. Number events logically | Higher numbers represent later events in the network. |
| 12. Avoid unnecessary dummies | Use only required dummy activities. |
| 13. One start and one finish event | Give the project a clear beginning and ending. |
| 14. Avoid dangling | Keep the network properly connected. |
Exam-Friendly Answer
If the question in an examination is:
“State the rules/guidelines for drawing a network diagram.”
You can write:
- Each activity should be represented by one and only one arrow.
- No two activities should have the same starting and ending events.
- Dummy activities should be used when necessary to maintain correct network logic.
- The precedence relationship among activities must be correctly represented.
- The network should not contain loops.
- The network should preferably be drawn from left to right.
- Crossing of arrows should be avoided wherever possible.
- The length of an arrow has no significance.
- Event numbers should be unique and assigned in logical sequence.
- Unnecessary dummy activities should be avoided.
- The network should have one start event and one finish event.
- Dangling events or activities should be avoided.
Suggestions:
1. Avoid arrows that cross each other.
2. Use straight arrows.
3. Use arrows from left to right.
4. The development of a network should be based on logical or technical dependability.
5. The arrows representing various activities are only indicative of logical precedence; thus, the length and direction of the arrows are unimportant.
6. Two events are numbered in such a way that the event with the higher number can occur only after the event with the lower number has finished.
7. In the rough graph, you can use dummy activity as much as you want, but the final network should only have reluctant dummies.
8. The network has only one point of entry, known as the start event, and one point of emergence, known as the end event.
9. The angle formed by the arrows should be as large as possible.
Important Note
These rules are specifically appropriate for the Activity-on-Arrow (AOA) form of project network. They should not be presented as universal rules for every type of network diagram, because modern project-management literature also uses Activity-on-Node (AON) networks, which have different representation conventions. Taha's OR text treats CPM/PERT within its Network Models coverage, while Hillier and Lieberman also distinguish network optimization models from project time-cost analysis.
References
- Hamdy A. Taha, Operations Research: An Introduction, 10th Edition, Pearson.
- Frederick S. Hillier and Gerald J. Lieberman, Introduction to Operations Research, McGraw-Hill Education.
- J. K. Sharma, Operations Research: Theory and Applications, Macmillan India.
- Kanti Swarup, P. K. Gupta and Man Mohan, Operations Research, Sultan Chand & Sons.
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