Understanding and Applying Network Diagrams, Explained

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Understanding and Applying Network Diagrams

Project Management · Chapter 5: Project Management Tools and Analytical TechniquesSection 5.1 · lesson 30 of 7313 min · free with a free account

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In this lesson

Drawing and checking activity-on-node and activity-on-arrow project networks.

  • Compare the activity-on-node and activity-on-arrow conventions for drawing a project network
  • Draw a network from an activity list and check it by counting arrows
  • Identify paths, burst points, and merge points and total the durations along each path
  • Explain when dummy activities are needed and how to find loops, dangling activities, and redundant links

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Transcript

Everything said in the video, section by section (1,939 words). Read along, or search it.

Opening Question

One Missing Arrow, Five Extra Days

Dana, a scheduling coordinator, showed a skeptical board her plan to open a new clinic: 24 working days. One arrow was missing from her drawing. With it in place, the real figure was 29 days. How does a simple drawing catch an error like that, before anyone is booked? That is the job of a network diagram.

Purpose

Making Sequence and Dependency Visible

A network diagram is a drawing in which every activity appears once, and arrows show which must come before which. Its job is to make sequence and dependency visible, so logic errors show up before any dates are calculated. In a long table, every row looks reasonable on its own. On a drawing, the same mistake shows up as a floating box, a skipped step, or an arrow pointing backward. Date arithmetic takes the logic as given. Wrong logic gives precisely wrong dates, found late, when people are already booked. And the people doing the work can follow a drawing, and often spot a missing step. It shows sequence only, not a calendar.

Three Inputs

Activities, Predecessors, and Durations

Drawing needs three inputs from planning. First, the activity list, each activity with a unique identifier, a short code such as A or B. Second, each activity's predecessors, the activities that must come first. If B names A, then B is A's successor. Third, each activity's duration, the working time it should take. Before drawing, run four checks. Identifiers are unique. Every predecessor named is on the list. No activity names itself. And at least one activity has no predecessor, and at least one has no successor.

Activity-on-Node

Boxes Are Activities, Arrows Are Dependencies

Two conventions draw the same plan. In the activity-on-node convention, each activity is a box, called a node. The box carries the activity's identifier, its name, and its duration. The arrows between boxes show dependency, and nothing else. An arrow has no name and no duration. A start marker and a finish marker give the diagram one entry and one exit. They are not activities, and represent no work. This convention is also called the precedence diagramming method, and most scheduling software uses it.

Activity-on-Arrow

Arrows Are Activities, Circles Are Events

In the activity-on-arrow convention, the roles flip. Each activity is an arrow, with its identifier, name and duration written along it. The circles are events. An event is a point in time, when every arrow entering it has finished, and every arrow leaving it may begin. An event takes no time. The first event is the project's start, and the last is its completion. Events are numbered, usually lower at an arrow's tail than at its head. So an activity can be named by its pair of numbers, such as three, five. This is the older of the two conventions.

Side by Side

Opposite Meanings for Nodes and Arrows

Side by side, the two conventions give opposite meanings to nodes and arrows. In the node convention a node is an activity, but in the arrow convention it is an event. An arrow is a dependency in one, and an activity in the other. Only the arrow convention ever needs dummy activities, which we'll meet shortly. And only the node convention handles every relationship type and lag directly. The arrow convention is built for finish-to-start.

Worked Example

Ashgrove Library Tool Room Activities

Now build one. Ashgrove Community Library is fitting out a room with shared tools. Durations are in working days. A, approve the room plan, has no predecessor. B, order furniture, and C, order equipment, both follow A. D waits for the furniture delivery after B, and E assembles the furniture after D. F waits for the equipment after C, and G inspects it after F. H, arrange the room layout, needs both E and G. Then I, test and train staff, and finally J, open the room.

Drawing Order

Placing Boxes From Left to Right

Draw in a fixed order. Place a start marker at the left, then every activity with no predecessor. Only A qualifies. B and C each name only A, so they go to its right, one above the other, since neither depends on the other. Continue outward. D after B, then E after D. On the lower row, F after C, then G after F. H names both E and G, so it sits to the right of both, with an arrow from each. Then I after H, and J after I. J is the only activity nobody names, so it alone gets the arrow to the finish.

Arrow Count Check

Ten Predecessors Means Twelve Arrows

Now check it. Every activity except the markers needs an arrow in, and an arrow out. The quickest test is a count. The list named ten predecessors in all, so the drawing needs ten arrows between activities, plus one from the start, and one to the finish: twelve in all. Count them, and they match.

Paths

Parallel Chains, Burst and Merge Points

A path is a continuous chain you can follow along the arrows, from start to finish. Here, the upper chain B, D, E and the lower chain C, F, G are parallel paths. They split apart and rejoin, sharing nothing in between. Ordering furniture doesn't depend on ordering equipment, so both chains can run at the same time. Where they split is a burst point, an activity with more than one successor. Two arrows leave A. Where they rejoin is a merge point, an activity with more than one predecessor. Two arrows enter H, and H waits for both. H, I and J at the end form a sequential path, each waiting for the one before.

Path Totals

Eighteen Days Versus Nineteen Days

Reading a finished diagram needs no dates. Trace every route from start to finish, and add the durations along it. Path one runs through the upper chain: two, one, six, three, two, three, one. Eighteen days. Path two runs through the lower chain: two, two, seven, two, two, three, one. Nineteen days. The longest total, nineteen, is the shortest time in which all the work can be done. But a path total is a length of time, not a calendar.

Quick Check

Burst Point, Merge Point, or Both

Quick check, on a new plan. In a shop refit, activity K needs three activities to finish first, and two other activities wait on K. Is K a burst point only, a merge point only, or both? Pause, and decide. Both. Three arrows enter K, so it is a merge point, and it can't begin until all three are finished. Two arrows leave it, so it is also a burst point. One activity can be both at once.

Dummy Activities

Keeping the Logic True

Back to the arrow convention. It has one tool the node convention never needs: the dummy activity. A dummy is a dashed arrow between two events. It takes no time, uses no resources, and does no work. It only carries a dependency. First use: keeping the logic true. X must wait for P and Q, but Y waits for Q only. If P and Q ended at one event, Y would wrongly wait for P as well. So P ends at event two, and Q at event three. A dummy from three to two tells X to wait for Q too.

Dummy Activities

Giving Each Activity a Unique Number Pair

Second use: a unique pair of numbers. S and T both start at event one, and both must finish before U. Drawn between the same two events, both would be called one, two, and software that names activities by pair can't tell them apart. So T ends at its own event three, and a dummy from three to two lets U still wait for both.

Why Nodes Need None

Each Box Has Its Own Identity

The node convention needs no dummies, for a structural reason. Each box has its own identity, and can receive any mix of arrows. P, Q, X and Y are just four boxes, with arrows from P to X, from Q to X, and from Q to Y. And not every arrow diagram needs a dummy. The Ashgrove network converts cleanly: A is one, two, B is two, three, and so on, to J at nine, ten. Each activity starts at an event entered by exactly its listed predecessors. Many dummies are a warning sign of intricate logic, and each one is one more thing to check.

Common Mistakes

Loops, Dangling Activities, and Redundant Links

Four errors cause most faulty diagrams. A loop is a chain that returns to its own start. A waits for C, C waits for B, and B waits for A. None of them can ever begin. A dangling activity is attached at one side only. Ask the owner what really comes before or after it. Don't just tie it to the finish. A redundant link repeats a connection that a longer chain already implies, like an extra arrow from A to C when A leads to B, and B to C. Crossing lines don't change the logic, but they hide it. Rearrange the rows, so linked boxes sit close together. The arrow convention adds two more: two activities sharing one event pair, and a dummy that creates a dependency the list doesn't contain.

Review

Checking the Drawing Against the List

A review catches all of these by comparing the drawing with the list, in both directions. For every row of the list, the arrows entering that activity must match its predecessors. And every arrow on the drawing must appear in the list. The reviewer should be someone who didn't draw it. The person who drew it tends to read it as intended, not as drawn.

Quick Check

Choosing a Convention for a Hospital Plan

Quick check. A hospital team's plan has start-to-start links with lags. Nurses and managers will both read it, and it will be built in scheduling software. Which convention fits it best: activity-on-node, activity-on-arrow, or either one equally? Pause, and decide. Activity-on-node. It shows start-to-start links and lags directly on its arrows, new readers follow boxes easily, and it's what scheduling software builds. The arrow convention would have to split activities to fake those links, and the nurses would first need events explained.

Choosing a Convention

When Nodes or Arrows Fit

So when does each fit? The node convention needs no dummies, every box is a complete task, and it handles every relationship type. Its costs are space, and arrows that give no sense of time. The arrow convention draws simple finish-to-start logic compactly, and its events make natural reporting points. Its costs are dummies, and an idea of events that new readers must learn. A simple finish-to-start plan, reported by event, or an existing arrow plan, may suit arrows. Switching convention mid-project can itself cause errors. Which should be the default is argued. Whether people really make fewer errors with one is an empirical question, and no settled study is cited here. Which to teach first depends on what the teaching is for. This course carries the node convention forward, because the date calculations are built on it.

Back to the Clinic

The Missing Inspection Sign-Off

Back to Dana and her clinic. Her first drawing used the arrow convention, because it fit on one page. At the briefing, one board member asked what the circles were, and another read the arrows as things to buy. The meeting went on how to read the drawing. She redrew it in the node convention, then checked it against the list in both directions. The box for opening to patients had one arrow entering it, but the list named two predecessors. The inspection sign-off was missing. With that arrow added, the longest path grew from 24 days to 29. She presented the longer figure now, rather than correct it later.

Key Takeaways

Nodes, Arrows, Points, and Review

To recap. A network diagram makes the logic visible, before any dates. Node: boxes are activities, and arrows are dependencies. Arrow: arrows are activities, and circles are events. Count arrows. Two or more leaving is a burst point, and two or more entering is a merge point. Dummies exist only in the arrow convention, to keep the logic true. And review the drawing against the list, both ways.

Reflection

Helping Readers Who Never Draw Networks

Something to think about. Your plan will be read by people who will never draw one. Which convention would you hand them, and what would you add to help them read it?

About Project Management at UPI Study

Project Management (Business 230) is a self-paced online course of 73 video lessons in 12 chapters, from starting and defining a project to planning, budgets, scheduling tools, proposals, contracts, execution, monitoring, closure, teams and certification. It carries a NCCRS credit recommendation for 3 semester credits.

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Why students take Project Management with UPI Study

How projects are planned, run and closedProject Management teaches how to deliver work on time and on budget: scope, schedules, the critical path, budgets and earned value, risk, contracts, monitoring and closing a project, and leading the team. It is a common course in business, management and engineering degrees.
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130,000+students helped with college creditsACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.

Where the credit goes

Universities that work with NCCRS

Project Management carries a NCCRS credit recommendation. These universities work with NCCRS; some are UPI Study's signed partners. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.

Thomas Edison State UniversityThomas Edison State UniversitySigned partnerUniversity of the PeopleUniversity of the PeopleSigned partnerCharter Oak State CollegeCharter Oak State CollegeSigned partnerStrayer UniversityStrayer UniversitySigned partnerColumbia Southern UniversityColumbia Southern UniversitySigned partnerIndiana TechIndiana TechSigned partnerPenn StatePenn StateWorks with NCCRSSouthern New Hampshire UniversitySouthern New Hampshire UniversityWorks with NCCRSSUNYSUNYWorks with NCCRS +many more cooperating universitiesFind my college →

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FAQ

Questions students ask us

About Understanding and Applying Network Diagrams

What is the difference between activity-on-node and activity-on-arrow diagrams?
In activity-on-node diagrams each activity is a box and arrows show only dependencies, while in activity-on-arrow diagrams each activity is an arrow and the circles are events. Activity-on-node, also called the precedence diagramming method, handles every relationship type and lag directly and is what most scheduling software uses. Activity-on-arrow is the older convention, built for finish-to-start logic, and may need dummy activities.
What is a dummy activity in a network diagram?
A dummy activity is a dashed arrow in an activity-on-arrow diagram that takes no time, uses no resources, and only carries a dependency. It keeps logic true, for example when X waits for P and Q but Y waits only for Q. It also gives two parallel activities their own pair of event numbers. Activity-on-node diagrams never need dummies.
What are burst points and merge points in a project network?
A burst point is an activity with more than one successor, and a merge point is an activity with more than one predecessor. If three activities must finish before activity K and two others wait on K, then K is both a merge point and a burst point. A merge point cannot begin until every one of its predecessors has finished.
What are common errors in project network diagrams?
The most common errors are loops, dangling activities, redundant links, and crossing lines that hide the logic. A loop is a chain that returns to its own start, so none of its activities can begin. A dangling activity is attached on one side only. A redundant link repeats a connection a longer chain already implies. A reviewer who did not draw the diagram should check it against the activity list both ways.

About the Project Management course

How many college credits is Project Management?
Project Management (Business 230) carries a NCCRS credit recommendation for 3 semester credits. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.
How much does Project Management cost and what is included?
$250, paid once, with lifetime access: all 73 video lessons, a practice quiz after each, the graded work and final exam, and an official transcript when you finish. Students who want several courses choose UPI Study PRO instead.
Which universities accept UPI Study credits?
UPI Study has signed partner agreements with universities such as Thomas Edison State University, University of the People and Charter Oak State College, and works with universities such as Penn State, SNHU and SUNY. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities. Use "Find my college" on this page to check yours.
How long does Project Management take?
It is self-paced with no deadlines. The 73 lessons total about 15 hours of video; most students add reading and practice time and finish in a few weeks to a few months, on their own schedule.
How are the exams done?
Quizzes and assignments are online in the course. The final exam is taken online with proctoring; a person on the UPI Study team checks assignments, usually within two days.
How do my credits reach my college?
When the course shows 100% complete, request the official transcript from your dashboard. It is sent to the college you name, and you can send it to more than one. Check your college first with "Find my college" on this page, or ask Athena.

Ready for the full course? Earn 3 credits in Project Management.

73 video lessons, a quiz after each one, and the graded work that earns the credit. Recommended for credit by NCCRS.

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