DSA1 | Week 3
Representing Graphs
Graphs
Model relationships between entities.
Graphs: Terminology
Vertices & Edges
Vertices are adjacent if there is an edge between them; and they are the endpoints of said edge.
An edge is incident to its endpoints.
The (out)-neighbors of a vertex X are all the vertices Y such that (X,Y) is an edge.
The degree of a vertex is the number of neighbors it has.
Representing Graphs
1. Adjacency Matrix
2. Adjacency Lists
3. Edge Lists
Three popular styles.
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Adjacency Matrix
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Adjacency Matrix
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Adjacency Matrix
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Adjacency Matrix
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Adjacency Matrix
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Adjacency Matrix
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& so on.
Adjacency List
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Adjacency List
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Adjacency List
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Adjacency List
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& so on.
Edge List
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Edge List
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Edge List
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Edge List
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& so on.
Official Running Times
Brilliant.
When the procedure only needs constant time.
Decent.
When the procedure always wraps up in, and sometimes needs,
time proportional to the maximum degree of the graph.
(n/m)-tolerable.
When the procedure always wraps up in, and sometimes needs,
time proportional to the number of vertices/edges in the graph.
(n/m)-painful.
When the procedure always wraps up in, and sometimes needs,
time proportional to the number of vertices/edges in the graph squared.
| Adj. Matrix | Adj. List | Edge List | |
|---|---|---|---|
| Adding a vertex | |||
| Deleting a vertex | |||
| Adding an edge | |||
| Deleting an edge | |||
| Finding degree(v) | |||
| Check if (u,v) is an edge |
| Adj. Matrix | Adj. List | Edge List | |
|---|---|---|---|
| Adding a vertex | Painful | ||
| Deleting a vertex | Painful | ||
| Adding an edge | Brilliant | ||
| Deleting an edge | Brilliant | ||
| Finding degree(v) | Tolerable | ||
| Check if (u,v) is an edge | Brilliant |
| Adj. Matrix | Adj. List | Edge List | |
|---|---|---|---|
| Adding a vertex | Painful | Tolerable | |
| Deleting a vertex | Painful | Tolerable | |
| Adding an edge | Brilliant | Brilliant | |
| Deleting an edge | Brilliant | Decent | |
| Finding degree(v) | Tolerable | Decent | |
| Check if (u,v) is an edge | Brilliant | Decent |
| Adj. Matrix | Adj. List | Edge List | |
|---|---|---|---|
| Adding a vertex | Painful | Tolerable | Decent |
| Deleting a vertex | Painful | Tolerable | Tolerable |
| Adding an edge | Brilliant | Brilliant | Brilliant |
| Deleting an edge | Brilliant | Decent | Tolerable |
| Finding degree(v) | Tolerable | Decent | Tolerable |
| Check if (u,v) is an edge | Brilliant | Decent | Tolerable |
Recap: what we have seen so far
Arrays v/s Lists
| Lookups | Addition (at start) |
Addition (at end) |
Deletions | |
|---|---|---|---|---|
| Arrays | Easy | Hard | Depends | Prop to location of element being deleted |
| Lists | Hard | Easy | Depends | Prop to location of element being deleted |
| Adj. Matrix | Adj. List | Edge List | |
|---|---|---|---|
| Adding a vertex | Painful | Tolerable | Decent |
| Deleting a vertex | Painful | Tolerable | Tolerable |
| Adding an edge | Brilliant | Brilliant | Brilliant |
| Deleting an edge | Brilliant | Decent | Tolerable |
| Finding degree(v) | Tolerable | Decent | Tolerable |
| Check if (u,v) is an edge | Brilliant | Decent | Tolerable |
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Try them all
Explore one thoroughly
What do you do when you have many different options?
Navigating Graphs
Navigating Graphs
Try them all
Explore one thoroughly
What do you do when you have many different options?
Try them all
Explore one thoroughly
What do you do when you have many different options?
Navigating Graphs
DSA1 | Week 3
By Neeldhara Misra
