Can an undirected graph be disconnected?
up vote
0
down vote
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This may be a rather trivial question but I am still trying to get the hang of all the graph theory terms. Nonetheless, I haven't found a source that explicitly says that an undirected graph can only be connected so is it possible to have an undirected graph that is disconnected? And if so, may I have an example one?
Much thanks!
graph-theory connectedness directed-graphs
edited Dec 4 at 23:42
Scientifica
6,33141333
asked Dec 4 at 23:23
DevAllanPer
1296
add a comment |
up vote
0
down vote
favorite
This may be a rather trivial question but I am still trying to get the hang of all the graph theory terms. Nonetheless, I haven't found a source that explicitly says that an undirected graph can only be connected so is it possible to have an undirected graph that is disconnected? And if so, may I have an example one?
Much thanks!
graph-theory connectedness directed-graphs
edited Dec 4 at 23:42
Scientifica
6,33141333
asked Dec 4 at 23:23
DevAllanPer
1296
if they are made of separate pieces.
– hbm
Dec 4 at 23:30
5
Here's an example of (the diagram of) a disconnected undirected graph: $$huge ○,,,, ○$$
– Git Gud
Dec 4 at 23:30
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
This may be a rather trivial question but I am still trying to get the hang of all the graph theory terms. Nonetheless, I haven't found a source that explicitly says that an undirected graph can only be connected so is it possible to have an undirected graph that is disconnected? And if so, may I have an example one?
Much thanks!
graph-theory connectedness directed-graphs
edited Dec 4 at 23:42
Scientifica
6,33141333
asked Dec 4 at 23:23
DevAllanPer
1296
This may be a rather trivial question but I am still trying to get the hang of all the graph theory terms. Nonetheless, I haven't found a source that explicitly says that an undirected graph can only be connected so is it possible to have an undirected graph that is disconnected? And if so, may I have an example one?
Much thanks!
graph-theory connectedness directed-graphs
graph-theory connectedness directed-graphs
edited Dec 4 at 23:42
Scientifica
6,33141333
asked Dec 4 at 23:23
DevAllanPer
1296
edited Dec 4 at 23:42
Scientifica
6,33141333
asked Dec 4 at 23:23
DevAllanPer
1296
edited Dec 4 at 23:42
Scientifica
6,33141333
edited Dec 4 at 23:42
Scientifica
6,33141333
edited Dec 4 at 23:42
Scientifica
6,33141333
6,33141333
asked Dec 4 at 23:23
DevAllanPer
1296
asked Dec 4 at 23:23
DevAllanPer
1296
asked Dec 4 at 23:23
DevAllanPer
1296
1296
if they are made of separate pieces.
– hbm
Dec 4 at 23:30
5
Here's an example of (the diagram of) a disconnected undirected graph: $$huge ○,,,, ○$$
– Git Gud
Dec 4 at 23:30
add a comment |
if they are made of separate pieces.
– hbm
Dec 4 at 23:30
5
Here's an example of (the diagram of) a disconnected undirected graph: $$huge ○,,,, ○$$
– Git Gud
Dec 4 at 23:30
if they are made of separate pieces.
– hbm
Dec 4 at 23:30
if they are made of separate pieces.
– hbm
Dec 4 at 23:30
5
5
Here's an example of (the diagram of) a disconnected undirected graph: $$huge ○,,,, ○$$
– Git Gud
Dec 4 at 23:30
Here's an example of (the diagram of) a disconnected undirected graph: $$huge ○,,,, ○$$
– Git Gud
Dec 4 at 23:30
add a comment |
4 Answers
4
active
oldest
votes
up vote
7
down vote
accepted
Undirected just mean The edges does not have direction. connected means that there is a path from any vertex of the graph to any other vertex in the graph. so take any disconnected graph whose edges are not directed to give an example. following is one:
answered Dec 4 at 23:32
mathnoob
1,744322
add a comment |
up vote
4
down vote
Yes. The simplest such graph is just two vertices (no edges).
answered Dec 4 at 23:30
platty
3,330320
add a comment |
up vote
2
down vote
The definition of graph that I know is the following: A graph consists of two sets $(V,E)$ where $V$ is the set of vertices and $E$ is the set of edges.
The elements of $E$ are subsets (or multisets in the case of loops) of cardinality $2$ of $V$.
A graph is undirected if ${x,y}={y,x}$ where ${x,y},{y,x}in E$ and it is directed if ${x,y}neq {y,x}$.
Therefore, by taking $V={a,b,c}$ and $E={{a,b}}$, you obtain a disconnected undirected graph.
answered Dec 4 at 23:31
Karen
855
add a comment |
up vote
1
down vote
I believe, since you can define a graph $G = (E,V)$ by its edge and vertex sets, it is perfectly ok to have a disconnected graph (i.e. a graph with no path between some vertices). In fact, taking $E$ to be empty still results in a graph.
answered Dec 4 at 23:32
Stuartg98
586
add a comment |
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
7
down vote
accepted
Undirected just mean The edges does not have direction. connected means that there is a path from any vertex of the graph to any other vertex in the graph. so take any disconnected graph whose edges are not directed to give an example. following is one:
answered Dec 4 at 23:32
mathnoob
1,744322
add a comment |
up vote
7
down vote
accepted
Undirected just mean The edges does not have direction. connected means that there is a path from any vertex of the graph to any other vertex in the graph. so take any disconnected graph whose edges are not directed to give an example. following is one:
answered Dec 4 at 23:32
mathnoob
1,744322
add a comment |
up vote
7
down vote
accepted
up vote
7
down vote
accepted
Undirected just mean The edges does not have direction. connected means that there is a path from any vertex of the graph to any other vertex in the graph. so take any disconnected graph whose edges are not directed to give an example. following is one:
answered Dec 4 at 23:32
mathnoob
1,744322
Undirected just mean The edges does not have direction. connected means that there is a path from any vertex of the graph to any other vertex in the graph. so take any disconnected graph whose edges are not directed to give an example. following is one:
answered Dec 4 at 23:32
mathnoob
1,744322
answered Dec 4 at 23:32
mathnoob
1,744322
answered Dec 4 at 23:32
mathnoob
1,744322
answered Dec 4 at 23:32
mathnoob
1,744322
1,744322
add a comment |
add a comment |
up vote
4
down vote
Yes. The simplest such graph is just two vertices (no edges).
answered Dec 4 at 23:30
platty
3,330320
add a comment |
up vote
4
down vote
Yes. The simplest such graph is just two vertices (no edges).
answered Dec 4 at 23:30
platty
3,330320
add a comment |
up vote
4
down vote
up vote
4
down vote
Yes. The simplest such graph is just two vertices (no edges).
answered Dec 4 at 23:30
platty
3,330320
Yes. The simplest such graph is just two vertices (no edges).
answered Dec 4 at 23:30
platty
3,330320
answered Dec 4 at 23:30
platty
3,330320
answered Dec 4 at 23:30
platty
3,330320
answered Dec 4 at 23:30
platty
3,330320
3,330320
add a comment |
add a comment |
up vote
2
down vote
The definition of graph that I know is the following: A graph consists of two sets $(V,E)$ where $V$ is the set of vertices and $E$ is the set of edges.
The elements of $E$ are subsets (or multisets in the case of loops) of cardinality $2$ of $V$.
A graph is undirected if ${x,y}={y,x}$ where ${x,y},{y,x}in E$ and it is directed if ${x,y}neq {y,x}$.
Therefore, by taking $V={a,b,c}$ and $E={{a,b}}$, you obtain a disconnected undirected graph.
answered Dec 4 at 23:31
Karen
855
add a comment |
up vote
2
down vote
The definition of graph that I know is the following: A graph consists of two sets $(V,E)$ where $V$ is the set of vertices and $E$ is the set of edges.
The elements of $E$ are subsets (or multisets in the case of loops) of cardinality $2$ of $V$.
A graph is undirected if ${x,y}={y,x}$ where ${x,y},{y,x}in E$ and it is directed if ${x,y}neq {y,x}$.
Therefore, by taking $V={a,b,c}$ and $E={{a,b}}$, you obtain a disconnected undirected graph.
answered Dec 4 at 23:31
Karen
855
add a comment |
up vote
2
down vote
up vote
2
down vote
The definition of graph that I know is the following: A graph consists of two sets $(V,E)$ where $V$ is the set of vertices and $E$ is the set of edges.
The elements of $E$ are subsets (or multisets in the case of loops) of cardinality $2$ of $V$.
A graph is undirected if ${x,y}={y,x}$ where ${x,y},{y,x}in E$ and it is directed if ${x,y}neq {y,x}$.
Therefore, by taking $V={a,b,c}$ and $E={{a,b}}$, you obtain a disconnected undirected graph.
answered Dec 4 at 23:31
Karen
855
The definition of graph that I know is the following: A graph consists of two sets $(V,E)$ where $V$ is the set of vertices and $E$ is the set of edges.
The elements of $E$ are subsets (or multisets in the case of loops) of cardinality $2$ of $V$.
A graph is undirected if ${x,y}={y,x}$ where ${x,y},{y,x}in E$ and it is directed if ${x,y}neq {y,x}$.
Therefore, by taking $V={a,b,c}$ and $E={{a,b}}$, you obtain a disconnected undirected graph.
answered Dec 4 at 23:31
Karen
855
answered Dec 4 at 23:31
Karen
855
answered Dec 4 at 23:31
Karen
855
answered Dec 4 at 23:31
Karen
855
855
add a comment |
add a comment |
up vote
1
down vote
I believe, since you can define a graph $G = (E,V)$ by its edge and vertex sets, it is perfectly ok to have a disconnected graph (i.e. a graph with no path between some vertices). In fact, taking $E$ to be empty still results in a graph.
answered Dec 4 at 23:32
Stuartg98
586
add a comment |
up vote
1
down vote
I believe, since you can define a graph $G = (E,V)$ by its edge and vertex sets, it is perfectly ok to have a disconnected graph (i.e. a graph with no path between some vertices). In fact, taking $E$ to be empty still results in a graph.
answered Dec 4 at 23:32
Stuartg98
586
add a comment |
up vote
1
down vote
up vote
1
down vote
I believe, since you can define a graph $G = (E,V)$ by its edge and vertex sets, it is perfectly ok to have a disconnected graph (i.e. a graph with no path between some vertices). In fact, taking $E$ to be empty still results in a graph.
answered Dec 4 at 23:32
Stuartg98
586
I believe, since you can define a graph $G = (E,V)$ by its edge and vertex sets, it is perfectly ok to have a disconnected graph (i.e. a graph with no path between some vertices). In fact, taking $E$ to be empty still results in a graph.
answered Dec 4 at 23:32
Stuartg98
586
answered Dec 4 at 23:32
Stuartg98
586
answered Dec 4 at 23:32
Stuartg98
586
answered Dec 4 at 23:32
Stuartg98
586
586
add a comment |
add a comment |
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if they are made of separate pieces.
– hbm
Dec 4 at 23:30
5
Here's an example of (the diagram of) a disconnected undirected graph: $$huge ○,,,, ○$$
– Git Gud
Dec 4 at 23:30