Adjacency matrix of a line graph











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Suppose that $G'$ is a line graph of $G$. How can we calculate the adjacency matrix of $G$ if we have adjacency matrix for the graph $G'$ ?






graph-theory







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  • L(G) = laplacian of the graph = adjacency matrix minus diag. matrix of degrees $d_{ii}$ ? How can it be equal to the adjacency matrix (unless no pair of vertices are connected ...) ?
    – Jean Marie
    2 days ago








  • 1




    Notation is misleading: $G'$ is a graph; $L(G)$ is a matrix.
    – Rócherz
    2 days ago










  • I corrected the question
    – atos
    2 days ago










  • What do you mean by "is a line graph of $G$" ?
    – Jean Marie
    2 days ago










  • Line graph formally $L(G)$ of a graph $G$ is a graph whose vertices represents the edges of $G$ and two vertices of $L(G)$ are connected if the edges they represent are adjacent. Here is the wiki link:en.wikipedia.org/wiki/Line_graph
    – mathnoob
    2 days ago

















up vote
0
down vote

favorite












Suppose that $G'$ is a line graph of $G$. How can we calculate the adjacency matrix of $G$ if we have adjacency matrix for the graph $G'$ ?






graph-theory







share|cite|improve this question
























  • L(G) = laplacian of the graph = adjacency matrix minus diag. matrix of degrees $d_{ii}$ ? How can it be equal to the adjacency matrix (unless no pair of vertices are connected ...) ?
    – Jean Marie
    2 days ago








  • 1




    Notation is misleading: $G'$ is a graph; $L(G)$ is a matrix.
    – Rócherz
    2 days ago










  • I corrected the question
    – atos
    2 days ago










  • What do you mean by "is a line graph of $G$" ?
    – Jean Marie
    2 days ago










  • Line graph formally $L(G)$ of a graph $G$ is a graph whose vertices represents the edges of $G$ and two vertices of $L(G)$ are connected if the edges they represent are adjacent. Here is the wiki link:en.wikipedia.org/wiki/Line_graph
    – mathnoob
    2 days ago















up vote
0
down vote

favorite









up vote
0
down vote

favorite











Suppose that $G'$ is a line graph of $G$. How can we calculate the adjacency matrix of $G$ if we have adjacency matrix for the graph $G'$ ?






graph-theory







share|cite|improve this question















Suppose that $G'$ is a line graph of $G$. How can we calculate the adjacency matrix of $G$ if we have adjacency matrix for the graph $G'$ ?






graph-theory




graph-theory






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 2 days ago

























asked 2 days ago









atos

113




113












  • L(G) = laplacian of the graph = adjacency matrix minus diag. matrix of degrees $d_{ii}$ ? How can it be equal to the adjacency matrix (unless no pair of vertices are connected ...) ?
    – Jean Marie
    2 days ago








  • 1




    Notation is misleading: $G'$ is a graph; $L(G)$ is a matrix.
    – Rócherz
    2 days ago










  • I corrected the question
    – atos
    2 days ago










  • What do you mean by "is a line graph of $G$" ?
    – Jean Marie
    2 days ago










  • Line graph formally $L(G)$ of a graph $G$ is a graph whose vertices represents the edges of $G$ and two vertices of $L(G)$ are connected if the edges they represent are adjacent. Here is the wiki link:en.wikipedia.org/wiki/Line_graph
    – mathnoob
    2 days ago




















  • L(G) = laplacian of the graph = adjacency matrix minus diag. matrix of degrees $d_{ii}$ ? How can it be equal to the adjacency matrix (unless no pair of vertices are connected ...) ?
    – Jean Marie
    2 days ago








  • 1




    Notation is misleading: $G'$ is a graph; $L(G)$ is a matrix.
    – Rócherz
    2 days ago










  • I corrected the question
    – atos
    2 days ago










  • What do you mean by "is a line graph of $G$" ?
    – Jean Marie
    2 days ago










  • Line graph formally $L(G)$ of a graph $G$ is a graph whose vertices represents the edges of $G$ and two vertices of $L(G)$ are connected if the edges they represent are adjacent. Here is the wiki link:en.wikipedia.org/wiki/Line_graph
    – mathnoob
    2 days ago


















L(G) = laplacian of the graph = adjacency matrix minus diag. matrix of degrees $d_{ii}$ ? How can it be equal to the adjacency matrix (unless no pair of vertices are connected ...) ?
– Jean Marie
2 days ago






L(G) = laplacian of the graph = adjacency matrix minus diag. matrix of degrees $d_{ii}$ ? How can it be equal to the adjacency matrix (unless no pair of vertices are connected ...) ?
– Jean Marie
2 days ago






1




1




Notation is misleading: $G'$ is a graph; $L(G)$ is a matrix.
– Rócherz
2 days ago




Notation is misleading: $G'$ is a graph; $L(G)$ is a matrix.
– Rócherz
2 days ago












I corrected the question
– atos
2 days ago




I corrected the question
– atos
2 days ago












What do you mean by "is a line graph of $G$" ?
– Jean Marie
2 days ago




What do you mean by "is a line graph of $G$" ?
– Jean Marie
2 days ago












Line graph formally $L(G)$ of a graph $G$ is a graph whose vertices represents the edges of $G$ and two vertices of $L(G)$ are connected if the edges they represent are adjacent. Here is the wiki link:en.wikipedia.org/wiki/Line_graph
– mathnoob
2 days ago






Line graph formally $L(G)$ of a graph $G$ is a graph whose vertices represents the edges of $G$ and two vertices of $L(G)$ are connected if the edges they represent are adjacent. Here is the wiki link:en.wikipedia.org/wiki/Line_graph
– mathnoob
2 days ago

















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