Block triangular decomposition of directed graph into strongly connected components
$begingroup$
Let $G=(V,E)$ with $Esubseteq Vtimes V$ be a directed graph with (directed) adjacency matrix $A=A(G)$.
I remember having seen a decomposition of $G$ into subgraphs $S_i=(V_i,E_i)$ for $iinmathcal J$ some index set $mathcal J$, such that
- $V=bigsqcup_{iinmathcal J}V_i$
$S_isubseteq G$ is a stronlgy connected subgraph (possibly trivial, i.e. a point)
$E ,bigcap ,(V_itimes V_j)=emptyset$ whenever $j<i$.
This also casts $A$ into a block triangular form.
Q) What is the name of this decomposition? Or is there anything fishy with it?
graph-theory reference-request topological-graph-theory
asked Dec 2 '18 at 23:21
MarloMarlo
455414
$endgroup$
add a comment |
$begingroup$
Let $G=(V,E)$ with $Esubseteq Vtimes V$ be a directed graph with (directed) adjacency matrix $A=A(G)$.
I remember having seen a decomposition of $G$ into subgraphs $S_i=(V_i,E_i)$ for $iinmathcal J$ some index set $mathcal J$, such that
- $V=bigsqcup_{iinmathcal J}V_i$
$S_isubseteq G$ is a stronlgy connected subgraph (possibly trivial, i.e. a point)
$E ,bigcap ,(V_itimes V_j)=emptyset$ whenever $j<i$.
This also casts $A$ into a block triangular form.
Q) What is the name of this decomposition? Or is there anything fishy with it?
graph-theory reference-request topological-graph-theory
asked Dec 2 '18 at 23:21
MarloMarlo
455414
$endgroup$
add a comment |
$begingroup$
Let $G=(V,E)$ with $Esubseteq Vtimes V$ be a directed graph with (directed) adjacency matrix $A=A(G)$.
I remember having seen a decomposition of $G$ into subgraphs $S_i=(V_i,E_i)$ for $iinmathcal J$ some index set $mathcal J$, such that
- $V=bigsqcup_{iinmathcal J}V_i$
$S_isubseteq G$ is a stronlgy connected subgraph (possibly trivial, i.e. a point)
$E ,bigcap ,(V_itimes V_j)=emptyset$ whenever $j<i$.
This also casts $A$ into a block triangular form.
Q) What is the name of this decomposition? Or is there anything fishy with it?
graph-theory reference-request topological-graph-theory
asked Dec 2 '18 at 23:21
MarloMarlo
455414
$endgroup$
Let $G=(V,E)$ with $Esubseteq Vtimes V$ be a directed graph with (directed) adjacency matrix $A=A(G)$.
I remember having seen a decomposition of $G$ into subgraphs $S_i=(V_i,E_i)$ for $iinmathcal J$ some index set $mathcal J$, such that
- $V=bigsqcup_{iinmathcal J}V_i$
$S_isubseteq G$ is a stronlgy connected subgraph (possibly trivial, i.e. a point)
$E ,bigcap ,(V_itimes V_j)=emptyset$ whenever $j<i$.
This also casts $A$ into a block triangular form.
Q) What is the name of this decomposition? Or is there anything fishy with it?
graph-theory reference-request topological-graph-theory
graph-theory reference-request topological-graph-theory
asked Dec 2 '18 at 23:21
MarloMarlo
455414
asked Dec 2 '18 at 23:21
MarloMarlo
455414
asked Dec 2 '18 at 23:21
MarloMarlo
455414
asked Dec 2 '18 at 23:21
MarloMarlo
455414
asked Dec 2 '18 at 23:21
MarloMarlo
455414
455414
add a comment |
add a comment |
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