# Graphs, trees and simplicial complexes

(2016-11-04)Graphs and simplicial complexes A one-dimensional simplicial complex is a graph. That is, $K=(X_ K,\Phi_ K)$ where $V(K) = X_ K$ is the set of vertices and $\Phi_ K$ is the set of simplexes, with $\Phi_ K = \Phi^1_ K \cup \Phi^0_ K$, where $E(K) = \Phi^1_ K$ are the 1-dimensional simplexes (termed edges of $K$) and $\Phi^0_ K = \{ \{P\} : P \in X_ K \}$ are the $0$-dimensional simplexes (sometimes termed again vertices of $K$).

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