Use this if you are using igraph from R
A graph is chordal (or triangulated) if each of its cycles of four or more nodes has a chord, which is an edge joining two nodes that are not adjacent in the cycle. An equivalent definition is that any chordless cycles have at most three nodes.
is_chordal( graph, alpha = NULL, alpham1 = NULL, fillin = FALSE, newgraph = FALSE )
graph 
The input graph. It may be directed, but edge directions are ignored, as the algorithm is defined for undirected graphs. 
alpha 
Numeric vector, the maximal chardinality ordering of the
vertices. If it is 
alpham1 
Numeric vector, the inverse of 
fillin 
Logical scalar, whether to calculate the fillin edges. 
newgraph 
Logical scalar, whether to calculate the triangulated graph. 
The chordality of the graph is decided by first performing maximum
cardinality search on it (if the alpha
and alpham1
arguments
are NULL
), and then calculating the set of fillin edges.
The set of fillin edges is empty if and only if the graph is chordal.
It is also true that adding the fillin edges to the graph makes it chordal.
A list with three members:
chordal 
Logical scalar, it is

fillin 
If requested,
then a numeric vector giving the fillin edges. 
newgraph 
If requested, then the triangulated graph, an 
Gabor Csardi csardi.gabor@gmail.com
Robert E Tarjan and Mihalis Yannakakis. (1984). Simple lineartime algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM Journal of Computation 13, 566–579.
## The examples from the TarjanYannakakis paper g1 < graph_from_literal(AB:C:I, BA:C:D, CA:B:E:H, DB:E:F, EC:D:F:H, FD:E:G, GF:H, HC:E:G:I, IA:H) max_cardinality(g1) is_chordal(g1, fillin=TRUE) g2 < graph_from_literal(AB:E, BA:E:F:D, CE:D:G, DB:F:E:C:G, EA:B:C:D:F, FB:D:E, GC:D:H:I, HG:I:J, IG:H:J, JH:I) max_cardinality(g2) is_chordal(g2, fillin=TRUE)