A connected (vertex-)induced subgraph of 
is a vertex-induced
subgraph of 
that is connected.
The number of undirected 
-cycles in a graph 
is given by
 |
where the sum is over connected induced subgraphs 
of 
, 
denotes the number of neighbors of 
in 
(namely vertices 
of 
which are not in 
and such that there exists at least one edge from 
to a vertex of 
), 
denotes the matrix trace,
and 
is the 
th
matrix power of the adjacency matrix of the graph 
(Giscard et al. 2016).
