The term chain graph has distinct meanings in graph theory and graphical models.
In graph theory, a chain graph is a bipartite graph 
for which the graph
neighborhoods of the graph vertices in each part
can be linearly ordered by inclusion. Equivalently, a bipartite
graph is a chain graph if it contains no induced
subgraph isomorphic to 
, the graph consisting of two disjoint graph
edges. Chain graphs are also known as difference graphs.
In graphical models, a chain graph represents dependence relations among random variables and may contain both directed and undirected graph edges, but no graph cycle with at least one directed graph edge whose directions are consistent around the cycle. Removing the directed graph edges leaves undirected components of the graph.
