Graphs are mathematical structures used to model pairwise relations between objects (abstract data types representing relations or connections). A graph is made up of vertices, nodes, or points which are connected by edges, arcs, or lines. Nodes and edges can have some auxiliary information.
Lots of problems are formulated and solved in terms of graphs
Graph theory is rapidly moving into the mainstream of mathematics because of its applications in diverse fields which include biochemistry (genomics), electrical engineering (communications networks and coding theory), computer science (algorithms and computations) and operations research (scheduling). Here I will be focusing on graph matching for following the De-anonymizing Social Networks hack trail of Arvind Narayanan and Vitaly Shmatikov.