A hierarchical map that depicts relationships between its elements which are concepts.
A concept map is a diagram showing the relationships among concepts. It is a graphical tool for organizing and representing knowledge. Concept map consists of the focus question, which sets the context for the map, the selected concepts and hierarchical links and cross-links with linking phrases which specify the relationships between the concepts.
The main difference between concept maps and mind maps is that a mind map tends to have a single main concept, while a concept map may have several related and interconnecting ideas, themes or topics. As a result of this difference, a mind map can be represented as a "tree", whilst a concept map may need a more complex network to fully represent the ideas contained within it.
A concept map diagram shows knowledge objects as nodes and the relationships between them as links (usually labelled arrows). Any types of concepts and relationships can be used.
Concept mapping technique was developed by Prof. Joseph D. Nonack of Cornell University (Novak, J. D. 1998)  as a technique for visually representing the structure of information. It is about how concepts within a domain are interrelated.
Concept mapping is one the most effective graphical methods of acquiring and representing implicit knowledge. Although the graphical display of implicit knowledge has been in use for centuries as a method of expressing individual thinking, concept maps provide a functionality, which enables the user to share his or her knowledge, to collaborate with others, and to show the logical connection between concepts. Furthermore, concepts can be re-used, and information in the form of voice, documents, or movie clips can be added. Concept maps are therefore a very useful cognitive tool in acquiring knowledge and making it available to others in the science and business environment.
Normally concept maps are organized hierarchically; however, the hierarchy of complex concepts is not always clear. The structuring of concept maps requires us to identify the following components -- concepts, relationships, and dependencies. By identifying cross-links, new patterns and relationships among the knowledge concepts often reveal themselves.
Another important characteristic of concept maps is the inclusion of cross-links.
There are two features of concept maps that are important in the facilitation of creative thinking: the hierarchical structure that is represented in a good map and the ability to search for and characterize new cross links.
Benefits of concept maps
The value of concept maps lies in the ability to formalize and display tacit knowledge, as well as to transfer it with the help of pictures, movie clips, voice, text, structure or other forms of description to explicit knowledge.
In addition, concept maps are a learning tool and access point for the domain of knowledge represented. In simplistic form, they provide a graphic interface into the structure and relationships of knowledge.
Structure of concept map
Concept maps are hierarchical maps with the most general concepts located at the top or center of the map. Context of a concept map is set by the focus question which defines the problem which the concept map should provide an answer to.
In a concept map, hierarchical links depict the hierarchical relationships between the concepts. A concept map may also include so-called cross links which represent the relationships between different domains of the map. Words explicitly written on the links, referred to as linking words or linking phrases, specify the relationship between the two concepts.
An example of a concept map is given in Fig. 1, describing the structure of 'knowledge management' concept with most important elements and their relationships.
Creating a concept map
Creating a concept map is described in Concept mapping article
 Joseph D. Novak, Alberto J. Cañas, The Theory Underlying Concept Maps and How to Construct and Use Them, Technical Report IHMC CmapTools 2006-01 Rev 2008-01, http://cmap.ihmc.us/Publications/ResearchPapers/TheoryCmaps/TheoryUnderlyingConceptMaps.htm.