Definition of Artificial Neural Networks (ANNs) is made by computer scientists, artificial intelligence experts and mathematicians in various dimensions. Many of the definitions explain ANN by referring to graphics instead of giving well explained mathematical definitions; therefore, misleading weighted graphs (as in minimum cost flow problem networks) fit the definition of ANN. This study aims to give a clear definition that will differentiate ANN and graphical networks by referring to biological neural networks. The proposed definition of ANN is a mathematical definition, from the point of graph theory which defines ANN as a directed graph. Then differences between ANNs and other networks will be explained by examples using proposed definition. (C) 2010 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Guest Editor.