This chapter presents a new paradigm of Artificial Neural Networks (ANNs): the Auto-
Contractive Maps (Auto-CMs). The Auto-CM differs from the traditional ANNs under many viewpoints: the
Auto-CMs start their learning task without a random initialization of their weights, they meet their convergence
criterion when all their output nodes become null, their weights matrix develops a data driven warping
of the original Euclidean space, they show suitable topological properties, etc. Further two new algorithms,
theoretically linked to Auto-CM are presented: the first one is useful to evaluate the complexity and the topological
information of any kind of connected graph: the H Function is the index to measure the global hubness
of the graph generated by the Auto-CM weights matrix. The second one is named Maximally Regular
Graph (MRG) and it is a development of the traditionally Minimum Spanning Tree (MST).
Keywords: Artificial Neural Networks, Contractive Maps, Artificial Adaptive Systems, Theory of Graph,
Minimum Spanning Tree.