Beyond graphs: A new synthesis

Artificial neural networks, electronic circuits, and gene networks are some examples of systems that can be modeled as networks, that is, as collections of interconnected nodes. In this paper we introduce the concept of the terminal graph (t-graph for short), which improves on the concept of graph as a unifying principle for the representation, computational synthesis, and inference of technological and biological networks. We begin by showing how to use the t-graph concept to better understand the working of existing methods for the computational synthesis of networks. Then, we discuss the issue of the “missing methods”, that is, of new computational methods of network synthesis whose existence can be inferred using the perspective provided by the concept of t-graph. Finally, we comment on the application of the t-graph perspective to problems of network inference, to the field of complex networks, social networks, and to the understanding of biological networks and developmental processes.

Research highlights► Networks are typically modeled as graphs, but the graph concept is not ideal when the identity of the network devices must be preserved, or the devices composing the network exchange multiple signals having different character. ► The new concept of “terminal graph” (t-graph) is introduced, which improves on the graph concept for the computational synthesis and inference of networks. ► The t-graph perspective gives a better understanding of existing methods for the computational synthesis and inference of networks. ► The t-graph perspective permits the identification of new methods for the computational synthesis and inference of networks. ► The t-graph perspective provides an original point of view on complex technological and biological networks, and on their evolution.