O'Reilly logo

Analysis of Complex Networks by Frank Emmert-Streib, Matthias Dehmer

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

8.3 Semiotic Systems as Conceptual Graphs

So far we have gained several novel subclasses of the class of GTs. It was Dehmer's [15] task – who first and, up to that time, most comprehensively formalized GTs – to define a similarity measure for classifying given sets of GTs. That is, for a triple of GTs Dehmer [15] determines the most similar pair of GTs. In this chapter we have taken one step back in order to approach an answer to the following question: Given a single graph, which of the GTs derivable from it satisfies which topologically and semiotically founded constraints? Following this line of research we have introduced the notion of a minimum spanning generalized tree (MSGT), of a generalized shortest path tree (GSPT), and of a generalized shortest paths tree (GPST). Especially by the subclass of GPSTs we have gained a detailed semantics of kernel, vertical, reflexive, and lateral edges where the latter have further been divided into the subset of cross-reference and shortcut edges. In Section 8.2.6 we have given a functional semantics of kernel edges as search facilities, of vertical edges as abridging facilities, of shortcut edges as association facilities (in support of large cluster values), and of cross-reference edges as randomization facilities (in support of short average geodesic distances). GTs are a class of graphs that impose functional restrictions on the typing of their edges, which locate this class in between the class of trees and general graphs. In this ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required