Graph Realizations Constrained by Skeleton Graphs

Graph Realizations Constrained by Skeleton Graphs

In 2008 Amanatidis, Green and Mihail introduced the Joint Degree Matrix (JDM) model to capture the fundamental difference in assortativity of networks in nature studied by the physical and life sciences and social networks studied in the social sciences. In 2014 Czabarka proposed a direct generalization of the JDM model, the Partition Adjacency Matrix (PAM) model. In the PAM model the vertices ...

Realizations of Hexagonal Graph Representations

Conditions for Unique Graph Realizations

The graph realization problem is that of computing the relative locations of a set of vertices placed in Euclidean space, relying only upon some set of inter-vertex distance measurements. This paper is concerned with the closely related problem of determining whether or not a graph has a unique realization. Both these problems are NP-hard, but the proofs rely upon special combinations of edge l...

Biased graphs IV: Geometrical realizations

A gain graph is a graph whose oriented edges are labelled invertibly from a group G, the gain group. A gain graph determines a biased graph and therefore has three natural matroids (as shown in Parts I–II): the bias matroid G has connected circuits; the complete lift matroid L0 and its restriction to the edge set, the lift matroid L, have circuits not necessarily connected. We investigate repre...

Evolving Graphs by Graph Programming

Rule-based graph programming is a deep and rich topic. We present an approach to exploiting the power of graph programming as a representation and as an execution medium in an evolutionary algorithm (EGGP). We demonstrate this power in comparison with Cartesian Genetic Programming (CGP), showing that it is significantly more efficient in terms of fitness evaluations on some classic benchmark pr...