The Design of a Universal Graph Model

Abstract

In this research, we designed a universal graph model. We targeted this work on improving graph data organization representation, flexible formation of graph substructures for complex system modeling and generic processing of data organization. We form coherently composed graph modeling features including inheritance hierarchy of basic graph types, data participating graphs of multiple aspects, hierarchically composed and connected graphs, and property-based graph models based on existing graph models. Design cases are used to illustrate its achievement of our design goal. Keywords—graph theory; graph model, multi-aspect graph; hierarchical graph I. INTRODUCTION Computer modeling plays a key role to apply computer's capability in various fields of applications. Effective support of computer modeling should consist of data representation capability, data access and navigation capability, and generic operations for forming more general and reusable generic algorithms. As computer applications keep growing complex in wider areas, we need enhanced computer models capable of supporting these applications. Graph data models are one of the most extensively used discrete mathematical models in computer modeling of various applications from VLSI circuit design, computer system design and modeling, network modeling, etc. Traditional graph libraries such as LEDA(1), Boost Graph Library(2), LINK(3), and GraphStream(4) focuses on single- level directed and undirected graph modeling. Lee's work(5) utilized decorator and visitor patterns to add new vertex data and attach processing during graph traversal. Pizzonia's (6) employed static object-oriented extension of graph property classes associated with corresponding graph operations. Bertault(7) employed an extensible graph property class hierarchy and dynamic property checking. Directed and undirected hypergraphs are not supported in these approaches. Hyperedges in hypergraphs can be represented as vertices in ordinary graphs. Hypergraphs cannot be treated as super types of directed and undirected graphs to support generic algorithms with ordinary graphs. On data organization point of view, these approaches provide various graph organization types but only as single- level specialized graph type. Each of them should be utilized distinctly. Once these graph models need to be combined in a complex data model, designers should add artificial data structures to join them together. Still, such combined data model or its selected subparts cannot be viewed and utilized as if in a single graph model. This requires designers to add more application-specific gluing data structures, processing codes of distinct graph substructures and their gluing logic, and semantically similar but redundant non-generic codes. It thus hinders effective development and reuse of computer models for various complex applications. From our literature survey, we did not find any previous work providing combinational features for flexibly composing graph structures. Our design goal lies in three improvement directions, representation of complex system data organization, flexible formation of graph substructures for processing, and generic processing of data organization as well as individual data. Our main approach is to form coherently composed graph modeling features including inheritance hierarchy of basic graph types, vertex data participating in graphs of multiple aspects, hierarchically composed and connected graphs, and property-based graph models based on existing graph models. It forms a universal graph model of combinations of complex graph-oriented data organizations, flexibly forms various virtual graph substructures for complex system modeling and processing, and support generic processing capability at the graph structure levels and at the leaf data levels. In section 2, we describe refined design goals and the approach of our work. In the following sections, we in sequence introduce planned composed graph modeling features of our universal graph model, including generic accesses among basic graph models, joining multiple graphs into a multi-aspect graph model, generic structuring of graph models, and generic accesses of property-based graph models. In section 7, we introduce its software design and a design case. The last section concludes this research.