Besides the need for a better understanding of networks, there is a need for prescriptive models and tools to specify requirements concerning networks and their associated graph representations. We propose class-based graphs as a means to specify requirements concerning object-based graphs. Various variants of membership are proposed as special relations between class-based and object-based graphs at the local level, while various variants of compliance are proposed at the global level.
Deep Dive into Membership(s) and compliance(s) with class-based graphs.
Besides the need for a better understanding of networks, there is a need for prescriptive models and tools to specify requirements concerning networks and their associated graph representations. We propose class-based graphs as a means to specify requirements concerning object-based graphs. Various variants of membership are proposed as special relations between class-based and object-based graphs at the local level, while various variants of compliance are proposed at the global level.
During the last decade, the Web has been transformed from a siloed information medium into a highly dynamic network of information, created by individuals and organizations mostly in a participatory manner. This network is currently referred to as the Web 2.0 [1].
A reason for such a transformation may be the better understanding of the structure and the functioning of networks, especially small-world networks [2,3]. It has been shown that many networks, from Web pages [4] to food webs [5], from research paper co-authoring [6] to human brain functional networks [7], share a set of common characteristics, e.g., their average shortest path is relatively low, while their clustering coefficient is rather higher than in random networks.
Networks have also been studied as regards their dynamics. As an example, network percolation, with its potential application to explain disease epidemics and gossip propagation, has received significant attention [8,9].
Social websites, such as Facebook or Twitter, are playing a major role on the Web 2.0. These sites support social networks, i.e., networks of individuals and organizations linked by their relationships. Once again, the characteristics of social websites and the social networks they support is the subject of many research works [10,11].
Besides the descriptive approach of the works mentioned above, prescriptive tools are needed. Not only should networks be understood, but tools to specify constraints on networks are required. With the ubiquity of networks, tools are needed to check if a chosen subset of a given network satisfies a predefined set of constraints. These constraints should concern both the nodes of the network and the arcs between them. To draw an analogy with collective sports, it is important not only to understand how a team is performing, but also to be able to define requirements about the various players and their potential relations. The coach would then be Email address: picard@kti.ue.poznan.pl (Willy Picard) able to check if a given set of players satisfies his/her expectations defined as requirements.
The problem addressed in this paper may be stated as follows: how to specify a type of networks with constraints on both nodes and arcs, and how to define the concept of compliance of a given network with these constraints. Many applications of this problem may be found, such as the establishment of the cast of a movie, the specification of emergency crews, the definition of a set of chemical substances needed for a given chemical reaction, the specification of the set of web services required to implement a given serviceoriented application, and the definition of crews in hospitals for surgical operations.
For the sake of readability and conciseness, an simplified example based on William Shakespeare’s tragedy Romeo and Juliet is presented in this paper. Besides the criterion of succinctness, the choice of this example is guided by the assumption that the popularity of this play will ease the understanding of the various illustrative networks presented in the rest of the paper, networks consisting of characters from Romeo and Juliet.
Addressing this problem encompasses two main issues. First, the development of tools supporting the definition of constraints on networks implies both a representation for networks and a representation for the constraints. Second, different types of relations between the networks and the constraints may occur and should precisely be defined.
Three IT areas partially address the proposed problem: object-oriented languages, database schemata, and ontologies. Object-oriented languages rely on the concept of class to model constraints on objects [12]. A network of classes may therefore constrain a network of objects. Similarly, database schemata, either in relational, object-oriented, or XML databases, constraint the database [13]. Finally, classes in ontologies constrain individuals [14]. However, in these three approaches, classes and database schema have to exist to be instantiated as objects, data, and individuals. Therefore, classes and database schema have to precede objects. In the case of social networks (or former mentioned collective sports), the network usually exists before the constraints do. Additionally, in these three approaches, a limited support for arcs is proposed. In object-oriented languages, relations between classes are limited to has-a and is-a relations, via class attributes and inheritance. In relational database, the only mechanism to connect relations are joins. Finally, similarly to the object-oriented approach, the relations between classes in ontologies are limited to class properties and inheritance. It should be possible to specify constraints on arcs in a more subtle manner, encompassing a more complex representation of the arcs among nodes of a network.
In this paper, we propose to represent networks as objectbased graphs. Constraints on networks may then be represented as
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