Matthew Hopkins

Graphs and how to make them

We encounter graphs all around us both in the physical world and in representations of that world. It turns out that simple graphs are intuitively easy for people to understand, and so they are often used to represent information. Our families are collections of entities (people) who have relationships to one another (marriage or by birth). Science has found a great many uses for graphs as they explore systems which have a great many actors and numerous relationships among them. They have devised numerous methods over the years to explore these graphs and quantify their characteristics. This chapter introduces a few graphs we encounter in everyday life, and then explores some common characteristics of graphs. It discusses some of the challenges related to modeling systems as graphs. Finally it provides a brief overview of major categories of graph analytic techniques.

Networks in economics and business

This chapter looks at graph representations of business organizations, the economy they comprise, and even the cities they inhabit. Some topics include network representations of management and collaboration within organizations, supply chains, and economic models. Many of these models predate the emerging science of networks, but nevertheless reflect an understanding that businesses and economic interactions run on connections, attracting investors with capital, bringing together creative people to implement ideas, managing supply lines for raw materials to create products, tackling challenges related to moving products from place to place, and stores to connect consumers to those products.

14 – Social networks

This chapter introduced the concept of social network analysis (SNA), which, although not invented by, was certainly made famous by Stanley Milgram and his “six degrees of separation” findings. It described how a social network can be represented as a graph, with people as nodes and the relationships among people serving as edges where edges can also reflect things like whether the relationship is strong or weak, and whether it has directionality. It introduced some terms specific to the SNA community such as homophily and multiplexity, and it described the graph analytic techniques that can be used to explore social networks. Finally we explored two upper level Semantic Web ontologies for representing facts about a social network, the Friend of a Friend ontology for expressing facts about people, and the Organization ontology, for describing organizations, and a person’s relationship to and role in an organization.

Graph analytics techniques

There are many ways to analyze a graph. There are graph-wide metrics to quantify attributes of a graph such as diameter and density. You can compare your instance graph with a comparable regular, small-world, or random graph. The shape and size of a graph may tell you some interesting things about that graph. Fine-grained characteristics that are also useful consider connectivity of nodes in the graph, characteristics of paths, and the presence and size of clusters within the graph. This chapter provides a conceptual overview of analytics that fall into those three categories. It describes several node-based metrics such as degree and betweenness centrality, which can be used to learn more about a given node or about the distribution of degrees of connectivity within a graph. Path metrics can be used to calculate the shortest path between nodes, the average path length, or to look for special kinds of paths such as cycles in directed graphs. Clusters are groupings of nodes that have a special relationship to one another as compared to the graph as a whole, revealed by the relatively interconnectedness of nodes that fall within the cluster as compared to those which do not.

15 – Upper ontologies

The process of defining an ontology is typically an effort to document what is known in a particular domain, what things it contains, their properties, and their relationships to one another. But there are fundamental types of knowledge that are not the purview of any particular knowledge domain. Everyone from a biologist to a sociologist to a librarian may be interested in referencing a geographic location. Physical objects have dimensions, structure, and displace space. A chemical reaction, a rocket launch, a genetic mutation, and an opera all have a starting point in time. This chapter introduces some ontologies that have broad applications. These include the Organization ontology for describing organization, the Event ontology which is concerned with temporal information, the Provenance ontology which is used to ascribe attribution related to the creation of an intellectual product, two location ontologies, an ontology for defining thesauri, and a pair of ontologies that can be used to describe some aspects of various kinds of scientific data sets.

Library networks—coauthorship, citation, and usage graphs

The next six chapters step back from Semantic Web graphs to look at graph models of systems in various domains, starting with libraries. Traditional use of library resources often involves what is generically referred to as “research.” What is meant in this particular context is the process of locating materials on a particular topic or produced by a particular author, determining coauthorship and topical relationships, reviewing the citation relationships, and then exploring all of these various relationships to identify other items of potential interest. These organic, explicit networks grow over time and exhibit some of the characteristics found in other types of networks. This chapter looks at how this data can be modeled as graphs, and the process of analyzing and traversing these graphs. It illustrates the use of some common graph theory techniques in the context of library data and systems, including coauthorship analysis and citation graphs between papers. It also briefly explores how usage data can be modeled using graphs to explore research trends and generate recommendations for library patrons. It introduces first-mover advantage and scale-free networks.

Library metadata ontologies

The Semantic Web is not a library. It is not even a catalog, per se. It is a way of representing, sharing, and linking with basic statements of fact about things. The granularity of the Semantic Web is not at the level at which libraries have been traditionally concerned with information. Libraries collected and described intellectual products that consist of some form of narrative, a book, a journal, a research paper, a movie, an album, or a song. More recently libraries have begun to assist scientists in cataloging their data sets. But the cataloging of individual facts was left to Webster’s, encyclopedias, survey papers, and the like. And yet it makes a great deal of sense to take the fine-grained descriptive data that libraries have meticulously crafted about these various objects, and generate Semantic Web data from it, because this represents knowledge. This chapter takes a look at the issues and challenges of publishing library metadata as Semantic Web data. It briefly reviews several applicable ontologies that have been used by various projects to create triples about bibliographic metadata and subject and author authority data. It also looks at a few Linked Open Data efforts that have been undertaken by libraries.

Graphs and the Semantic Web

The Semantic Web is a collection of technologies and standards that utilizes graphs to model knowledge. It is called the Semantic Web because the technologies coexist with and leverage Web technologies that allow us to access and create links between Web pages. It uses links to formalize representations of knowledge that convey their meaning in a context that is not unlike how humans classify things as they process information. The vision behind something like the Semantic Web has existed for decades, but only with the advent of computer networks and the World Wide Web, has it been possible to make it a reality. The formalization is an abstract model called RDF, which relies on a fundamental knowledge unit referred to as a triple. This triple is a graph segment with two nodes and a directed edge between them. This chapter introduces some of the fundamental technologies and concepts behind the Semantic Web. It introduces the process of modeling information using RDF. It explains the basics of linking within the Semantic Web and illustrates how graph analytics can be applied to RDF graphs.

23 – Case studies

Software case studies explore the process of designing and building a software application. So in this final chapter, we present two case studies that mirror the two tracks of this book. EgoSystem is a system that was designed from inception to use a property graph. It aggregates the public social networks of a population of individuals, as well as their first-degree social networks, to support outreach and ongoing engagement of an alumni community. InfoSynth is a library application that facilitates exploration of collections of bibliographic metadata that have been harvested, aggregated, and normalized to a common RDF model. These datasets incorporate semantic annotations from Linked Open Data sources. For each system, we discuss use cases, data modeling, and implementation details. These case studies also touch on the challenges and trade-offs with building graph and Semantic Web applications. These narratives are intended to give you some idea of what is involved in building real applications using a property graph or Semantic Web technologies.

Networks in chemistry and physics

Like other physical sciences, the depths of physics and chemistry can be plumbed using networks. Some of the earliest approaches to modeling molecular structures were graph based. The physical arrangement of atoms in matter can also be modeled using graphs. Dynamic graphs can be used to explore phenomena such as phase transitions and percolation. This chapter looks at how graphs are used to model and understand processes in physics. Interestingly enough, the patterns that emerge when modeling phase transitions have shown to occur in graph models of other systems. This chapter also looks at chemical graph models and how they enable certain types of chemistry in silica. Graph concepts introduced include percolation, phase transitions, and graph rewriting.