Status and Challenges of Network Science
Although no universal consensus exists in the research community that a field of investigation called network science exists today, many researchers describe their work as potentially related to such a field. Many techniques for designing and analyzing networks exist in a variety of application domains, as explored in Chapter 5. In this chapter, the committee draws upon responses to a questionnaire to identify a suite of common characteristics and concerns that span these domains. The questionnaire was circulated to active researchers, identified from literature studies, recursive tracing of collaborative ventures, conference attendance, mailing lists, and interviews with the authors of recent books and reviews. First, the committee describes the questionnaire process and the respondents. Then it summarizes the respondents’ assessments of the existence, nature, and challenges of a possible field of network science. Further analysis and discussion are provided in Appendix D.
From an analysis of over a thousand questionnaire responses, the committee extracted four messages:
There is no universal consensus among researchers that an identifiable field of network science now exists, in part because there is no accepted definition of what the discipline of network science might be.
Analysis of the definitions put forth and the research interests of the respondents reveals a suite of input attributes and output properties that could constitute a common core of topics underlying network science.
Researchers across diverse domains share an implicit understanding that a network is more than topology alone. It also entails connectivity, resource exchange, and locality of action.
Of seven major challenges identified, the most critical involve characterization of the dynamics and information flow in networked systems; modeling, analysis, and acquisition of experimental data for extremely large networks; and rigorous tools for the design and synthesis of robust, large-scale networks.
The questionnaire was developed through an iterative process, starting with an analysis of the statement of task. After a beta-test phase, the final version of the questionnaire was posted on the Web from December 20, 2004, to May 31, 2005. The complete text of the questionnaire is contained in Appendix D. It asked for information about the respondents, their work, and their views on “network science” as a field. It also gave respondents the opportunity to provide as much further information as they wished.
The goal of the ensuing questionnaire invitation process was to reach as large, diverse, and representative a sample of the many relevant research communities as feasible within the study’s resources. Overall, the findings that surfaced from the responses and that are presented here are consistent with views held by the committee members. This helped to overcome concerns about the depth and breadth of coverage or other limitations in the questionnaire process. Issues such as reaching beyond the basic snowballing effect, detecting hoax responses, and determining the degree of coverage of the researcher community are discussed further in Appendix D.
Finding 6-1. Responses to the questionnaire show a diverse and worldwide network research community with shared concepts and concerns.
Finding 6-2. The results of analyzing the questionnaire responses are consistent across diverse subgroups of respondents.
The responding community is diverse in terms of both geographic distribution and the breadth of interests represented. Responses were received from 29 countries and from 39 states in the United States. Fourteen fields were selected by at least 10 percent of the respondents, and, on average, each respondent selected 3.6 fields. The findings presented in this report do not depend significantly on the field of study or the locale of the respondents but could be limited by the fact that most of them (72 percent) are in the academic community. Further details are given in Appendix D.
Finding 6-3. Seventy percent of the responses to the questionnaire accept the idea that network science is a definable field of investigation.
The questionnaire analysis reveals a widespread but not universal consensus among the respondents that a definable field of network science exists. When the reasons for saying there is no such field as “network science” are analyzed, they break down into five kinds of concern: the phrase has no coherent definition; it is broad to the point of vacuity; it is too early to define such a field; it is merely a new name for already existing fields; or, defining such a field is the wrong approach. In addition, respondents also indicated that the field suffered from excessive hype. The distribution of these responses is shown in Figure 6-1.
Of the responses, 70 percent were affirmative to question Q3a: “Is there an identifiable field of network science?” Twenty-three percent of respondents answered no, and 7 percent did not answer. These percentages show little dependence on the backgrounds of the respondents.
The pervasiveness of dissenter concerns across the responding communities reinforces the need for a clear definition of the field of network science, anchored in the expressed approaches of the researchers involved. It also reinforces the idea that care must be taken not to overstate what is achievable in such a field. More positively, articulating an explicit definition of the term “network science” may address some of these concerns.
DEFINING THE FIELD
The first question in considering a possible field of network science is this: What are its contents and scope? Questions 3a and 3b directly address this issue and provide empirical data on the nature of network science as practiced by current researchers. The responses to four other questions proved highly relevant. Further analysis is presented in Appendix D.
The committee structured its analysis in terms of two basic questions: What are the defining attributes of a network? What are the derived properties of interest? If these questions have answers that are common across many application domains, then network science might be identified as the insights, lexicon, measurements, theories, tools, and techniques that allow one to map between desired output properties of a given network and its input attributes. Mapping is needed in both directions: (1) determining the output properties that arise from specific input attributes and (2) determining the input attributes that could be designed into a new network or achieved by intervention in an existing network in order to realize particular output properties.
If network science is to exist in a meaningful way, these approaches also must be effective over many application domains, with well-understood techniques to apply general tools, methods, and models to specific domains. As a hypothetical example, one might envision a simulation tool that deals with network models across a wide range of size scales and timescales, with a growing suite of model libraries customized to specific application domains—for example, ecological networks, metabolic networks, transportation networks, and so on.
Attributes of a Network
Finding 6-4. Analysis of the responses reveals three common attributes of networks: (1) they consist of nodes connected by links, (2) nodes exchange resources across the links, and (3) nodes only interact through direct linkage.
Few responses captured all three attributes, but all three appear consistently, either explicitly or implicitly (in more domain-specific entries), across a wide range of subject domains. The percentage of responses in which an attribute was mentioned explicitly is indicated in Figure 6-2. For brevity, these attributes are designated “connectivity,” “exchange,” and “locality”:
Connectivity. A network has a well-defined connection topology in which each discrete entity (“node” in graph-theoretic terminology) has a finite number of defined connections (“links”) to other nodes. In general, these links are dynamic.
Exchange. The connection topology exists in order to exchange one or more classes of resource among nodes. Indeed, a link between two nodes exists if and only if resources of significance to the network domain can be directly exchanged between them.
Locality. The exchanged resource is delivered, and its effects take place, only in local interactions (node to link, link to node). This locality of interaction entails autonomous agents acting on a locally available state.
These attributes are discussed in more detail in Appendix D.
Derived Properties of Networks
Finding 6-5. Respondents expressed a need for network science to provide tools that answer a common set of questions across a broad range of applications.
Thirty-three percent of the responses provided definitions relating to the output properties of networks. Analysis of the proposed definitions identified six output properties that spanned a wide range of application domains: characterization, cost, efficiency, evolution, resilience, and scalability. However, only 7 percent of the responses explicitly mentioned classes of tools to address the derivation of these properties. The most frequently mentioned were modeling, simulation, and optimization. These themes also appear in the respondents’ research challenges, discussed below.
The responses that proposed driving applications for network science pointed to a highly disparate set of applications, generally tightly bound to five major communities of research: technological, biological, social sciences, interdisciplinary, and physical sciences and mathematics. The distribution of these responses is indicated in Figure 6-3.
The analysis of the questionnaire responses also identified three significant problem dimensions that account for the difficulty of many associated challenges and of the research effort required to address them: complexity, the wide range of interacting scales, and network-to-network interactions.
Future Evolution of the Definition of Network Science
Networks and their associated research programs could be classified and analyzed based on any one of three descriptive categories: input, output, or problem dimension. It is also possible that the categories could become the basis for more precise formal definitions of network science. The questionnaire responses provide evidence that there is a recognizable, coherent common core to the research already being done on network science, and that the scope of the nascent field is both narrow enough to study and deep enough to capture concerns that recur across a diverse range of application domains.
Finding 6-6. Respondents identified seven major challenges requiring substantial future work (Figure 6-4).
Dynamics, spatial location, and information propagation in networks. Better understanding of the relation-
ship between the architecture of a network and its function is needed.
Modeling and analysis of very large networks. Tools, abstractions, and approximations are needed that allow reasoning about large-scale networks, as well as techniques for modeling networks characterized by noisy and incomplete data.
Design and synthesis of networks. Techniques are needed to design or modify a network to obtain desired properties (such as the output properties discussed in the section “Derived Properties of Networks”).
Increasing the level of rigor and mathematical structure. Many of the respondents to the questionnaire felt that the current state of the art in network science did not have an appropriately rigorous mathematical basis.
Abstracting common concepts across fields. The disparate disciplines need common concepts defined across network science.
Better experiments and measurements of network structure. Current data sets on large-scale networks tend to be sparse, and tools for investigating their structure and function are limited.
Robustness and security of networks. Finally, there is a clear need to better understand and design networked systems that are both robust to variations in the components (including localized failures) and secure against hostile intent.
THE SOCIAL STRUCTURE OF NETWORK SCIENCE
The questionnaire data were provided to Katy Börner, associate professor of information science at Indiana University, for analysis of the visible social structure of research
in network science. Her analysis considered the 1,241 unique names of network science researchers identified during the course of the questionnaire and citation studies.1 Names were replaced by unique identification numbers to preserve the anonymity of the respondents. Relationships among the initial invitees, respondents, and identified collaborants are depicted in Figure 6-5.
Figure 6-6 shows the major components (connected graphs of size greater than or equal to 10 nodes) of the resulting network science researcher network (NSRN). The Pajek shows exactly 630 of the 1,241 unique researchers and their association with collaborations and invitations to complete the questionnaire plot (Batagelj and Mrvar, 1997). Each researcher is represented by a node. The nodes are color coded to identify researchers who submitted (brown) or did not submit (orange) questionnaires. The size of the circle (node) reflects the number of times the researcher is mentioned by other researchers.
The details of the visualization analysis are provided in Box D-1 of Appendix D. Upon reviewing the results of the analysis, the committee agreed to include the following two findings on the empirical state of the proposed field of network science:
Finding 6-7. Analysis of the social and collaboration networks of the respondents provides additional evidence that network science is an emerging area of investigation.
Finding 6-8. Analysis of the social and collaboration networks of the respondents provides additional evidence of the multidisciplinary nature of network science.
Batagelj, V., and A. Mrvar. 1997. Pajek: Program Package for Large Network Analysis. University of Ljubljana, Slovenia. Available at http://vlado.fmf.uni-lj.si/pub/networks/pajek/. Accessed August 18, 2005.