Synthetic benchmarks are especially useful in the context of large instances where real data is typically unavailable in sufficient size, quantity, or variety. Network models also enable or supplement experimental campaigns as a versatile source of synthetic data with controllable independent variables. In practice, such results tend to be more relevant than worst-case analysis based on pathologic structures that are implausible in applications. Then we can derive realistic formal performance predictions using average-case analysis, smoothed complexity, et cetera. In algorithmics we may, for instance, assume that meaningful inputs are random instances of a suitable network model. Popular models are designed such that we Footnote 1 can expect certain topological properties from a randomly drawn instance: a particularly interesting goal is to reproduce the loosely defined class of complex networks which, among others, encompasses most social networks.īy expressing network models as random graphs, we inherit a rich set of tools from combinatorics, stochastics, and graph theory. These distributions are almost always parametrized (e.g., for the graph size or density) and typically follow implicitly from some randomized construction algorithm. Networks are commonly modeled by so-called random graphs and, therefore, represent probability distributions over the set of graphs . Research into and applications of these models are deeply intertwined with various fields of science. Network models are just that: a mathematical tool to describe and analyze realistic graphs. However, a formal grammar capturing the inner structure of the data expected to be processed is required to provide tailor-made solutions. They are fed by billions of interconnected sensors and computerized personal devices that produce enormous volumes of network data to be exploited.Ĭomputer science provides the means to face this big data challenge. Nowadays, modern computers offer sufficient storage and processing capacity to map out most aspects of human life and the world we inhabit. The practical importance of networks, however, only sky-rocketed with the advent of the information age. As such, humanity is seeking to understand their structures, rules, and implications for centuries (see also Sect. Networks are the very fabric that makes societies . In this chapter, we survey the results obtained for these so-called graph generators. As several SPP 1736 projects engineered practical graph algorithms, multiple sampling algorithms for various graph models were designed and implemented to supplement experimental campaigns. While there exist public network libraries with numerous datasets, the available instances do not fully satisfy the needs of experimenters, especially pertaining to size and diversity. From an algorithmics point of view, structural insights into networks can guide the engineering of tailor-made graph algorithms required to face the big data challenge.īy design, network models describe graph classes and therefore can often provide meaningful synthetic instances whose applications include experimental case studies. Network models are developed and used in various fields of science as their design and analysis can improve the understanding of the numerous complex systems we can observe on an everyday basis.
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