Abstract

A network N = (V, L, P, W) consists of a set of nodes V, a set of links L, a set of node properties P, and a set of link properties (weights) W. In conventional network analysis, properties are measured using traditional measurement scales (numerical, ordinal, nominal), which assign a simple value (number or label) to each unit (node/link). In network analysis, we must also determine how to calculate with the selected property - select the appropriate algebraic structure on the property value range. A network N is symbolic iff at least one property takes symbolic values, such as interval, set of labels, distribution, temporal quantity, etc. Symbolic networks appear, for example, in the temporal analysis of international trade networks, bibliographic networks [1], bicycle-rental networks, and news networks [2]. A special netsJSON file format is used to describe symbolic networks [3].

In this paper, we will introduce some concepts that enable symbolic network analysis and illustrate them with examples from real-world network analyses. The data and R programs used will be available at https://github.com/bavla/symbNets.

[1] Batagelj, Vladimir, and Daria Maltseva. "Temporal bibliographic networks." Journal of Informetrics 14, no. 1 (2020): 101006.

[2] Batagelj, Vladimir. "Clustering and blockmodeling temporal networks: two indirect approaches." Classification and data science in the digital age, Springer (2023): 63-71.

[3] Batagelj, Vladimir, Tomaž Pisanski, Iztok Savnik, Ana Slavec, and Nino Bašic. "Towards a Format for Describing Networks." SiKDD 2025 Proceedings, Ljubljana (2025), pages 102-105.