Please cite this article as: K. Angelou, M. Maragakis, K. Kosmidis et al., A hybrid model for the patent citation network structure, Physica A (2019) 123363, https://doi.org/10.1016/j.physa.2019.123363. Physica A xxx (xxxx) xxx Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa A hybrid model for the patent citation network structure Konstantinos Angelou a,b , Michael Maragakis a,b,c , Kosmas Kosmidis a,b , Panos Argyrakis a,b,∗ a Department of Physics, University of Thessaloniki, Greece b Center of Complex Systems, University of Thessaloniki, Greece c Department of Physics, International Hellenic University, Kavala, Greece article info Article history: Received 29 March 2019 Received in revised form 18 October 2019 Available online xxxx Keywords: Patent citation networks Percolation Preferential attachment Hybrid networks abstract Percolation theory on the patent citation network is studied and the percolation threshold points are identified. The results show that there is a significant change of the threshold throughout our dataset years, implying changes in the formation process of the patent citation network. There is a first shift at around 2001, and a very delayed transition point after 2008. Giant component formation in such networks is an indication of the existence of inter-disciplinary patents. In order to explain the changes observed, a hybrid model for creating networks is suggested here. The model is based on a combination of random networks and preferential attachment. It is also compared with results from the well-known configuration model. The hybrid model fits better the data of the patent citation network, rather than a single scale-free or a single Erdős–Rényi network, and explains the increase in preferential attachment in later years. Both the degree distribution and the results of the analysis through percolation theory agree well with real data. This enables the formation of a plausible explanation for the structural changes of the patent citation network’s evolution. © 2019 Elsevier B.V. All rights reserved. 1. Introduction Percolation is a prototype model that reveals a phase transition. Broadbent and Hammersley first introduced the term in order to model the flow of fluid in a porous medium with randomly blocked channels [1]. Its simplest application is on a two dimensional square lattice. Some of the lattice sites are open and some are closed, which means that they cannot be accessed. We start with a lattice of no open sites and increase their concentration progressively, by adding open sites randomly. When a path of open sites from one end of the lattice to the other is formed for the first time, we say that the percolating giant component has just been emerged, and that we have reached the percolation threshold. Percolation has been studied intensely [2–5], as it has application on numerous real-world systems, in a wide variety of scientific fields. For example, it is applied in chemistry [6], electromagnetism [7,8], geology [9] and many more. In addition to lattice system the idea of percolation can be used in networks. Here if an extended cluster of network sites exists, then this corresponds to a system above its percolation threshold, whereas if only small isolated network clusters are present, then this corresponds to the system being below its percolation threshold. Thus, percolation has been extensively used on networks to study their resilience against the random removal of nodes [10,11] and the spread of diseases [12,13]. In addition, it has been applied to social systems to estimate a community’s lifetime [14], and to collaborative networks to identify how scientists are connected with other scientists of their field [15–17]. ∗ Corresponding author at: Department of Physics, University of Thessaloniki, Greece. E-mail address: panos@auth.gr (P. Argyrakis). https://doi.org/10.1016/j.physa.2019.123363 0378-4371/© 2019 Elsevier B.V. All rights reserved.