European LNG Import Network Analysis and Investigation of Supply Security

Abstract

The shift of European countries to more environmentally friendly sources of energy is leading to an increase in the share of natural gas in the energy mix. At the same time, the flexibility and cost-effectiveness of maritime transport are making liquefied natural gas (LNG) more competitive compared to traditional forms of natural gas, despite recent geopolitical, health and economic events threatening its supply chain. The aim of this study is to analyze the European LNG import network using network theory indicators to identify trading communities in the network and to investigate the security of supply through network failure simulation. The network model was developed using a programming code in MATLAB R2022B software. The results of the analysis can be summarized as follows: (a) a shift in the center of gravity of LNG trade from the Mediterranean to the Atlantic shores was identified; (b) a gradual consolidation of Europe’s import network was noted; (c) an increasing dependence of Europe on a limited number of countries was observed; and (d) the most critical nodes for network resilience were identified through modeling. Based on these findings, recommendations are proposed to strengthen Europe’s energy security and independence.

1. Introduction

Since the first maritime transport of liquefied natural gas (LNG) in 1958 from Lake Charles in the USA to the UK, the natural gas trade has seen significant growth [1]. Global consumption increased rapidly during the period 2000–2016, from 2404.6 to 3670.4 bcm per year, with an average annual growth rate of 2.50% [2]. Compared to conventional liquid fuels, natural gas is advantageous both in terms of its environmental footprint and its production costs [3]. In fact, according to [4], natural gas causes 55% fewer carbon emissions than coal and 17% fewer emissions than crude oil, making it a leading cleaner energy source. The reduction in the carbon footprint, however, is not the only factor that makes natural gas a useful vehicle for the energy transition. The integration of new technologies makes LNG more competitive than ever, compared to other energy sources, while the rush to comply with recent environmental regulations also plays a significant role.

Primarily, the transport, and therefore the trade, of natural gas is carried out either by pipeline (PNG) or through its liquefaction by maritime transport (LNG). Despite LNG’s more complex supply chain compared to PNG, LNG is steadily gaining ground [5]. In 2015, the share of LNG in the natural gas trade was 32%; however, forecasts suggest that it is expected to increase to 48% by 2040 [6,7], or even surpass the share of PNG by 2050 [8]. The significant geographic decentralization of natural gas demand contrasts with the geographically limited, almost monopolistic concentration of gas reserves, with more than 70% concentrated in the Commonwealth of Independent States (CIS) and Middle East regions [9]. This strong imbalance is compensated by international trade, as the flexibility and low cost over long distances provided by LNG are a competitive advantage.

At the same time, the shift of European countries towards the search for more sustainable energy sources, combined with increasing instability in the international landscape, jeopardizes Europe’s energy security. According to BP [9], in 2019, Russia and the USA had an almost equal share of its supply. Since then, rising transportation costs, due to emerging terrorism, supply chain disruptions due to the COVID-19 pandemic, and disturbances resulting from the Russian–Ukrainian conflict have brought radical changes to Europe’s imports, threatened its supply security, and caused a rapid increase in gas prices [10]. Due to the aforementioned events, the five-year period from 2018 to 2022 was selected to examine potential changes in the structure and characteristics of the network.

This work aims to model and analyze Europe’s LNG import network for the selected time period using complex network theory indicators such as network density, connectivity, degree of connectivity, network centrality, average shortest path length, and clustering coefficient. The study also relies on a community detection algorithm to investigate Europe’s supply security and the resilience of LNG ports through simulation techniques based on node failures. It attempts to provide answers to the following questions:

• What is the current landscape of the European LNG import market?
• Which are the main trading communities involved?
• Is the European LNG supply network able to cope with disruptions to the supply chain that could endanger the prosperity of European nations?

The contribution of this research lies in its emphasis on the trade and network resilience of European LNG. The methodology used, based on modularity, provides a quantitative and robust approach to identifying trade communities, offering critical insights into trends regarding the evolution of the most critical nodes in the network. The study collects LNG data at a port level and thus conducts the analysis on a country-to-port basis. Data were collected over a five-year period (2018–2022), highlighting the impact of geopolitical, health, and economic disruptions to the European LNG supply chain. By simulating intentional and random attacks on critical nodes and chokepoint failures, the research highlights significant impacts on the LNG network and the importance of a resilient European LNG supply chain.

Therefore, Section 1 in this study provides an introduction to natural gas, LNG, and the related challenges faced by Europe. A review of the existing literature is presented in Section 2. Section 3 includes the theoretical part of the developed model and describes the collection and manipulation of the collected data. Section 4 and Section 5 present the results from the model analysis and provide an interpretation and discussion, as well as the main conclusions and policy implementations.

2. Literature Review

A two-fold process was used in the analysis of previous studies. First, works related to the analysis of trade flow networks are presented. Second, a literature review of applied methodologies for investigating the resilience of LNG networks is provided.

Table 1. Relevant research on LNG trade.

Study	Approach	Data Source	Reference Period
[11]	Global LNG and PNG trade network spatial structure and communities	AIS DATA (HiFleet)	2013–2017
[8]	Global LNG and PNG trade network spatial structure	UN Comtrade Database	2000–2021
[12]	Global LNG and PNG trade network spatial structure and integration	BP Statistical Review	2000–2011
[2]	BRI LNG trade network spatial structure and future projection	UN Comtrade Database	1992–2016
[13]	Global LNG trade network spatial structure and future projection	UN Comtrade Database	2019
[7]	Global LNG exporters competition network analysis	UN Comtrade Database	2005–2014
[14]	Global LNG trade network spatial structure and future projection	UN Comtrade Database	2015
[15]	Global LNG exporters competition network analysis	UN Comtrade Database	2000–2020
[4]	Global LNG trade network spatial resilience and communities during the Ukrainian War	AIS DATA (Shipxy)	2021–2022
[16]	China’s LNG trade network resilience	AIS DATA (HiFleet)	2011–2017
[17]	Global LNG trade network resilience	BP Statistical Review & UN Comtrade Database	2010, 2015, 2020
[10]	Global LNG trade network spatial structure, communities and resilience	AIS Data (HiFleet)	2018–2020

presents the relevant research analysis.

2.1. Freight Flow Network Analysis

In recent years, network analysis has been widely accepted for investigating trade in liquid fuels and mineral resources and has been used for various purposes, as follows:

• Investigations of the spatial structure and evolution of the maritime oil trade, both at the state level [18,19,20] and at the port level [21]. Apart from crude oil, similar research has been conducted on the trade network for coal [22], energy [7], and fossil fuels in general [23,24];
• Identification of commercial communities where most algorithms are based on the concept of modularity. One widely used algorithm was proposed by [25], and has been used to identify communities by [26] for the oil trade, by [27] for fossil fuel trade, and by [11] for the LPG trade;
• Examination of trade dependencies in the fossil fuel trade [28] or, more specifically, in the oil trade [29];
• Optimization of the trade structure, with one study [30] attempting to optimize the oil trading network;
• Investigation of competitive relationships, as in the case of [31], in which the competitive relationships of international crude oil importers were examined. Additionally, [32] studied iron ore trade, [33] examined the graphite trade, [34] studied the coal trade, and [35,36] explored the tungsten trade and lithium trade, respectively. Finally, the rare earth trade was examined in terms of importers’ competition by [37] and in terms of exporters’ competition by [38].

Focusing more on natural gas, ref. [12] constructed the global gas network using BP reporting data for the period 2000–2011. Ref. [2] based their analysis on a sample of 66 countries in the Belt and Road Initiative trade area, seeking to conduct a comparative analysis of LNG and pipeline (PNG) trade networks, while [8] expanded the analysis of LNG trade to 215 countries for the period 2000–2021, thus examining the influence of the COVID-19 pandemic.

At the port level, ref. [11] exploited massive ship trajectory data and mapped the most well-connected ports in the network from 2013 to 2017 to identify the hub ports for global trade. They observed that the top three ports, in terms of connected routes, remained stable over time; the Port of Singapore consistently retained the top spot, with those of Khawr Fakkan in the UAE and Ras Laffan in Qatar also being among the top three.

To investigate the spatial structure of these networks, many different indicators from complex network theory were employed [39], as follows: (a) Network density has been exploited in studies several times, with [2,8] finding a steady increase in the density of both the LNG and PNG trade; (b) Two studies [8,11] concluded that the network clustering factor, and thus the tightness of trade links, showed a steady increase, while [2,12] added that this increase is more rapid in the case of LNG versus PNG; (c) The average shortest path length of a route was shown to have a long-term decrease, and hence that trading partners are more directly linked to each other, showing strong fluctuations [8,11]; (d) Other studies [2,12] found a significant increase in the centrality of connection degrees in LNG trade networks, while monopolistic features were shown to be more pronounced in the exporter market, as exemplified by Qatar, which owned 10.25% of the global market share in 2000 and 31.01% of the global market share in 2011; and (e) Studies [11,12] have mapped the distribution of the degree of connectivity to examine whether a network is a scale-free network, showing that a narrow core of nodes is becoming increasingly important for the network.

At the same time, although the segmentation of the global trade network is steadily increasing and the international LNG trade is becoming increasingly decentralized [11], the European LNG market seems to be consolidating into a single trading community [10]. In addition, the emergence of natural gas as an energy source has led to the use of forecasting algorithms as another application of network analysis [2,13,14].

2.2. Applied Methods of Investigating Security of Supply

According to [40], potential disruptions in the energy supply chain can include, as follows: increased demand, price volatility, the political instability of exporters, longer distances resulting from trade globalization, and piracy and armed conflicts along trade corridors.

The ability of the transport infrastructure to perform its purpose in the face of potential supply chain disruptions can be examined in the following two ways [41]: by approaching it as a system (system-based); or as a network (network-based). An illustrative example of a system-based approach is the assessment of the impact of the disruption of geographically critical network points, which was carried out by [42]. A network-based analysis of the system was carried out [41]. Other examples include, as follows: (a) mathematical optimization of network resilience by maximizing proportional indicators [43] or minimizing costs [44]; (b) using past data to examine indicators representing network resilience under the influence of specific events, such as the COVID-19 pandemic [45] or the Russia-Ukraine conflict [4]; and (c) simulating disturbances in a network model through node or link failures [46].

Distinctions between the quantities representing the ability of a network to cope with disruptions is not always clear in the literature. This is why, in some studies [4,17] the quantification of reliability, robustness and vulnerability is considered part of the assessment of the overall resilience of the system, for which the indicators are divided into three main categories [41], as follows:

• Indicators focusing on the performance of the system during failure, such as the number of TEUs that could be delivered to their destination on the failed network [46] or the costs caused by the failure [47];
• Indicators focusing on operational characteristics, indicative of the system stability index and the supplier reliability index [40], or the normalized mutual information (NMI) stability index used by [23] to compare gas, crude oil, and coal supply networks;
• Indicators of complex network theory [48] reflecting their topological features, where either the evolution over time [46] or the percentage change [10] are shown.

More specifically, to investigate LNG supply security, ref. [49] used network interconnectivity, invulnerability, and resilience, as indicators that depend on the topological characteristics of the network. Using these indicators, ref. [17] found a decrease in network resilience over the period 2010–2020. The same indicators were also exploited by [4], revealing that only the failure of specific critical nodes, such as the Straits of Hormuz or Malacca, can drastically affect the international LNG trade, while targeted attacks result in more significant losses compared to random failures. Ref. [10] reached the same conclusions, using topological indicators.

Overall, it is evident that international trade, particularly in the European market, is shifting away from its decentralized form towards integration. Despite increasing competition among importers to meet their energy needs, European countries are collaborating within a unified energy policy framework. Therefore, exploring the European LNG market is crucial, even though the Asian market has traditionally been the main focus due to its size.

3. Materials and Methods

3.1. Network Modelling

A directed network G(V,E,W) was generated to represent all pairs of trade relations between countries or ports on an annual basis [2,11]. The nodes V = {v₁, v₂, v₃, …, v_n} represent the exporting countries, import or transshipment ports, and certain chokepoints of the maritime trade routes. The set E = {e_ij} represents the links between nodes i and j, with each element assigned the value 1 if the relationship exists, or 0 if not. The weight of each link in the network W = {w_ij} expresses the volume transported between the two ports i and j in million tons (MT). The network is represented by an origin–destination table A = {a_ij = w_ij}.

The adoption of a directed network contributes to a better understanding of the flow and direction of trade flows. A significant majority of existing studies in the literature focus on analysis at a country level, while the few studies that have conducted an analysis at the port level [4,10,11] have used AIS data. This study aims to explore LNG trade involving port elements. Furthermore, despite the critical importance of chokepoints in maritime trade [50,51], the inclusion of chokepoints in international LNG trade research is limited [4,17]. According to the International Energy Agency, chokepoints are defined as “narrow channels along widely used global shipping routes, some of which are so narrow that constraints regulate the size of ships that can be served”. The Panama and Suez Canals and the Straits of Gibraltar, Sunda, and Hormuz were included in the context of this analysis, based on the study by [42].

3.2. Topological Indicators

In order to analyze the network, the following indicators of the complex network theory were used:

• Network size

Network size is not always defined consistently. For example, ref. [4] defines it as the sum of nodes, while [17] defines it as the sum of nodes and links. In this research, network size is considered to be equal to the set of nodes in the largest connected component (LCC). This means that it is the largest subnetwork where it is possible to reach any node from any other node within the same subnetwork. This distinction is necessary because the disruptions that will be simulated in the framework of this research may fragment the network into smaller disconnected networks. In practice, network size represents all exporting countries and ports for LNG importers.

• Network density

The density of a network is defined as follows:

Δ = l/(n(n − 1)),

(1)

where l is the number of links in the network and n is the number of nodes. The density takes values from 0 to 0.50. Higher values indicate better connectivity between nodes in the network [8,12];

• Unweighted and weighted degree of connectivity

The in-degree (k_iⁱⁿ) and out-degree (k_i^out) of connectivity, unweighted, express the degree for the number of nodes within the exporting to and importing from relationship, respectively, as follows:

$${\mathrm{k}}_{\mathrm{i}}^{\mathrm{i}\mathrm{n}}={\sum }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{a}}_{\mathrm{j}\mathrm{i}}$$

(2)

$${\mathrm{k}}_{\mathrm{i}}^{\mathrm{o}\mathrm{u}\mathrm{t}}={\sum }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{a}}_{\mathrm{i}\mathrm{j}}$$

(3)

where for node i, a_ij = 1 if there is a trade flow from node i to node j, or 0 if there is not.

The weighted in-strength ${(\mathrm{s}}_{\mathrm{i}}^{\mathrm{i}\mathrm{n}})$ and out-strength ${(\mathrm{s}}_{\mathrm{i}}^{\mathrm{o}\mathrm{u}\mathrm{t}})$ of node i represent the annual export and import volume, as follows:

$${\mathrm{s}}_{\mathrm{i}}^{\mathrm{i}\mathrm{n}}={\sum }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{a}}_{\mathrm{j}\mathrm{i}}{\mathrm{w}}_{\mathrm{j}\mathrm{i}}$$

(4)

$${\mathrm{s}}_{\mathrm{i}}^{\mathrm{o}\mathrm{u}\mathrm{t}}={\sum }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{a}}_{\mathrm{i}\mathrm{j}}{\mathrm{w}}_{\mathrm{i}\mathrm{j}}$$

(5)

where w_ij is the trade volume from node i to j [12];

• Network connectivity

According to related studies [4,17], network connectivity is defined as the set of possible paths established in the network. A higher value of network connectivity indicates a strong and consistent connectivity between nodes, offering alternative routes;

• Degree of network centrality

The out-degree (${\mathrm{C}}^{\mathrm{o}\mathrm{u}\mathrm{t}})$ and in-degree ${(\mathrm{C}}^{\mathrm{i}\mathrm{n}})$ of network centrality indicate the degree of monopoly and competition in the export and import markets, respectively [12]. They are calculated as follows:

$${\mathrm{C}}^{\mathrm{o}\mathrm{u}\mathrm{t}}={\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{k}}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{o}\mathrm{u}\mathrm{t}}-{\mathrm{k}}_{\mathrm{i}}^{\mathrm{o}\mathrm{u}\mathrm{t}})}{{(\mathrm{n}-1)}^2}}$$

(6)

$${\mathrm{C}}^{\mathrm{i}\mathrm{n}}={\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{k}}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{i}\mathrm{n}}-{\mathrm{k}}_{\mathrm{i}}^{\mathrm{i}\mathrm{n}})}{{(\mathrm{n}-1)}^2}}$$

(7)

where k_iⁱⁿ and k_i^out represent the in-degree and out-degree of node i, respectively, and k_maxⁱⁿ and k_i^out are the maximum in-degree and out-degree of the nodes, respectively;

• Average shortest path length

The average shortest path length represents the average topological distance between all possible pairs of paths from the perspective of transshipments [11] and is calculated using the following formula:

$$\mathrm{L}={\displaystyle \frac{1}{\mathrm{n}(\mathrm{n}-1)}}{\sum }_{\mathrm{i},\mathrm{j}}\mathrm{d}({\mathrm{v}}_{\mathrm{i}},{\mathrm{v}}_{\mathrm{j}}),$$

(8)

where n is the number of nodes in the network and d(v_i,v_j) is the length of the shortest distance to travel from node v_i to node v_j;

• Clustering coefficient

The clustering coefficient of a node (C_i) is defined as the ratio of the number of existing links (e_i) connecting neighboring nodes (${\mathrm{k}}_{\mathrm{i}})$ to the maximum possible links between them. It expresses how well the neighboring nodes are connected and reflects the efficiency and robustness of the network [10]. The node and network clustering coefficients are calculated as follows:

$${\mathrm{C}}_{\mathrm{i}}={\displaystyle \frac{{\mathrm{e}}_{\mathrm{i}}}{{\mathrm{k}}_{\mathrm{i}}({\mathrm{k}}_{\mathrm{i}}-1)/2}}$$

(9)

The average clustering coefficient of the network ($\overline{\mathrm{C}}$) is as follows:

$$\overline{\mathrm{C}}={\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{i}}$$

(10)

• Network resilience

The index measures the resilience of the network against disturbances. It is a qualitative representation [4,17] and is equal to, as follows:

$${\mathrm{R}}_{\mathrm{s}}={\displaystyle \frac{\mathrm{N}\mathrm{V}\times \mathrm{n}}{\mathsf{\Delta }\times \mathrm{C}\mathrm{i}\mathrm{n}}}$$

(11)

where NV and n are defined as connectivity and network size, respectively, and are directly proportional to resilience. Conversely, Δ and Cⁱⁿ represent the network density and centrality, respectively.

3.3. Community Detection Algorithm

Ref. [52] defined community structure as a scenario in which nodes in a network belong to a group of nodes with strong connections among them. Modularity expresses the quality of this separation [11], and is derived from the following formula:

$$\mathrm{Q}={\displaystyle \frac{1}{2\mathrm{m}}}{\sum }_{\mathrm{i},\mathrm{j}}[{\mathrm{A}}_{\mathrm{i}\mathrm{j}}-{\displaystyle \frac{{\mathrm{k}}_{\mathrm{i}}{\mathrm{k}}_{\mathrm{j}}}{2\mathrm{m}}}]\mathsf{\delta }({\mathrm{c}}_{\mathrm{i}},{\mathrm{c}}_{\mathrm{j}})$$

(12)

where A_ij = w_ij, k_i represents the degree of connectivity of node i, m is half of the total weights of the links in the network, and the function δ(c_i,c_j) takes the value of 1 if nodes i and j belong to the same community; otherwise, the value is 0. Based on maximizing the modularity in the network, ref. [26] applied the following community separation algorithm:

Step 1: Each node is considered a separate community;

Step 2: Each pair of neighboring nodes i and j is merged, forming a new community. Calculate the change in the value of the modularity in the network, ΔQ_ij;

Step 3: Each node is moved to the community to which its movement brings the maximum possible increase in modularity, if it is positive;

Step 4: Steps 2 and 3 are repeated until ΔQ_ij is less than or equal to zero for each pair of adjacent nodes i and j.

3.4. Simulation of Network Failures

In this study, a network-based approach was followed to analyze the resilience of transportation systems, a method that has been widely used in previous research [4,10,17], making it the most reliable choice. The approach involves simulating network node failures and observing specific network characteristics or their changes. Two types of failures were simulated, as follows:

• Cumulative failures, which simulate consecutive sequential failures due to systemic factors within a limited timeframe that is insufficient for repair and recovery of the damages. They are further divided into random failures and intentional failures depending on the sequence of the node failure. In the case of random failures, nodes are randomly selected to fail, representing the scenario where certain nodes fail due to random factors such as natural disasters, technical issues, or sociopolitical factors affecting their operation. In intentional failures, nodes are removed in the order of their importance based on their weighted connectivity [4], simulating potential failures caused by targeted military operations, terrorist attacks, or acts of sabotage. During these simulated failures, the following three indexes are monitored in relation to the initial number of nodes in the network [46]: the network resilience index; the network clustering coefficient, and the percentage of nodes remaining in the largest connected component (LCC);
• Individual failures, where nodes fail independently [46,48]. The same indexes used in the previous case are calculated, along with an additional measure of network efficiency. In this study, network performance is defined as the percentage of total imported LNG that can still be delivered despite the failure of an individual node.

3.5. Data

The majority of studies in the literature concerning LNG trade at port level use AIS data. The collection of reliable data for LNG trade flows without the use of AIS data limited this study to a ‘country-to-port’ level. This is mainly due to the high decentralization and flexibility of the international LNG trade as well as the continuous increase in the share of direct markets (spot markets) that replace long-term supply contracts. The following data were collected for the years between 2018 and 2022 (

Table 2. Variables used for the modeling analysis.

Description	Time Frequency	Source	Unit
Trade LNG volumes between countries	Annually	GIIGNL (International Group of LNG Importers)	Million tons
Volumes of European ports	- Quarterly - Annually	- Eurostat’s dataset: mar_go_qm_detl - GOV.UK table: Port0499	Thousand tons
Import volumes for each terminal	Daily	GIE’s Aggregated LNG System Inventory (ALSI) database	Thousand m3

):

• Trade volumes of LNG flows between countries;
• Volumes of LNG transported from European ports hosting LNG import terminals to all potential trading partners;
• Import volumes for each terminal based on regasification and sent-out volumes.

The category of liquefied gas (code 11) was selected as a type of cargo, which also included butane and propane. The data synthesis was carried out through the following steps, repeated for each of the five study years:

• The quarterly cargo volumes of the ports, extracted from the Eurostat database were are aggregated to convert the data to an annual level;
• The daily inflow values were extracted from the GIE ALSI database and summed up to convert them into annual quantities. The annual inflow volumes of terminals within the same port were then combined to convert the volumes to a port-level basis. The resulting data show minimal deviations compared to the transnationally traded volumes reported in the GIIGNL reports;
• Using the port data extracted from Eurostat, specifically the import flows of each port (inward flows), combined with the LNG transnational trade data from GIIGNL reports, direct commercial flows between exporters and importers were derived;
• The remaining flows were supplemented by following trade flows from exporting countries to other trading countries where transshipments were presumed to occur until they reach the importing country, according to GIIGNL reports.

Direct flows between exporters and importers were determined using port data from Eurostat and LNG trade volumes between countries. According to data from GIIGNL, any observed volumes greater than traded ones were excluded as excess volume, as they were considered to represent bulk-liquefied categories other than LNG. If flows reported in the Eurostat database were not reflected in the GIIGNL reports, the data were supplemented under the assumption that the quantities in question were delivered through transshipments. The port whose handled quantity had not been completed was used as a point of entry, as derived from the ALSI database.

Following the methodology of [17], chokepoints were identified from SeaRates (www.searates.com/gr/distance-time, accessed on 20 May 2024) annual origin–destination tables, based on the volumes of LNG traded on each route. Figure 1 illustrates the European LNG import and export infrastructure within the network.

The calculation methodology and failure simulation were carried out using code developed in MATLAB. The code manages data input, extraction, calculation of the selected indicators, division of the network into communities through the execution of the selected algorithm, simulating network failures, displaying indicator values during the simulation, and creating corresponding diagrams. It is important to emphasize that the code developed for this work can be applied to analyze and simulate any network, making it a versatile tool with many applications. The code consists of 22 functions, including basic functions that are used to create more complex operations and 4 functions to plot and visualize the results of the analysis. A sum of the basic and complex functions can be seen in

Table 3. Main functions for code development.

Functions	Output
dataYEAR.m	Annual network register, with nodes including only the importing ports and exporting countries
dataYEARc.m	Annual network register, with nodes including chokepoints
nodesnumber.m	Initial size of LCC nodes, excluding other non-connected subnetworks New table with the remaining LCC nodes
degree.m	In-degree of connectivity Out-degree of connectivity Weighted in-strength of node Weighted out-strength of node
ncentrality.m	In-degree of network centrality Out-degree of network centrality
resilience.m	Network resilience
asplength.m	Average shortest path length
clusteringc.m	Clustering coefficient
nwanalysis.m	Complex function that includes 9 basic functions and calculates the set of network theory indicators
communities.m	Complex function that calculates modularity and community structure
simulation.m	LCC/Resilience/Clustering coefficient (Intnetional failures) LCC/Resilience/Clustering coefficient (Random failures) LCC/Resilience/Clustering coefficient (Individual failures)

.

The flow chart of the analysis process is illustrated in Figure 2.

4. Results

The outcomes of the selected indicators are outlined in

Table 4. Values of the topological indicators of the examined LNG trade network.

Year	2018	2019	2020	2021	2022
Number of nodes	38	39	39	43	49
Number of links	110	154	154	137	197
Density (Δ)	0.08	0.10	0.10	0.08	0.08
Connectivity (NV)	280	456	658	261	1270
In-degree (Cin)	69.27	78.10	93.05	81.64	137.77
Out-degree (Cout)	154.69	168.44	194.13	170.89	561.33
Average shortest path length (L)	0.16	0.24	0.33	0.11	0.23
Clustering coefficient (Ci)	0.000902	0.000495	0.001348	0.000654	0.000857
Resilience (Rs)	1963.41	2191.29	2653.95	1812.15	5392.72
Modularity (Q)	0.67	0.52	0.43	0.52	0.04
Number of trade communities	11	15	15	12	16

below.

4.1. Evolution of Spatial Network Structure

Network nodes increased sharply by 25.64% from 2020 to 2022, possibly as a delayed reaction to the market. The market noticed a rapid increase in consumption and quickly sought out new trading partners to meet the demand. Import ports increased from 26 to 32, while exporters increased from 12 to 17. There was also a significant 79.09% increase, from 2018 to 2022, in the number of links in the network representing trade relations. This increase occurred during a period of intense disturbances, highlighting the sensitivity of the supply to maritime trade. This suggests that the international LNG trade is still developing. The consistent trend in the number of links in 2019 and 2020, followed by a decline in 2021, coincides with the years of the COVID-19 pandemic. According to Figure 3, where the sources of LNG imports during the study period are depicted along with the corresponding imported quantities, the trade volume increased by 166.40%; from 41,188 to 109,724 MT. This significant increase in imported LNG was largely supported by the USA, which increased LNG exports to Europe from 5.98% in 2018 to 44.34% in 2022. The growth of the USA market share was particularly rapid from 2021 onwards, highlighting the impact of the Russian–Ukrainian conflict and European sanctions. These events forced EU member states to seek alternative sources of natural gas imports [4].

Analyzing the degrees of network centrality provides critical insights into the evolution of the most important nodes in the network and the geographical center of gravity of LNG trade to Europe. Important nodes are defined as nodes, ports, or chokepoints through which significant quantities of LNG critical to the network are transported.

Table 5. Ranking of the top 15 nodes based on their maximum in- and out-degree (years 2018, 2020 and 2022).

Network Nodes Degree Change
	2018		2020		2022
1	Qatar	14.206	Gibraltar	20.196	USA	48.648
2	Suez	14.206	Qatar	19.726	Gibraltar	30.760
3	Hormuz	14.206	Suez	19.726	Suez	19.713
4	Gibraltar	12.065	Hormuz	19.726	Hormuz	18.820
5	Algeria	5.805	USA	16.269	Qatar	18.757
6	Nigeria	5.780	Russia	12.400	Russia	13.799
7	Marseille Fos	5.337	Nigeria	8.350	Zeebrugge	13.591
8	Rovigo LNG	4.580	Milford Haven	7.745	Milford Haven	12.028
9	Russia	4.456	Rotterdam	5.897	Rotterdam	11.973
10	Nantes Saint-Nazaire	4.372	Zeebrugge	5.875	Nantes Saint-Nazaire	10.690
11	Barcelona	3.895	Algeria	5.836	Dunkerque	9.637
12	Rotterdam	3.595	Nantes Saint-Nazaire	5.829	Nigeria	8.044
13	Milford Haven	3.566	London	5.275	London	6.891
14	Huelva	3.435	Rovigo LNG	5.230	Rovigo LNG	5.612
15	Norway	3.263	Marseille Fos	4.875	Marseille Fos	5.569

lists the top 15 nodes in terms of maximum in- and out-degrees in descending order for the years 2018, 2020 and 2022.

At first glance, there is a noticeable decline in the importance of Qatar as a supplier of LNG to Europe. This trend is also evident for Nigeria and, to a greater extent, Algeria. Conversely, while the USA did not rank among the top 15 nodes in 2018, by 2022 it had become the most crucial hub for suppling Europe.

This shift in supply sources is reflected in the broader network structure. Ports with easier and more cost-effective access from the USA, such as Zeebrugge, Milford Haven, and Rotterdam on the Atlantic coast of Europe, are gaining significance. On the other hand, ports, such as Marseille, Barcelona, Huelva and the Rovigo LNG terminal, which have been strategically positioned for routes from Qatar, appear to be losing importance. This shift underscores the European market’s move towards exporters from the West and the relocation of the supply center to the Atlantic shores of Europe. Furthermore, the evolution of congestion points, with three congestion points consistently among the top four major nodes, aligns with the broader network changes. Specifically, the importance of the Strait of Gibraltar is increasing relative to the Suez Canal and the Straits of Hormuz, a trend also supported by [4] in the context of total international LNG trade.

The upward trend in the in-degree and out-degree (Figure 4) indicates a rise, with the latter consistently higher than the former, suggesting stronger monopolistic characteristics in the export market. The 262.83% increase in the out-degree over the study period indicates the growing dependence of European countries on a limited number of exporters. In 2018, the top three exporters held about 62% of the market share compared to 74% in 2022.

In addition, the average shortest path length remains extremely low, despite its increasing value. This indicates that most trading partners are directly connected rather than connected through successive transshipments. At the same time, the clustering coefficient experienced a slight decrease over the study period. The range of its values suggests that, on average, network nodes only engaged in 8 and 9% of the maximum possible trade relations with each other. The slight increase in the average shortest path length, combined with the decrease in the clustering coefficient, are typical characteristics of an expanding network. The rapid growth in network nodes results in commercial links becoming looser, with transshipments playing a more significant role in total traffic.

Finally, the resilience index of the network, though temporarily disrupted in 2021, probably due to the insecurity and instability caused by the COVID-19 pandemic, shows an overall upward trend throughout the study period.

4.2. Trade Communities

Although it may seem as if the number of trading communities on the network is increasing, in reality, the number of communities decreases from 8 in 2018 to 7 in 2022 when nodes that do not participate in a community are removed. At the same time, modularity, which ranges from −1 to 1, approaches zero in 2022. These findings suggest that the European LNG supply market is gradually integrating, possibly due to the development of common energy policies [10].

A significant change is the consolidation of the two trading communities that, in 2018 included the majority of the North Sea and Baltic Sea ports. The first community, in 2018, consisted of ports in the west of the Iberian Peninsula and UK ports, primarily supplied by the USA. The second community comprised Scandinavian and Baltic ports, supplied mainly through transshipments at the port of Dunkirk. In 2022, a new unified community emerged, incorporating the hubs of Qatar and Rotterdam.

Additionally, there is a community of hubs with Russia as the main exporter and the port of Rotterdam as the main transshipment point, with Zeebrugge in Belgium following. This community has expanded, with the inclusion of ports on the north coast of Spain and the port of Nantes.

Major West African exporting countries joined a joint trading community with Egypt in 2018, exporting LNG primarily to the ports of Zeebrugge and Livorno. In 2022, it seems that ports on the Mediterranean coast of Spain, supplied mainly by Trinidad and Tobago, will join this community. Finally, a significant trade community has formed through the commercial relations between Algeria and the ports of Marseille and La Spezia on the Mediterranean.

4.3. Security of Supply

The evolution of indicators during the simulation of failures was visualized through the developed code. Specifically, in the case of individual node failures, the failing nodes are placed on the horizontal axis, and the percentage change of each index during the failure is presented on the vertical axis. Figure 5 illustrates the change in network performance during the failure of individual nodes.

The abrupt removal of key importers from the network, such as Russia, Qatar and the USA, results in a significant decrease in delivered quantities. Ports with significant transshipment traffic, such as Milford Haven, Rotterdam and Zeebrugge, also have a major impact, while the seaports of Gibraltar, Suez, and Hormuz play an even more crucial role. This becomes more evident when examining the largest connected component (LCC) of the network, revealing that a potential disruption of the Strait of Gibraltar or the Suez Canal would isolate approximately 45% or 16% of the network nodes from the rest.

Additionally, there is an interesting increase in the resilience index when the USA is withdrawn from the network. This fact of strong monopolistic elements reduces the degree of network centrality, thus enhancing its resilience.

Nodes with a high clustering coefficient are part of closely cooperating groups, such as exporters from Mozambique, Oman, UAE, and others. Nodes with high throughput rates in disconnected nodes, such as the Suez Canal node, contribute to an increase in the coefficient when they fail (Figure 6). Conversely, the failure of core commercial communities in 2022, such as those in the ports of Nantes and Algeria, or key points connecting commercial communities to the network, such as the Strait of Gibraltar, lead to a significant decrease in the network clustering factor (red circles in Figure 6).

In the case of cumulative failures, the total number of nodes removed is plotted on the horizontal axis and the index value is plotted on the vertical axis in each diagram displaying both random and intentional failures. Figure 7 shows the evolution of the percentage of the remaining LCC size of the network in relation to the total size of the original network. During random failures, the index decreases almost linearly after the first 17 nodes fail. On the contrary, intentional attacks result in network shrinkage and collapse much earlier, as noted in [10,17]. It is important to highlight that the failure of the three most crucial nodes leads to approximately 50% of the nodes being disconnected from the network.

In terms of the resilience index, as shown in Figure 8, the trend is not linear when it comes to the decrease in the index during random failures. It is interesting to observe that temporarily increasing the resilience of the network by decentralizing connectivity and removing the most important nodes can lead to greater resilience [4].

Based on the above, potential attacks or failures at the ports along the Atlantic coast could more drastically reduce the network’s resilience, affecting its performance and connectivity. As also revealed by the network structure analysis, this segment has gained vital importance in recent years, while the criticality of the Strait of Gibraltar surpasses that of the Suez Canal. The search for new, sustainable energy sources in Europe and the effort to reduce dependence on Russian natural gas, which was traded as PNG through pipelines, appear to be major contributing factors. In any case, the resurgence of terrorism and geopolitical unrest in the Middle East are expected to further threaten the stability of the network.

5. Conclusions

In general, the results extracted from this work are in significant agreement with previous studies in the literature. The results of the analysis could be particularly useful to market participants, regulators, or other parties involved in the trade. The main conclusions drawn, which may provide the base for future research, are summarized below:

• The European LNG import network in the years 2018–2022 experienced a significant shift in its center of gravity from the Mediterranean to the Atlantic coast. This shift occurred as the large increase in LNG demand in Europe was mainly met by the USA, possibly as a result of Europe’s efforts to decouple from Russian gas;
• The substantial increase in the number of LNG importers in Europe and the imported volumes did not see a corresponding increase in exporters. Europe’s growing dependence on a limited number of countries is creating strong monopolistic characteristics in the LNG export market, threatening European energy security;
• The number of non-member communities seems to be decreasing and the boundaries between communities are becoming less clear. This suggests the consolidation of Europe’s LNG import network as a possible result of the single energy strategy;
• Targeted attacks will have a much more significant and immediate impact on Europe’s supply network, causing its complete collapse much earlier than random failures. Critical points include ports with high transshipment traffic, ports serving as the exclusive route for certain exporters to Europe, the Strait of Gibraltar, and the hub representing the USA.

Under this framework, European countries should adjust their investments to the shift in the center of gravity of trade by strengthening infrastructure on the Atlantic coast. Diversifying import sources could also be addressed by switching to alternative trading partners to mitigate the risk of high dependence on a limited number of exporters. The increased risk of targeted attacks indicates the necessity of implementing measures to protect the critical network infrastructure identified. It is important to note that this research only provides general policy directions based on the analysis results, while specific recommendations must be tailored for each individual infrastructure.

Research on the LNG trade, particularly on the security of its supply chain, is expected to become a focus in the upcoming period. Due to challenges in the data collection process, the current analysis was conducted at a country-to-port level. This difficulty has led to a limitation in the analysis as a result of the imbalance between exporters and importers. This disrupts the uniformity among the nodes and, consequently, and may mean that indicators, such as network size and connectivity, as well as those derived from them, are misleading. Therefore, conducting the analysis at a port-to-port level could provide a more comprehensive and accurate view of the network. In addition, a more thorough understanding of Europe’s energy security could be achieved by including hubs of the PNG import and distribution network in the LNG import network under analysis. This would allow for an examination of the structure and resilience of the entire gas import network. Lastly, the use of a network forecasting model that considers various working scenarios (case studies) as well as artificial intelligence applications, such as machine learning techniques [53,54], would contribute to a deeper understanding of LNG market trends.