Many systems can be intuitively modeled as knowledge graphs using entities and their relationships. However, we often have only partial or little knowledge of the inherent processes of complex, changing systems such as biomedical, economic or ecological systems. As a result, the construction of knowledge graphs often sufers from incompleteness which can lead to inaccurate analysis results and incorrect conclusions. A widely used approach is to monitor and analyse complex changing systems using time series of measurements. To understand a complex temporal network of processes, it is crucial to identify inherent temporal relationships and interactions. A complete temporal knowledge graph model could provide a better foundation for applications in complex systems and increase its potential to add context and connections that allow uncovering hidden or unknown relationships in data. We propose a snapshotbased knowledge graph model and temporal link prediction algorithm to find relationships between examined objects in successive time points of multivariate time series. We evaluate and demonstrate the functionality in an environmental chemistry use case and predict the transformations of molecules for two datasets. Our approach is able to discover previously unknown relationships in a snapshot-based knowledge graph helping to better understand the dynamics of the examined system. Knowledge representation and reasoning, Graph-based database models, Temporal data, Network algo2nd International Workshop on Knowledge Graph Reasoning for Explainable Artificial Intelligence, December 09, 2023, ∗Corresponding author.
CEUR ceur-ws.org
Understanding mechanics and dynamics in complex networks has become an active field
of research in recent years [
Most real-world systems are subject to constant change and therefore should not be treated as a static network [9]. In a graph, this means that nodes and edges can appear or disappear over time and that properties can change, leading to a completely new topology and dynamics. In many complex networks the transitions between the individual time points, i.e. the relationships, are completely unknown and can hardly be determined by experts. Nevertheless, it is common to record various values experimentally with the help of time series in order to better understand the development of e.g. processes over time [10, 11].
In most cases, the actual temporal relationships between individual time series cannot be derived directly from the collected multivariate time series [12, 13]. In order to track temporal developments in the data and to increase the accuracy of graph analyses, the underlying system should store data over a longer period of time and assign temporal properties such as timestamps [9].
We here present a new snapshot-based model for temporal knowledge graphs to find so far unknown relationships and interactions in complex systems. The prediction is based on measured quantities for large numbers of objects from multivariate time series such as molecule intensities in mass spectrometry experiments or vehicle counters for trafic monitoring. Our graph structure inherently integrates temporal properties to model and predict directed edges between entities in multivariate time series. The snapshot-based knowledge graph model and temporal link prediction are particularly useful when no temporal edges are known in advance and real-time monitoring is not or insuficiently possible. Our approach is generic and could be adopted to diferent complex changing systems, e.g. biological, economic or trafic networks. The temporal graph approach allows us to better represent the dynamic nature of temporal networks and to gain new insights into temporal dynamics based on graph analysis. We evaluate our approach to show its ability to uncover unknown information about the analysed system. Our main contributions are 1. A novel snapshot-based knowledge graph model to represent multivariate time series as a temporal graph structure. 2. A temporal link prediction algorithm to identify directed temporal edges between nodes across successive time points. 3. An evaluation of the approach using two datasets representing complex environmental chemistry systems.
The methods have been implemented in a graph database management system and can be analysed visually and statistically. In [14] we first introduced a temporal graph model specifically designed for molecules and chemical transformations. Compared to the previous publication, we here generalize the data model to objects and temporal edges without specific domain focus. Moreover, we here present the generalized methodology and actual link prediction algorithm that were not the focus of the use case in [14]. We further add a new dataset to the evaluation.
The paper is further organized as follows. We first discuss related work in Section 2. We present the snapshot-based temporal knowledge graph model in Section 3 and the temporal link prediction algorithm in Section 4. We then evaluate the model and algorithm in an environmental chemistry use case in Section 5 and conclude in Section 6.
The property graph model represents a directed heterogeneous multirelational network with
properties at nodes and edges. It is one of the standard models for representing data with
graph-like structure as a knowledge graph [
A central topic in graph analysis is the search for missing structures in an incomplete network, this is called link mining, more precisely link prediction in the domain of complex networks [28] and knowledge graph completion in the domain of knowledge graphs [29, 21]. Link prediction algorithms use the existing structure given by the nodes and edges to try to infer missing relationships based on properties and already observed relationships. The various approaches to predict missing relationships in a temporal knowledge graph use, for example, graph embedding [30], machine learning methods [31], similarity-based methods, or probabilistic methods [32]. The adapted algorithms have the goal of predicting missing links in an existing graph or predicting links that will occur in the future [28, 33]. Existing approaches usually try to predict edges based on already known structures in the graph, but lack the ability to find edges when relationships are mostly unknown in the first place.
In many domains, multivariate time series are used to understand the underlying structure of the data [10, 11]. Many of the systems under consideration have a graph-like structure [13], but it is often dificult or impossible to capture the relationships between the individual time series. Proposed approaches for analysing the relationships between time series include transforming the time series as a multilayer visibility graph [34, 13], as recurrence networks [35, 36] or mapping it as a graph based on causality patterns [12]. These methods focus on comprehensive analysis to find general correlations and patterns in a complex system, rather than inferring actual transformations or interactions between thousands to millions of objects undergoing unknown changes. Previous network-like approaches on multivariate time series do not preserve snapshots while enriching it with temporal edges. We are interested in the relationships that take place between successive snapshots and lead to changes in the measured values of the individual time series. Our approach introduces a new knowledge graph model that represents multivariate time series with a graph-like structure to allow the tracking of single time series and understanding influences on their development.
Our snapshot-based knowledge graph model and temporal link prediction is based on multivariate time series and is particularly useful when actual relationships representing transformations, interactions or flows between nodes in succeeding snapshots are unknown, although there is evidence that they exist.
We here consider multivariate time series data, i.e. there is a time series for each considered object of interest in a larger set of objects. We assume each discrete time point in each time series contains some kind of measurable quantity per object. This quantity changes over time and we expect the objects to be related to each other. Depending on the domain, the repeatedly measured quantity of objects could be manifold, e.g. number of transferred goods or vehicles at monitoring stations, measured intensities of molecules, concentrations of chemical compounds or nutrients in a water treatment plant. Potential connections may be known in advance, but the actual relationships are unknown. For instance, • there are chemical rules about how molecules can be transformed into other molecules, but we do not know what transformations have actually taken place, • we know a network of roads, but we do not know which routes have actually been used by vehicles.
Applying our approach to this scenario, the quantity value is based on the measured intensities from the mass spectra. Identified molecules will be object nodes in the graph with their quantities as property. The molecules of the first mass spectrum ( 0) form the first snapshot, the molecules of the second mass spectrum ( 1) form the second snapshot of the knowledge graph, and so on. Between the two successive mass spectra, the quantities and proportions of the molecules change, indicating that chemical transformations have taken place between the molecules [37]. We will focus on this chemical scenario for examples in the remainder of this paper, but the approach is applicable to other time series data with repeated measurements on large object sets.
We propose a snapshot-based knowledge graph model to represent multivariate time series as a temporal graph structure. Our graph model is a temporal extension of the widely used standard ”Labeled Property Graph” model [15] and belongs to the group of the snapshot-based temporal graphs, e.g. [24, 27]. It includes one graph (or snapshot) for each discrete time point. Snapshots consist of object nodes that will be connected by temporal edges (see Section 4) and together form the snapshot-based knowledge graph.
Figure 2 shows our temporal knowledge graph model. The model contains nodes of one type (‘Object’) and connects them by three diferent types of temporal edges (‘SAME_AS’, ‘POTENTIAL’, ‘PREDICTED’). All types of temporal edges in the model connect a node in one snapshot to a node in a subsequent snapshot and do not exist between nodes within one snapshot as illustrated in Figure 3 C. An ‘Object’ node describes an entity such as a molecule in a chemical network. The node can be identified by its name and snapshot properties, e.g. a molecule’s formula and snapshot 0, which describes the object at the first time point in the data. In addition, each node has a quantity property that describes a value that can change over time, such as the measured intensity of a molecule in a sample.
Initially, each discrete time point in the time series forms a snapshot, which means that the same objects can occur more than once and be identified by the name property. An ‘Object’ can be uniquely identified by the combination of name property and snapshot. Snapshots can be distinguished and ordered by the snapshot property at the ‘Object’ nodes. ‘Object’ nodes with the same name property are connected across successive snapshots via the ‘SAME_AS’ edges. Every ‘SAME_AS’ edge contains the relative change of the quantities of the successive nodes as property, which is termed quantity trend. The calculation is shown in Formula 1: _ = − (1)
It subtracts the quantity of the previous node ( ) from the quantity of the successive node ( ) and divides the result by the quantity of the previous node ( ). The possible interpretations of the quantity trend are increasing, decreasing and consistent, which is important for our temporal link prediction algorithm (see Section 4). A quantity trend of exactly 0 is considered consistent, above it is considered increasing (0, ∞) and below it is considered decreasing (−∞, 0). Additionally, an error margin e around zero (+/ − 12 ) can be applied to expand the range considered as consistent. The error margin takes into consideration the immanent analytical uncertainties caused by instrumental variability (i.e., noise).
The second edge type describes the potential transformations from an ‘Object’ node to another node in a successive snapshot and is called a ‘POTENTIAL’ edge. ‘POTENTIAL’ edges must be determined based on existing knowledge beforehand. For instance, experts in a domain know basic rules on possible interactions or transformations or for transport networks maps contain all known roads. However, transformations or interactions that actually took place or actual routes of transportation are unknown. In the chemical scenario, the ‘POTENTIAL’ transformations might be computed based on all chemically possible transformations of the molecules in the considered use case (e.g. single reactions or chains of reactions).
The third type of edges describes the predicted transformations that are likely to occur and are called ‘PREDICTED’ edges. They are a subset of the ‘POTENTIAL’ edges and indicate the transformations that likely occurred out of all potential transformations. For instance, the ‘PREDICTED’ edges could describe the various chemical transformations that have actually taken place in a molecule after an conditional experiment measured as multivariate time series. The ‘PREDICTED’ edges are computed using the ‘Transformation Prediction Algorithm’ described in Section 4.
Figure 3 illustrates the step-wise construction of the snapshot-based knowledge graph from multivariate time series data for several objects. Each discrete time point in the time series represents a snapshot of the graph and each ‘Object’ represents a node (see Figure 3 (A and B)). The exemplary graph consists of 3 consecutive snapshots ( 0, 1, 2) and four ‘Object’ nodes (green A-D). Each snapshot has a diferent composition, i.e. nodes can be present in all (e.g., 0 , 1 , 2 ) or some of the snapshots (e.g., 1 , 2 ). Figure 3 (C) illustrates the creation of new edges between succeeding points in time. This includes the ‘SAME_AS’ edges between same ‘Object’ nodes and the ‘POTENTIAL’ edges, which describe possible transformations. The edges are directed and always end at a node in the successive snapshot, i.e. no edges exist within a snapshot. Note, that the snapshots do not necessarily represent equidistant points in time . The same edge color describes the same transformation (e.g., from 0 to 1 and 1 to 2 ).
At this point, the snapshot-based knowledge graph contains all the necessary information to describe temporal data as a complex network. However, snapshots are not interconnected via temporal edges describing the transformations in the considered system. We developed the ‘Transformation Prediction Algorithm’ to identify the likely occurred transformations based on the potential transformations and the known quantity trends (e.g. from measurements). Knowing the direction of the transformations and assuming that a decrease in quantity in one ‘Object’ node is reflected by an increase in quantity in another ‘Object’ node and vice versa, it is possible to predict the likely transformations responsible for the dynamics in the snapshot-based knowledge graph. For instance in a network of molecules, potential chemical transformations can be specified by experts and the intensity of the molecules in samples is measured by mass spectrometry. When the quantity of one molecule decreases, the quantity of another increases. The prediction is based on the following three considerations and illustrated in Figure 4: 1. Consideration 1: If the quantity between ‘Object’ node and +1 increases from snapshot to +1 , the transformations of and from snapshot to +1 are assumed to be relevant and the transformation from to other nodes in snapshot +1 are assumed to be non-relevant. Therefore, outgoing potential transformations from the node are excluded and incoming edges to the node +1 are included in the consideration of the ‘PREDICTED’ edges. 2. Consideration 2: If the quantity between ‘Object’ node and +1 decreases from snapshot to +1 , the transformations of and from snapshot to +1 are assumed to be non-relevant and the transformation from to other nodes in snapshot +1 are assumed to be relevant. Therefore outgoing potential transformations from the node are included and incoming edges to the node +1 are excluded in the consideration of the ‘PREDICTED’ edges. 3. Consideration 3: If the quantity between ‘Object’ node and +1 is consistent, the ‘Object’ node has a balancing number of transformations. Therefore, all incoming and outgoing potential transformations from and to +1 are excluded. This means that the node in snapshot and the node in snapshot +1 can be connected by a ‘PREDICTED’ edge only if both nodes have an opposite quantity trend.
Algorithm 1 describes the ‘Transformation Prediction Algorithm’ for creating the ‘PREDICTED’ edges in the snapshot-based knowledge graph. The input is graph consisting of nodes and edges as well as the defined error margin (line 1). As output, we generate the graph G enriched with the added predicted likely occurring transformations (line 2). We define two variables for the edge types and to increase readability of the pseudo code (line 4-5). The error margin represents the uncertainty in the measured quantity in the data and is set to a value between 0 and 1 (line 6) (e.g., 0.05 for 5 % or 0 to neglect error margin). A quantity trend above + 21 is considered as increasing while a trend below − 1 is considered as decreasing. For each node in graph (line 7), we check the quantity 2 trend of the current node from the preceding snapshot to the current snapshot along ‘SAME_AS’ edge (line 8-9) and continue only if the quantity trend is considered as increasing (line 10) (see also step 1 in Figure 5). We then collect all nodes ′ with a ‘POTENTIAL’ edge to the current node (line 11-12). For each collected node ′ (line 13), we check the quantity trend from their current snapshot to the succeeding snapshot along their ‘SAME_AS’ edge (line 14-15) (see also step 2 in Figure 5). If the quantity trend is considered as decreasing (line 16), we add a ‘PREDICTED’ edge from the remaining collected nodes ′ to the currently observed node (line 17) (see also step 3 in Figure 5). The process is repeated until all nodes have been viewed (line 7). As a result, we return the graph with all added predicted likely occurring transformations (edge ) (line 18).
We further assign each ‘PREDICTED’ edge a weight as edge property. The weight describes the most influential ‘PREDICTED’ edges that lead to an increase in the quantity of a node. For instance, if a node has two incoming ‘PREDICTED’ edges describing the increase in quantity, then the higher weight describes the edge with the greater influence on the increase. The weight is calculated during link prediction according to Formula 2: The formula for calculating the weighting requires two factors. The first factor is the quantity of the starting node at the ‘PREDICTED’ edge (i.e. the node with a decreasing quantity trend) ( ). The second factor is the absolute value of the quantity trend at the ‘SAME_AS’ edge of the same node (| |). Note that the weight of the edge increases with a high quantity trend and a high quantity. Each weight is further normalized based on the weights of all incoming edges of an end node.
We evaluate our graph model and algorithm based on two data sets from environmental chemistry. One of the data sets has been previously published and discussed in more detail [37, 14]. A qualitative evaluation of our approach within the considered domain is dificult because the considered system is complex and the processes that take place are largely unknown. Moreover, there is currently no comparable approach to track the transformations that are likely to occur. However, a test with a simplified systems, i.e. a chemical model with known reactions proved the general suitability of the model [14]. The suggestions generated by our approach cannot be easily verified by straight forward labeling. The predicted transformations rather serve the planning of new experiments by providing a novel perspective on the complex system and iflling gaps between previously unconnected snapshot experiments.
So called dissolved organic matter (DOM) plays an important role in freshwater, e.g., it alters available light for photosynthesis and must be removed during drinking water production [38]. DOM is a complex system with widely unknown processes and chemical relationships. Therefore, the investigation of DOM is a suitable use case to benefit from our approach. The extreme chemical diversity and reaction pathways make it dificult to identify the actual transformations. Ultra-high resolution mass spectrometry (UHRMS) can be used to qualitatively and quantitatively measure the composition of DOM. The molecules and their quantities measured over multiple time points form the data basis of the snapshot-based knowledge graph. Figure 1 showed an example of the structure of data generated by ultra-high resolution mass spectrometry (UHRMS) on DOM over multiple time points. The first dataset considered was generated from samples of a drinking water reservoir inflow. Within the samples, molecules were determined over 13 time points using natural sunlight to induce photochemical transformations. The second dataset originates from samples of a wastewater treatment plant outflow, in which the molecules were determined over 8 time points. Here, photochemical transformations were induced by an artificial light source. 5.2. Setup We use Neo4j1 as the graph database management system together with its query language Cypher to create the snapshot-based knowledge graph. Besides manipulating the graph structure (insert, update, delete), users of the graph database can describe patterns to interactively select matching parts in the graph. Both datasets were transformed into nodes and properties according to the snapshot-based knowledge graph model and loaded into the graph database. Programming and preprocessing was done in Python along with the neo4j library, an oficial Neo4j driver that serves as an interface between the Neo4j graph database and Python. Both datasets are configured the same and processed with the same hardware and an error margin of 5 %. The open source project is publicly available on GitHub2.
A snapshot-based knowledge graph is created from each of the two datasets. The nodes in the graphs describe the molecules identified at a particular discrete time in the mass spectrum. Each node has several properties, e.g. the chemical formula, the atoms it consists of (i.e., C,H,O,N,S) and the quantity. Between each snapshot the molecules with the same chemical formula are connected by the ‘SAME_AS’ edges and are enriched with the quantity trend. The ‘POTENTIAL’ edges explain the potential chemical transformations between molecules of successive snapshots and are based on 22 diferent photochemical transformations considered [14]. The ‘PREDICTED’ edges describe the likely occurring chemical transformations calculated with the ‘Transformation Prediction Algorithm’ (see Algorithm 1). Note that in the current use-case of mass spectrometry data, the algorithm only provides relative trends of molecule abundances, not actual amounts changed. Figure 6 shows parts of the first three snapshots of the created graph based on dataset 1. Before using the ‘Transformation Prediction Algorithm’, it was not possible to determine the ‘PREDICTED’ edges drawn in yellow. Those novel edges enable new analyses and evaluations on the datasets. 1https://neo4j.com/ 2https://github.com/PhPlam/tegrom
Table 1 compares the nodes and edges of the generated snapshot-based knowledge graphs from the two datasets. Dataset 1 has 13 snapshots while dataset 2 has 8 snapshots matching the number of time points in the datasets. Dataset 2 has on average more 36 % more nodes per snapshot than dataset 1 and also a 27 % higher maximum number of nodes in a snapshot. In contrast the minimum number of nodes in a snapshot is 25 % lower in dataset 2 than in dataset 1 reflecting a more pronounced efect of the artificial irradiation. Dataset 2 has on average 36 % more ‘SAME_AS’ edges than dataset 1. The maximum (minimum) number of ‘SAME_AS’ edges between two snapshots is about 26 % higher (18 % lower) in dataset 2 than in dataset 1. We observe the three possible quantity trends along ‘SAME_AS’ edges. Averaged over all snapshots, dataset 1 (2) has 32 % (46 %) increasing, 21 % (14 %) consistent and 47 % (40 %) decreasing quantity trends. The diferences in the fractions of increasing and decreasing quantity trends matches the diferent maximum and minimum node values and is consistent with the stronger photochemical transformations induced by the artificial light (dataset 2) as compared to the natural light (dataset 1).
Using the ‘Transformation Prediction Algorithm’, we are able to identify novel, previously unknown ‘PREDICTED’ edges for both datasets (Table 1 bottom section). Dataset 2 has on average about factor 2.6 more ‘PREDICTED’ edges than dataset 1. The maximum (minimum) number of ‘PREDICTED’ edges between two snapshots is about 2.4 (1.4) times higher in dataset 2 than in dataset 1. Note, that we consider a closed system, i.e. no quantities enter from outside or leave the system, making the predicted edges particularly meaningful. The model results correspond to the expected behavior of molecules in the two datasets and will be analysed in more detail below.
Each of the previously unknown ‘PREDICTED’ edges reflects one of the 22 diferent photochemical transformations considered, which are identified by the ‘Transformation Prediction Algorithm’ as likely to have occurred. Figure 7 shows the average share of these transformations in both datasets. For instance, the figure depicts that in the sample of dataset 1, the transformations ”-C1 -O1”, ”-C1”, and ”H2 O1” occurred most frequently, while in the sample of dataset 2, the transformations ”O2”, ”-C4 -H4 -O1”, and ”-C2 -H2” occurred most frequently. The comparison of the two datasets reveals that the distribution of the transformations in the two samples and experiments is diferent. For instance, the share of ”-S1” is much higher (about 606 %) in dataset 2 as compared to dataset 1. This is expected since dataset 2 originates from a wastewater treatment plant outflow, in which a higher amount of sulfur-(S)-containing tensides is expected than in dataset 1, which originates from a pristine drinking water reservoir inflow. A higher share of transformations involving sulfur, i.e. ”-O3 -S1”, ”-S1” and ”-O1 -S1”, is thus expected reflecting pronounced tensides degradation over time. With this example the ‘Transformation Prediction Algorithm’ shows its basic ability to make reasonable predictions for the likely occurring transformations within the sample.
The snapshot-based knowledge graph allows instant evaluation of the previously unknown chemical transformations and easy access to trends and time courses with interactive queries in the graph database. The result of the database query in Figure 8 shows the evolution of a molecule (purple nodes) over time. Blue arrows represent an increasing quantity, red arrows represent a decreasing quantity, and gray arrows represent a constant quantity. The incoming and outgoing weighted yellow arrows represent the predicted chemical transformations. The example shows a way to create more interactive queries that help to capture the structure and relationships within the data.
We presented a novel snapshot-based knowledge graph model that allows to transform multivariate time series data into a feature-rich complex and highly connected network. The nodes and edges store not only static but also time-dependent properties. Starting with a set of potential transformations as they are inherent in many domains such as complex chemical networks, our temporal link prediction algorithm calculates new edges between nodes representing the likely occurring predicted transformations in consecutive snapshots. We evaluated the snapshot-based knowledge graph model and temporal link prediction algorithm in an environmental chemistry use case and demonstrated its functionality to represent graph-like data into a complex network and identify previously unknown relationships.
The temporal graph model presented in this study is not limited to specific applications and can be readily extended to other systems and processes that benefit from the enrichment with temporal edges. To apply and comparatively evaluate the model and algorithms for other domains in the future, we will develop a benchmark including gold standard datasets for link prediction in diferent complex networks. Moreover, we will test diferent approaches such as answer set programming, logical reasoning and graph neural networks to be compared with the current approach. By modeling large temporal datasets from multivariate time series as temporal graphs, further graph-based algorithms can be used to perform comprehensive analyses. Future extensions of the approach could incorporate temporal clustering to analyse temporal patterns and dynamics of recognized communities.
We thank Alexander Sobolev and Christin Wilske for conducting the photodegradation experiments and collecting samples. We also thank Jan Kaesler for performing FT-ICR-MS measurements and Peter Herzsprung for supporting data processing. networks: A survey of measurements, Advances in Physics 56 (2007) 167–242. doi:10. 1080/00018730601170527. [6] S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Complex networks: Structure and dynamics, Physics Reports 424 (2006) 175–308. doi:10.1016/j.physrep.2005.10. 009. [7] S. Sakr, A. Bonifati, H. Voigt, A. Iosup, K. Ammar, R. Angles, W. Aref, M. Arenas, M. Besta, P. A. Boncz, K. Daudjee, E. D. Valle, S. Dumbrava, O. Hartig, B. Haslhofer, T. Hegeman, J. Hidders, K. Hose, A. Iamnitchi, V. Kalavri, H. Kapp, W. Martens, M. T. Özsu, E. Peukert, S. Plantikow, M. Ragab, M. R. Ripeanu, S. Salihoglu, C. Schulz, P. Selmer, J. F. Sequeda, J. Shinavier, G. Szárnyas, R. Tommasini, A. Tumeo, A. Uta, A. L. Varbanescu, H.-Y. Wu, N. Yakovets, D. Yan, E. Yoneki, The future is big graphs, Communications of the ACM 64 (2021) 62–71. doi:10.1145/3434642. [8] X. Zou, A survey on application of knowledge graph, Journal of Physics: Conference
Series 1487 (2020) 012016. doi:10.1088/1742-6596/1487/1/012016. [9] P. Holme, Modern temporal network theory: a colloquium, The European Physical Journal
B 88 (2015). doi:10.1140/epjb/e2015-60657-4. [10] R. H. Shumway, D. S. Stofer, Time Series Analysis and Its Applications, Springer International Publishing, 2017. doi:10.1007/978-3-319-52452-8. [11] Y. Zou, R. V. Donner, N. Marwan, J. F. Donges, J. Kurths, Complex network approaches to nonlinear time series analysis, Physics Reports 787 (2019) 1–97. doi:10.1016/j.physrep. 2018.10.005. [12] M. Jiang, X. Gao, H. An, H. Li, B. Sun, Reconstructing complex network for characterizing the time-varying causality evolution behavior of multivariate time series, Scientific Reports 7 (2017). doi:10.1038/s41598-017-10759-3. [13] L. Lacasa, V. Nicosia, V. Latora, Network structure of multivariate time series, Scientific
Reports 5 (2015). doi:10.1038/srep15508. [14] P. Plamper, O. J. Lechtenfeld, P. Herzsprung, A. Groß, A temporal graph model to predict chemical transformations in complex dissolved organic matter, Environmental Science & Technology (2023). doi:10.1021/acs.est.3c00351. [15] I. Robinson, Graph databases new opportunities for connected data, 2015. [16] M. A. Rodriguez, P. Neubauer, Constructions from dots and lines (2010). doi:10.48550/
ARXIV.1006.2361. [17] O. Hartig, Reconciliation of rdf* and property graphs, arXiv preprint arXiv:1409.3288 (2014). doi:10.48550/ARXIV.1409.3288. [18] R. Angles, The property graph database model., in: AMW, 2018. [19] M. Ciglan, A. Averbuch, L. Hluchy, Benchmarking traversal operations over graph databases, in: 2012 IEEE 28th International Conference on Data Engineering Workshops, IEEE, 2012. doi:10.1109/icdew.2012.47. [20] R. kumar Kaliyar, Graph databases: A survey, in: International Conference on Computing,
Communication & Automation, IEEE, 2015. doi:10.1109/ccaa.2015.7148480. [21] B. Cai, Y. Xiang, L. Gao, H. Zhang, Y. Li, J. Li, Temporal knowledge graph completion: A survey, 2022. doi:10.48550/ARXIV.2201.08236. [22] P. Holme, J. Saramäki, Temporal networks, Physics Reports 519 (2012) 97–125. doi:10.
1016/j.physrep.2012.03.001.