![]() And if the dynamic system changes much faster than the speed of the dynamic connection, or if the edges in the graph are actively changing, then there is no need to model the dynamic system into a time-dependent graph. In general, when is a graph appropriate to be modeled and analyzed as a time-dependent graph? The system needs to be modeled as a time-dependent graph only when it conforms to the time-dependent framework and involves the time scale. That is to say, edges in such graphs are activated by sequences of time-dependent elements.Īn advantage of modeling a network as a time-dependent graph is that we can study the dynamic effect of time on the graph instead of the impact of the actual dynamics. In terms of modeling, a time-dependent graph can be thought as a special case of labeled graphs, in which labels capture some measure of time. Generally, in such networks, the weights associated with edges dynamically change over time (time-dependency). For example, when a user takes a transfer in flight transportation networks, the departure time of the second flight must be later than the arrival time of the first flight. The transportation network is one of the most suitable networks that can be modeled by a time-dependent graph, where the influence of time always needs to be considered. In transportation networks, there is usually a set of fixed routes on which a group of transport units moves over time. While time is a main reason for these changes. When a person leaves a group or a new group is established, the topological structure needs to be updated. In social networks, the topological structure of a graph represents a social relationship. The connections in biological functions are not always active but change over time. In bioinformatics networks, graphs are used to reflect the similarity and regulatory of biomolecules, such as proteins, genes, and enzymes. However, many real-life scenarios can be better modeled by time-dependent graphs, such as bioinformatics networks, transportation networks, social networks. Each edge represents a road segment between two adjacent intersections and the distance of the edge is an edge weight. Generally, for example, when we model a road transportation network into a graph, each vertex represents an intersection and the associated coordinates (latitude and longitude) are a vertex weight. In practical applications, vertices and edges of graphs often contain specific information, such as labels or particular weights (such as length and cost). Each edge represents a relation between each pair of vertices. A static graph (we use the “static graphs” to refer to classical graphs in this review to opposite it from time-dependent graphs) consists of two sets: vertices and edges. Moreover, graphs are extensively applied in social networks, biological networks, transportation networks, distributed systems, and so on. Almost every scientific domains, including mathematics, computer science, chemistry, and biology, can be modeled and studied by graphs. We try to keep the descriptions consistent as much as possible and we hope the survey can help practitioners to understand existing time-dependent techniques.Ī graph is a data structure which is widely used in network modeling. We also introduce existing time-dependent systems and summarize their advantages and limitations. In addition, we review some classic problems on time-dependent graphs, e.g., route planning, social analysis, and subgraph problem (including matching and mining). In this paper, we discuss the definition and topological structure of time-dependent graphs, as well as models for their relationship to dynamic systems. Though static graphs have been extensively studied, for their time-dependent generalizations, we are still far from a complete and mature theory of models and algorithms. In particular, the time-dependent graph is a very broad concept, which is reflected in the related research with many names, including temporal graphs, evolving graphs, time-varying graphs, historical graphs, and so on. Many real-life scenarios can be better modeled by time-dependent graphs, such as bioinformatics networks, transportation networks, and social networks. In such graphs, the weights associated with edges dynamically change over time, that is, the edges in such graphs are activated by sequences of time-dependent elements. A time-dependent graph is, informally speaking, a graph structure dynamically changes with time. ![]()
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