Temporal Networks (1108.1780v2)

Abstract: A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges. The network structure, describing how the graph is wired, helps us understand, predict and optimize the behavior of dynamical systems. In many cases, however, the edges are not continuously active. As an example, in networks of communication via email, text messages, or phone calls, edges represent sequences of instantaneous or practically instantaneous contacts. In some cases, edges are active for non-negligible periods of time: e.g., the proximity patterns of inpatients at hospitals can be represented by a graph where an edge between two individuals is on throughout the time they are at the same ward. Like network topology, the temporal structure of edge activations can affect dynamics of systems interacting through the network, from disease contagion on the network of patients to information diffusion over an e-mail network. In this review, we present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems. In the light of traditional network theory, one can see this framework as moving the information of when things happen from the dynamical system on the network, to the network itself. Since fundamental properties, such as the transitivity of edges, do not necessarily hold in temporal networks, many of these methods need to be quite different from those for static networks.

• The paper introduces temporal network measures including time-respecting paths and latency to capture dynamic interactions.
• The paper presents novel temporal models and adapted centrality metrics for analyzing spreading processes in real-world systems.
• The paper highlights that integrating temporal correlations and burstiness enhances intervention strategies in network dynamics.

An Overview of Temporal Networks Research

The paper "Temporal Networks" by Petter Holme and Jari Saramaki provides a comprehensive exploration into the field of temporal networks, detailing aspects that differentiate these from static network models and introducing methodologies for analyzing their unique topological and temporal structures. Temporal networks are crucial for understanding various dynamical systems spanning nature, society, and technology, such as email communication patterns, hospital patient proximity, and power grids. This essay summarizes key findings and methodologies from the paper, emphasizing the significance of temporal elements in network analysis and dynamics modeling.

Overview of Temporal Network Types

The paper categorizes temporal networks based on the nature of their interactions, including:

1. Person-to-Person Communication: Encompassing instant messages, mobile phone calls, and emails, these networks provide rich datasets for analyzing information or virus spreading dynamics.
2. One-to-Many Information Dissemination: Platforms like blogs and microblogs (e.g., Twitter) where broadcast-style communication allows for studying the spread of information.
3. Physical Proximity: Utilizing sensor data to examine face-to-face interactions and proximity in environments such as hospitals and schools, which are critical for studying disease transmission.
4. Distributed Computing: Examines systems where distributed computational units share information to perform tasks, important for estimating the age of information which vertices possess.
5. Infrastructural Networks: Although some infrastructure changes slowly, networks like air transport benefit from temporal analysis to understand centrality and path durations.
6. Ecological and Neural Networks: Modeling biological systems and interactions within ecosystems or neural connections in brains, which hold dynamic properties suited for temporal network methodologies.

Temporal Network Measures

A primary focus of the paper is the introduction of measures for characterizing temporal networks:

• Time-Respecting Paths: Critical for understanding reachability and the temporal sequence of interactions, these paths only consider sequences of edges that follow a time-ordered way.
• Latency and Fastest Paths: These measures determine how quickly vertices can reach one another, essential for analyzing the spread dynamics of diseases or information.
• Centrality Measures: Temporal generalization of metrics such as closeness and betweenness centrality are proposed. For instance, temporal closeness centrality evaluates how quickly a vertex can reach other vertices over time-respecting paths.
• Mesoscopic Features and Patterns: The paper discusses motifs and persistent subgraphs—the recurrence and over-representation of specific subgraph configurations—in temporal graphs.

Temporal Network Models

Temporal networks necessitate models that capture both stability and dynamic interactions:

1. Temporal Exponential Random Graph Models: These help in understanding the significance and frequency of subgraph occurrences over time.
2. Social Group Dynamics Models: They describe ephemeral social ties, emphasizing how group membership impacts dynamics.
3. Stochastic Pair Formation Models: For contact networks, especially useful in epidemiological studies, models simulate partnership formation and dissolution dynamics.

Implications for Dynamics and Control

One of the pivotal areas covered is the impact of temporal networks on spreading processes. The studies presented show that:

• Burstiness in Human Communication: Significantly slows down the spread of diseases or information compared to Poissonian approximations.
• Temporal Correlations: Whether through detailed amounts of communication or face-to-face interactions, maintaining temporal sequences and correlations can crucially affect the speed and reach of spreading processes.
• Disease Control Strategies: Incorporating temporal characteristics into models can enhance strategies for targeted interventions, such as vaccination schemes based on recent contact frequency.

Future Directions and Open Challenges

The paper delineates several future research directions and open challenges:

• Generative Models: Developing comprehensive models that can simulate real-world temporal network behavior.
• Temporal Network Measures: Creation of measures specifically suited for temporal structures beyond generalizations of static concepts.
• Driving Mechanisms: Understanding the causative factors behind temporal interactions remains an area ripe for exploration.
• Inference Problems: Addressing issues in constructing and predicting temporal networks from incomplete data.
• Visualization: Improved methods for visualizing temporal networks to capture and analyze their dynamic nature effectively.

Conclusion

Holme and Saramaki's review of temporal networks represents a significant contribution to the understanding and characterization of dynamic systems across multiple disciplines. By illustrating how temporal elements fundamentally alter network dynamics, their work establishes a solid foundation for future research, particularly in areas requiring precise modeling of time-dependent interactions. The prospects for utilizing temporal network methodologies extend to enhancing predictive accuracy and control mechanisms in complex networks, promising advancements in fields ranging from epidemiology to infrastructure management.