Editing Network theory (section)

== Temporal networks ==

Other networks emphasise the evolution over time of systems of nodes and their interconnections. Temporal networks are used for example to study how financial risk has spread across countries.<ref>{{Cite journal| last1= Franch|first1=F.| last2=Nocciola|first2=L.|last3=Vouldis| first3=A.|date=April 2024|title= Temporal networks and financial contagion|url=https://doi.org/10.1016/j.jfs.2024.101224|journal= Journal of Financial Stability| volume=71 |doi= 10.1016/j.jfs.2024.101224|issn=|url-access=subscription}}</ref> In this study, temporal networks are used to also visually trace the intricate dynamics of financial contagion during crises. Unlike traditional network approaches that aggregate or analyze static snapshots, the study uses a time-respecting path methodology to preserve the sequence and timing of financial crises contagion events. This enables the identification of nodes as sources, transmitters, or receivers of financial stress, avoiding mischaracterizations inherent in static or aggregated methods. Following this approach, banks are found to serve as key intermediaries in contagion paths, and temporal analysis pinpoints smaller countries like Greece and Italy as significant origins of shocks during crises—insights obscured by static approaches that overemphasize large economies like the US or Japan.

Temporal networks can also be used to explore how cooperation evolves in dynamic, real-world population structures where interactions are time-dependent.<ref>{{Cite journal |last1=Li |first1=A. |last2=Zhou |first2=L. |last3=Su |first3=Q. |last4=Cornelius |first4=S.P.|last5=Liu |first5=Y.|last6=L. |first6=Wang|last7=Levin|first7=S.A.|title=Evolution of cooperation on temporal networks |journal=Nature Communications |volume=11 |issue=2259 |date=8 May 2020|doi=10.1038/s41467-020-16088-w |bibcode=2020NatCo..11.2259L |url=https://doi.org/10.1038/s41467-020-16088-w|arxiv=1609.07569 }}</ref> Here the authors find that network temporality enhances cooperation compared to static networks, even though "bursty" interaction patterns typically hinder it. This finding also shows how cooperation and other emergent behaviours can thrive in realistic, time-varying population structures, challenging conventional assumptions rooted in static models.

In psychology, temporal networks enable the understanding of psychological disorders by framing them as dynamic systems of interconnected symptoms rather than outcomes of a single underlying cause. Using "nodes" to represent symptoms and "edges" to signify their direct interactions, symptoms like insomnia and fatigue are shown how they influence each other over time; also, disorders such as depression are shown not to be fixed entities but evolving networks, where identifying "bridge symptoms" like concentration difficulties can explain comorbidity between conditions such as depression and anxiety.<ref>{{Cite journal |last1=Jordan |first1=D.G. |last2=Winer |first2=E.S. |last3=Salem |first3=T. |title=The current status of temporal network analysis for clinical science: Considerations as the paradigm shifts? |journal=J Clin Psychol |volume=76 |year=2020 |issue=9 |pages=1591–1612 |doi=10.1002/jclp.22957|pmid=32386334 |url= https://doi.org/10.1002/jclp.22957|url-access=subscription }}</ref>

Lastly, temporal networks enable a better understanding and controlling of the spread of infectious diseases.<ref>{{Cite journal |last1=Masuda |first1=N. |last2=Holme |first2=P. |title=Predicting and controlling infectious disease epidemics using temporal networks |journal=F1000Prime Reports |volume=5 |year=2013 |page=6 |doi=10.12703/P5-6|doi-access=free |pmid=23513178 |pmc=3590785 }}</ref> Unlike traditional static networks, which assume continuous, unchanging connections, temporal networks account for the precise timing and duration of interactions between individuals. This dynamic approach reveals critical nuances, such as how diseases can spread via time-sensitive pathways that static models miss. Temporal data, such as interactions captured through Bluetooth sensors or in hospital wards, can improve predictions of outbreak speed and extent. Overlooking temporal correlations can lead to significant errors in estimating epidemic dynamics, emphasizing the need for a temporal framework to develop more accurate strategies for disease control.