3 research outputs found
Asymmetry through time dependency
Given a single network of interactions, asymmetry arises when the links are
directed. For example, if protein A upregulates protein B and protein B
upregulates protein C, then (in the absence of any further relationships between them) A
may affect C but not vice versa. This type of imbalance is reflected in the associated
adjacency matrix, which will lack symmetry. A different type of imbalance can arise when
interactions appear and disappear over time. If A meets B today and B meets C tomorrow,
then (in the absence of any further relationships between them) A may pass a message or
disease to C, but not vice versa. Hence, even when each interaction is a two-way exchange,
the effect of time ordering can introduce asymmetry. This observation is very closely
related to the fact that matrix multiplication is not commutative. In this work, we
describe a method that has been designed to reveal asymmetry in static networks and show
how it may be combined with a measure that summarizes the potential information flow
between nodes in the temporal case. This results in a new method that quantifies the
asymmetry arising through time ordering. We show by example that the new tool can be used
to visualize and quantify the amount of asymmetry caused by the arrow of time
Modern temporal network theory: A colloquium
The power of any kind of network approach lies in the ability to simplify a
complex system so that one can better understand its function as a whole.
Sometimes it is beneficial, however, to include more information than in a
simple graph of only nodes and links. Adding information about times of
interactions can make predictions and mechanistic understanding more accurate.
The drawback, however, is that there are not so many methods available, partly
because temporal networks is a relatively young field, partly because it more
difficult to develop such methods compared to for static networks. In this
colloquium, we review the methods to analyze and model temporal networks and
processes taking place on them, focusing mainly on the last three years. This
includes the spreading of infectious disease, opinions, rumors, in social
networks; information packets in computer networks; various types of signaling
in biology, and more. We also discuss future directions.Comment: Final accepted versio