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Benchmarking Measures of Network Influence

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ABSTRACT

Identifying key agents for the transmission of diseases (ideas, technology, etc.) across social networks has predominantly relied on measures of centrality on a static base network or a temporally flattened graph of agent interactions. Various measures have been proposed as the best trackers of influence, such as degree centrality, betweenness, and k-shell, depending on the structure of the connectivity. We consider SIR and SIS propagation dynamics on a temporally-extruded network of observed interactions and measure the conditional marginal spread as the change in the magnitude of the infection given the removal of each agent at each time: its temporal knockout (TKO) score. We argue that this TKO score is an effective benchmark measure for evaluating the accuracy of other, often more practical, measures of influence. We find that none of the network measures applied to the induced flat graphs are accurate predictors of network propagation influence on the systems studied; however, temporal networks and the TKO measure provide the requisite targets for the search for effective predictive measures.

No MeSH data available.


A simplified example of building a “temporal web” style intertemporal network from state-change and interaction data for an SIR model.This procedure differs from temporally layered networks in that the interaction edges are cross-temporal to capture simultaneous updating in the generated data, thus creating a single acyclic directed graph across time.
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f1: A simplified example of building a “temporal web” style intertemporal network from state-change and interaction data for an SIR model.This procedure differs from temporally layered networks in that the interaction edges are cross-temporal to capture simultaneous updating in the generated data, thus creating a single acyclic directed graph across time.

Mentions: We run our simulations using simultaneous updating so that each agents’ state at t + 1 depends on their state at t and interactions initiated at t. When represented as an intertemporal network the interaction edges therefore run across time from agents at t to other agents at t + 1 in addition to “inheritance edges” from each agent at t to its t + 1 self (see Fig. 1). We call this version of intertemporal networks a “temporal web” because it produces a single acyclic directed graph across time rather than connected layers.


Benchmarking Measures of Network Influence
A simplified example of building a “temporal web” style intertemporal network from state-change and interaction data for an SIR model.This procedure differs from temporally layered networks in that the interaction edges are cross-temporal to capture simultaneous updating in the generated data, thus creating a single acyclic directed graph across time.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5037445&req=5

f1: A simplified example of building a “temporal web” style intertemporal network from state-change and interaction data for an SIR model.This procedure differs from temporally layered networks in that the interaction edges are cross-temporal to capture simultaneous updating in the generated data, thus creating a single acyclic directed graph across time.
Mentions: We run our simulations using simultaneous updating so that each agents’ state at t + 1 depends on their state at t and interactions initiated at t. When represented as an intertemporal network the interaction edges therefore run across time from agents at t to other agents at t + 1 in addition to “inheritance edges” from each agent at t to its t + 1 self (see Fig. 1). We call this version of intertemporal networks a “temporal web” because it produces a single acyclic directed graph across time rather than connected layers.

View Article: PubMed Central - PubMed

ABSTRACT

Identifying key agents for the transmission of diseases (ideas, technology, etc.) across social networks has predominantly relied on measures of centrality on a static base network or a temporally flattened graph of agent interactions. Various measures have been proposed as the best trackers of influence, such as degree centrality, betweenness, and k-shell, depending on the structure of the connectivity. We consider SIR and SIS propagation dynamics on a temporally-extruded network of observed interactions and measure the conditional marginal spread as the change in the magnitude of the infection given the removal of each agent at each time: its temporal knockout (TKO) score. We argue that this TKO score is an effective benchmark measure for evaluating the accuracy of other, often more practical, measures of influence. We find that none of the network measures applied to the induced flat graphs are accurate predictors of network propagation influence on the systems studied; however, temporal networks and the TKO measure provide the requisite targets for the search for effective predictive measures.

No MeSH data available.