The effective use of limited resources for controlling spreading processes on
networks is of prime significance in diverse contexts, ranging from the
identification of "influential spreaders" for maximizing information
dissemination and targeted interventions in regulatory networks, to the
development of mitigation policies for infectious diseases and financial
contagion in economic systems. Solutions for these optimization tasks that are
based purely on topological arguments are not fully satisfactory; in realistic
settings the problem is often characterized by heterogeneous interactions and
requires interventions over a finite time window via a restricted set of
controllable nodes. The optimal distribution of available resources hence
results from an interplay between network topology and spreading dynamics. We
show how these problems can be addressed as particular instances of a universal
analytical framework based on a scalable dynamic message-passing approach and
demonstrate the efficacy of the method on a variety of real-world examples.

通过可扩展的动态消息传递方法，我们证明了如何将网络上限制传播过程的有效使用与优化任务结合起来，例如识别最具影响力的传播者、针对特定的监管网络进行干预、制定传染病和金融系统的传播策略，以及演示了该方法在多种实际场景中的效果。

最大化传播影响力的资源优化部署

Optimal Deployment of Resources for Maximizing Impact in Spreading  Processes

The identification of the most influential spreaders in networks is important
to control and understand the spreading capabilities of the system as well as
to ensure an efficient information diffusion such as in rumor-like dynamics.
Recent works have suggested that the identification of influential spreaders is
not independent of the dynamics being studied. For instance, the key disease
spreaders might not necessarily be so when it comes to analyze social contagion
or rumor propagation. Additionally, it has been shown that different metrics
(degree, coreness, etc) might identify different influential nodes even for the
same dynamical processes with diverse degree of accuracy. In this paper, we
investigate how nine centrality measures correlate with the disease and rumor
spreading capabilities of the nodes that made up different synthetic and
real-world (both spatial and non-spatial) networks. We also propose a
generalization of the random walk accessibility as a new centrality measure and
derive analytical expressions for the latter measure for simple network
configurations. Our results show that for non-spatial networks, the $k$-core
and degree centralities are most correlated to epidemic spreading, whereas the
average neighborhood degree, the closeness centrality and accessibility are
most related to rumor dynamics. On the contrary, for spatial networks, the
accessibility measure outperforms the rest of centrality metrics in almost all
cases regardless of the kind of dynamics considered. Therefore, an important
consequence of our analysis is that previous studies performed in synthetic
random networks cannot be generalized to the case of spatial networks.

该论文研究了九种中心度量如何与不同合成和现实网络中的疾病和传言传播的节点的扩散能力相关，并提出了一种随机游走可达性的新中心度量。研究结果表明，在非空间网络中，k - 核心和度中心度量与流行病传播最相关，而平均邻域度，紧密中心度和可达性则与谣言传播最相关，而在空间网络中，可达性度量在几乎所有情况下优于其余中心度量。