Implications of clustering (motif-structure) for network-based processes

网络是一种非常强大的思考（和建模）个体或粒子相互作用的方式。也许最熟悉的网络形式是我们与朋友、家人和同事建立的社会联系。这些社交网络是我们希望了解的典型网络类型：链接相对较少（与总人口相比，人们只有有限数量的联系人），存在可变性（有些人的联系人比其他人多得多），联系人聚集在一起（我的联系人可能彼此认识）。我们希望在这个拨款申请中研究的是聚类的最后一个性质，并将把传染病通过聚类网络的传播作为我们的主要例子。鉴于现代计算机的强大功能，可以快速而容易地模拟任何网络上的任何过程（例如感染的传播）的行为，这些模拟表明，网络内的聚类具有很强的效果。然而，这种方法有两个缺点。首先，为了模拟行为，我们需要知道精确的网络，不幸的是，网络数据的收集（特别是对人类来说）是困难和耗时的-因此，真正的网络的例子很少。第二个问题是，模拟结果只告诉我们我们正在使用的特定网络，我们不知道我们的结果是通用的还是特定于我们选择的网络。由于这些原因，我们希望使用更抽象的方法来提取一般性的结果，其中一种方法是使用成对近似法--它模拟了相互作用对的数量（和类型），但忽略了网络结构的其他元素。虽然这种成对模型在理解一系列复杂网络类型上的过程行为方面非常有用，但在尝试将这些近似用于聚类模型时存在几个根本性缺陷。该建议旨在克服这些缺陷，从而预测聚类对网络过程的一般影响。这对许多被认为是网络重要的学科领域都非常重要，包括计算机科学、系统生物学、遗传学、社会学、流行病学和复杂性理论。我们的新理论发展将主要应用于通过人类社交网络传播和控制传染病的问题。这一领域的改进将直接影响英国和其他地方用于支持公共卫生政策的模式。然而，还有大量的其他学科领域将直接受益于我们开发的方法。这些学科包括：遗传学、计算机科学、社会科学和生物学。因此，我们认为，我们的工作可能会对科学研究人员产生深远的影响，而这反过来又会使公众受益。

Networks are an incredibly powerful way of thinking about (and modelling) the interaction of individuals or particles. Probably the most familiar form of network is the social contacts that we form with friends, family and colleagues. These social networks are typical of the types of network we wish to understand: there are relatively few links (people only have a limited number of contacts compared to the total population), there is variability (some people have many more contacts than others), and the contacts are clustered (my contacts are likely to know each other). It is this final property of clustering that we wish to study in this grant proposal, and will focus on the spread of infectious diseases through clustered networks as our main example.Given the power of modern computers it is quick and easy to simulate the behaviour of any process (eg the spread of infection) on any network, and these simulations have shown that clustering within the network has a strong effect. However, this approach has two disadvantages. The first is that to simulate the behaviour we need to know the precise network, and unfortunately the collection of network data (especially for humans) is difficult and time-consuming - for this reason very few examples of true networks exist. The second problem is that simulation results only tell us about the particular network we are using, we do not know if our results are general or specific to our chosen network. For these reasons we want to used more abstract approaches that allow us to extract general results.One approach to achieve this is the use of pair-wise approximations - which model the number (and type) of interacting pairs, but ignore other elements of network structure. While such pair-wise models have been incredibly useful in understanding the behaviour of processes on a range of complex network types, there are several fundamental flaws when trying to use these approximations for clustered models. This proposal aims to overcome these flaws and therefore predict the general impact of clustering upon network processes. This has great importance for many subject areas where networks are considered important, including computer science, systems biology, genetics, sociology, epidemiology and complexity theory. Our new theoretical developments will be applied primarily to problems of infectious disease spread and control through human social networks. Improvements in this area will directly influence the models that are used to support public-health policies in the UK and elsewhere. However, there are a vast number of other subject areas that will directly benefit from the methods we develop. These include: genetics, computer science, social science and biology. We therefore feel that our work is likely to have far-reaching benefits for scientific researchers, which in turn will benefit the general public.