基于图基元的网络演化建模
Modeling Network Evolution Using Graph Motifs
摘要：
网络结构对政治学研究极为重要。它的子领域中的大部分数据都自然地表示为网络。这包括贸易、外交和冲突关系。一些组织的社会结构也是许多研究者感兴趣的，例如立法者的从属关系或恐怖分子之间的关系。研究社交网络的一个关键方面是理解这些结构随时间增长和变化的进化动力学和机制。虽然目前的方法非常适合描述网络的静态特征，但它们不太能够指定变化模型和模拟网络演化。在接下来的论文中，我提出了一种新的方法来建模网络的增长和演化。该方法依靠图的模体生成具有特定结构特征的模拟网络数据。这种技术在形式和功能上都明显不同于目前的方法。而不是一个封闭的形式的模型，或随机实现从一个单一的一类图，所提出的“图形图案模型”提供了一个框架，建立灵活和复杂的网络演化模型。本文的内容如下：首先，简要回顾了当前关于网络建模的文献，以将图基序模型置于上下文中。接下来，介绍了图模体模型，并给出了一个简单的例子。作为概念的证明，三个经典的随机图模型恢复使用图形模体建模方法：Erdos-Renyi二项随机图，Watts-Strogatz“小世界”模型，Barabasi-Albert偏好连接模型。在最后一节中，我将讨论这些模拟的结果以及使用这种技术来建模社交网络的优点和缺点。
英文摘要：
Network structures are extremely important to the study of political science. Much of the data in its subfields are naturally represented as networks. This includes trade, diplomatic and conflict relationships. The social structure of several organization is also of interest to many researchers, such as the affiliations of legislators or the relationships among terrorist. A key aspect of studying social networks is understanding the evolutionary dynamics and the mechanism by which these structures grow and change over time. While current methods are well suited to describe static features of networks, they are less capable of specifying models of change and simulating network evolution. In the following paper I present a new method for modeling network growth and evolution. This method relies on graph motifs to generate simulated network data with particular structural characteristic. This technique departs notably from current methods both in form and function. Rather than a closed-form model, or stochastic implementation from a single class of graphs, the proposed "graph motif model" provides a framework for building flexible and complex models of network evolution. The paper proceeds as follows: first a brief review of the current literature on network modeling is provided to place the graph motif model in context. Next, the graph motif model is introduced, and a simple example is provided. As a proof of concept, three classic random graph models are recovered using the graph motif modeling method: the Erdos-Renyi binomial random graph, the Watts-Strogatz "small world" model, and the Barabasi-Albert preferential attachment model. In the final section I discuss the results of these simulations and subsequent advantage and disadvantages presented by using this technique to model social networks.
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