#### Using Networks to Measure Influence and Impact

(MCM 2014C)

One of the techniques to determine influence of academic research is to build and measure properties of citation or co-author networks. Co-authoring a manuscript usually connotes a strong influential connection between researchers. One of the most famous academic co-authors was the 20th-century mathematician Paul Erdos who had over 500 co-authors and published over 1400 technical research papers. It is ironic, or perhaps not, that Erdos is also one of the influencers in building the foundation for the emerging interdisciplinary science of networks, particularly, through his publication with Alfred Rényi of the paper “On Random Graphs” in 1959. Erdos’s role as a collaborator was so significant in the field of mathematics that mathematicians often measure their closeness to Erdos through analysis of Erdos’s amazingly large and robust co-author network (see the website http://www.oakland.edu/enp/). The unusual and fascinating story of Paul Erdos as a gifted mathematician, talented problem solver, and master collaborator is provided in many books and on-line websites (e.g., http://www-history.mcs.st-and.ac.uk/Biographies/Erdos.html). Perhaps his itinerant lifestyle, frequently staying with or residing with his collaborators, and giving much of his money to students as prizes for solving problems, enabled his co-authorships to flourish and helped build his astounding network of influence in several areas of mathematics. In order to measure such influence as Erdos produced, there are network-based evaluation tools that use co-author and citation data to determine impact factor of researchers, publications, and journals. Some of these are Science Citation Index, H- factor, Impact factor, Eigenfactor, etc. Google Scholar is also a good data tool to use for network influence or impact data collection and analysis. Your team’s goal for ICM 2014 is to analyze influence and impact in research networks and other areas of society. Your tasks to do this include:

1) Build the co-author network of the Erdos1 authors (you can use the file from the website https://files.oakland.edu/users/grossman/enp/Erdos1.html or the one we include at Erdos1.htm ). You should build a co-author network of the approximately 510 researchers from the file Erdos1, who coauthored a paper with Erdos, but do not include Erdos. This will take some skilled data extraction and modeling efforts to obtain the correct set of nodes (the Erdos coauthors) and their links (connections with one another as coauthors). There are over 18,000 lines of raw data in Erdos1 file, but many of them will not be used since they are links to people outside the Erdos1 network. If necessary, you can limit the size of your network to analyze in order to calibrate your influence measurement algorithm. Once built, analyze the properties of this network. (Again, do not include Erdos --- he is the most influential and would be connected to all nodes in the network. In this case, it’s co-authorship with him that builds the network, but he is not part of the network or the analysis.)

2) Develop influence measure(s) to determine who in this Erdos1 network has significant influence within the network. Consider who has published important works or connects important researchers within Erdos1. Again, assume Erdos is not there to play these roles.

3) Another type of influence measure might be to compare the significance of a research paper by analyzing the important works that follow from its publication. Choose some set of foundational papers in the emerging field of network science either from the attached list (NetSciFoundation.pdf) or papers you discover. Use these papers to analyze and develop a model to determine their relative influence. Build the influence (coauthor or citation) networks and calculate appropriate measures for your analysis. Which of the papers in your set do you consider is the most influential in network science and why? Is there a similar way to determine the role or influence measure of an individual network researcher? Consider how you would measure the role, influence, or impact of a specific university, department, or a journal in network science? Discuss methodology to develop such measures and the data that would need to be collected.

4) Implement your algorithm on a completely different set of network influence data --- for instance, influential songwriters, music bands, performers, movie actors, directors, movies, TV shows, columnists, journalists, newspapers, magazines, novelists, novels, bloggers, tweeters, or any data set you care to analyze. You may wish to restrict the network to a specific genre or geographic location or predetermined size.

5) Finally, discuss the science, understanding and utility of modeling influence and impact within networks. Could individuals, organizations, nations, and society use influence methodology to improve relationships, conduct business, and make wise decisions? For instance, at the individual level, describe how you could use your measures and algorithms to choose who to try to co-author with in order to boost your mathematical influence as rapidly as possible. Or how can you use your models and results to help decide on a graduate school or thesis advisor to select for your future academic work?

6) Write a report explaining your modeling methodology, your network-based influence and impact measures, and your progress and results for the previous five tasks. The report must not exceed 20 pages (not including your summary sheet) and should present solid analysis of your network data; strengths, weaknesses, and sensitivity of your methodology; and the power of modeling these phenomena using network science.

* Your submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a maximum of 21 pages.

#### 合作网络中的影响力

(美国竞赛2014年C题)

确定学术研究的影响力的其中一项技术是建立和衡量引文或合著者网络的性能。共同创作的手稿（论文）通常蕴含研究者之间有很强的影响力的连接。其中最有名的学者共同作者是20世纪的数学家Paul Erdos拥有超过500合著者，并公布了1400技术的研究论文。这是具有讽刺意味的是，那埃尔德什也是在为新兴交叉科学的基础建设网络，特别是通过他和Alfred Rényi在1959年发表的论文“关于随机图”。Erdos 的作为合作者的角色在数学方面很惊人，体现在Erdos的超大，健壮的合著者网络分析测量（见网站）。Paul Erdos的不寻常的和引人入胜的故事是作为一个天才的数学家，天才的问题解决者，并掌握和提供合作者在许多书籍和在线网站（例如，这儿） 。也许他的流动生活中经常与他的合作者住在一起，以及花费不少的钱通过让学生提供解决方案，使他的合作关系蓬勃发展，并帮助建立他的在几个数学的领域有惊人影响力网络。为了衡量Erdos创造出的这种影响力，有基于网络的评估工具通过使用的共同作者和引文数据，以确定研究人员，出版物和期刊的影响因子。其中有些是科学引文索引， H因子，影响因子，特征因子等，谷歌学术搜索也是一个不错的数据工具，以用于网络影响力或影响数据的收集和分析。你的团队的ICM 2014年的目标是分析研究网络和社会其他领域的影响和冲击。

你的任务做到这一点，包括：

1)构建Erdos1的合著者网络(你可以使用我们网站)。你应该建立一个约有510名研究人员的合作者网络（数据从文件Erdos1中获取），谁与Erdos的合著一篇论文, 但不包括Erdos。这需要一些技术数据提取和建模工作获得正确设置的节点(Erdos合著者) 和他们的链接(彼此作为合作者的连接)。有超过18000行Erdos1的原始数据文件,但是很多人不会用因为它们链接Erdos1网络之外的人。如果有必要,你可以限制你的网络的规模分析,以校准你的影响力度量算法。一旦建立,分析该网络的属性。(同样，不包括Erdos——他是最有影响力的, 将连接到网络中的所有节点。在这种情况下, 它是包括Erdos合著营造网络, 但Erdos不属于网络或分析。

2)开发影响措施决定谁在这个Erdos1网络在网络中有显著的影响。考虑谁发表了重要的作品在Erdos1或连接重要人员。同样, 假设没有Erdos扮演这些角色。

3)另一种类型的影响的措施可能会按照其出版的论文的研究意义比较分析的工作。选择一套基本的文件在网络科学的新兴领域，无论是从所附清单或文件，你发现。使用这些文件来分析和建立一个模型来确定它们的相对影响。建立的影响（合著者或引用）的网络和计算你适当的措施分析。您的分析这在您所设定的论文，你认为是最有影响力的网络科学，为什么？是否有一个类似的方法来确定一个人的网络研究者的角色或影响的措施呢？考虑你将如何衡量网络科学中的作用，影响，或影响一个特定大学，部门或刊物？讨论的方法来开发这样的措施和你将要收集的数据。

4)实现你对一组完全不同的网络影响力数据的算法---比如，有影响力的作曲家，乐队的音乐，表演，电影演员，导演，电影，电视节目，专栏作者，记者，报纸，杂志，小说家，小说，博客，高音喇叭，或任何你关系的数据集进行分析。你不妨在网络限制到一个特定的流派或地区，或预定的规模。

5)最后，讨论科学、理解和建模的影响和影响在网络的效用。可以个人、组织、国家和社会使用影响方法改善人际关系,做生意,和做出明智的决定吗? 例如,在个体层面,描述如何使用你的措施和算法选择谁试图与合著者为了尽快提高你的数学的影响。或你如何使用你的模型和结果来帮助决定毕业学校或导师的选择为你的未来学术工作吗?

6)写报告解释您的建模方法,基于网络的影响和影响的措施,和之前的五项任务的进程和结果。报告不能超过20页(不包括你的汇总表),应该提供确凿的网络数据的分析,优劣评价,和灵敏度的方法,建模这些现象使用网络科学的力量。

你的提交应该由一个1页汇总表和您的解决方案不能超过20页最长21页。

### 各种数模竞赛赛题

### 参考资料

### 材料 及 优秀论文

优

Using Networks to Measure Influence and Impact,

张云昊, 李志浩, 孟龙(M)

Influence measure model in complex network,

金建栋, 曹逸轩, 柳陈文(M)