01/09: Boudourides

[jmausolf]

Comment below with questions or thoughts about the reading for this week's workshop.

Please make your comments by Wednesday 11:59 PM, and upvote at least five of your peers' comments on Thursday prior to the workshop. You need to use 'thumbs-up' for your reactions to count towards 'top comments,' but you can use other emojis on top of the thumbs up.

[hanjiaxu]

Thank you very much for presenting this research! As someone who is not familiar with this topic and social network, it was very difficult for me to keep track of the math in the papers. I am wondering if you could talk a little bit about the intuition you initially had for each problem and how those informed you to come up with those proofs? Also, I think a little bit of background about what the problems are for people who are not familiar with these techniques would also be helpful. Thank you!

[SoyBison]

Thank you for visiting our workshop! My question is related to the generalization of the algorithms discussed in Dominating sets and ego-centered decomposition in social networks to properties other than just relation. Do you think that similar algorithms can be employed to find other "domination" related sets? For example something like a Most Dominating Highly Connected Set. Thanks again!

[wanitchayap]

Thank you for your talk! In Dominating sets and ego-centered decomposition in social networks, you mentioned "the limitations" of the algorithm's heuristic "imposed by the complexity of the problem on the size of the network". To tackle these possible limitations, do you think this research's heuristic of classifying vertices into 3 types is still the best place to start? Or do you think we need a completely different strategy and algorithm? If so, what are they?

[nwrim]

Thank you for presenting in advance! In my past experience, I had seen many people that tried to put more "interpretable" names to concepts that originated from more theoretical, math-based fields. Although this has the benefit of making people outside the field more accessible to the concepts, it also has the side effect of people mistaking the core feature of the concept sometimes. For example, "entropy" interpreted as "disorderedness" could be useful to grasp the relatively vague concept, but it might lead to people believing that the theory of evolution contradicts the second law of thermodynamics. Due to my lack of knowledge in the field, I was consistently inclined to interpret the concept of "always dominant" as something closed to "important" or "central" upon reading your article Dominating sets and ego-centered decompositions in social networks. This made intuitive sense to me since I feel like if a node is required to form a dominating set, it must be "important". Examples made me feel that way too since Medici is probably a very important Renaissance Florentine family and Jean Valjean is a very important character in les miserables. Do you think this kind of interpretation of "domination" could be justified or correct enough? Or do you think this kind of approach is very dangerous and walking on thin ice? I am sorry for asking almost a philosophical question!

[zeyuxu1997]

Thanks for presentation. I'm not familiar with this topic and it seems like the graph theory in computer algorithm based on its setting, but much more complex. I wonder if you can draw some pictures to make it easier to understand. Another question is how to quantify abstract things like opinions and acceptance of others' opinions. Although you use s to represent susceptibility coefficient, it seems to work only for continuous variables while opinions are usually dummy variables. Could you please give more examples to show how to apply your research to real world?

[hihowme]

Thanks a lot for the presentation in advance! Using graph theory to analyze the social network is really popular these days. I like your research a lot because it brought out this concern that we should know where the boundary is between the applied graph theory and network science, which is important but could be easily ignored by people. My question is that in the Boundary Stimulation paper, you gave us a lot of hardcore math and you gave us 3 example at the end. As a social science student, I really want to know what is the perfect real-life counterparts for those example in the social network. My question is that could you give us some real-life example or intuition behind those math?

[Yilun0221]

Thank you for the presentation! My question is, when we split a large social network into several small parts and study them separately, is it possible that this separation will cause inaccurate research results? In other words, the connection with other parts of the social network will affect our results, and this factor is ignored when we focus on only one part of the social network.

[ydeng117]

thanks for the presentation! I am not familiar with this topic and also had a hard time to keep track of the mathematical explanations in the articles. However, it is fascinating to see how a scholar can use math models to quantify abstract concepts in social science. Could you explain more about the rationale behind the math models? Another question I want to ask is how would we apply these mathematical models to solve social problems in the real world? For example, how can the boundary stimulation contribute to our understanding of censorship in media?

[lulululugagaga]

Thanks for your presentation. It's definitely cool to see such mathematical application to the large social network studies, but I hope you can explain more about the models as the analysis highly relies on these models.

[ziwnchen]

Thanks a lot for your presentation. As a social science student, I am wondering if there are any common assumptions mathematicians use when modeling opinion dynamics/social influences based solely on network structure. For example, whether real-world opinion propagation is identical to the "heat" diffusion in the model? From your opinion, to what extent could the real-world social network opinion dynamics be explained by its topological structure?

[chun-hu]

Thanks for your presentation! It's a fascinating topic and I wish to learn more about the mathematical concepts behind these models and how I can effectively apply these models to solve real-world issues.

[tianyueniu]

Thank you for the presentation! I also have a hard time understanding the mathematics & models, can you please provide more background for the analysis and its real world implications?

[anuraag94]

Thanks in advance for your presentation. My question expands on @ziwnchen's question, since this has often been a concern of mine. I've encountered similarly stylized models of social dynamics coming from the statistical mechanics literature, and I've been frustrated at their purely atomistic treatment of human actors. How do you plan to more tractably map your simulations to real-world social networks? Do you have any plans to test your models by comparing their theoretical predictions to empirical observations?

[romanticmonkey]

Thank you for presenting to us. Network analysis is a relatively new academic field comparing to others in the social sciences. Simultaneously, the public audience usually have very little idea what the subject entails. Thus I am curious on your opinion on how the subject of network analysis can be brought into public attention, and how an introduction can be designed to educate the general audience.

[anqi-hu]

Thank you for the presentation in advance. Because whole-network and egocentric designs are essentially distinct, what factors would help determine the suitability of applying these two methods? That is, what are some characteristics of a network that render the egocentric design more appropriate? In addition, is it possible for one network to have significantly different or even contradictory implications using these two methods due to their scopes?

[timqzhang]

Thank you for your presentation on the social network. The analysis on the network always has huge potential to explore. I have mainly two questions.

1. What is the features of sets that could apply with the categorization into three types as mentioned in the paper? What if there exist alternative clustering methods that may also work? Or what if some network are exceptions from this method.
2. As other classmates mentioned, the main body of the paper is more theoretical with limited applications. Therefore, I am quite curious about how such method could be used on network analysis.

[RuoyunTan]

Thank you for the presentation. I really enjoyed reading your paper "Dominating sets and ego-centered decompositions in social networks". I have studied a bit about graph theory before and I was particularly interested in random walks on graphs and sampling from networks. In real life, as the number of individuals (vertices on the graph) increases, it is almost impossible to study the whole complex network. Or sometimes maybe we just want to study simple sub-networks like the spanning trees (the simplest). I previously studied the Wilson’s Algorithm and how to prove that mathematically it is a valid way to conduct sampling from all possible spanning trees, which means all possible spanning trees have the same probability of being generated by the Wilson’s Algorithm.

After reading your paper, I started to think maybe your way of decomposing a whole network can also be used to generate sample sub-networks. Could you share some thoughts on this?

Reference: D. Wilson, Generating random spanning trees more quickly than the cover time. Proceedings of the 28th annual ACM symposium on Theory of Computing, pp.296-303. ACM (1996)

[adarshmathew]

Thank you for your presentation. I find the concept of dominating sets and ego-centered decomposition fascinating (especially with applications to large-scale networks) and I'm looking forward to your extension to directed networks.

1. Application to network sub-sampling: As @RuoyunTan pointed out, computation on large-scale networks becomes increasingly prohibitive with network size and density. Would collapsing dominating nodes and their private alters into a single composite node be a reasonable application of your method? This could be explained as an elite-follower structure vis-a-vis spheres of influence, and help in data reduction, especially in sparse networks.

"Of course, in practical situations, this knowledge works like a new sort of centrality index, which, dissimilarly to the local computation for most centrality indices, now it is based on a combinatorial assessment of all possible structural circumstances enabling the constitution of the domination partition of an empirical network at hand."

2. Difference from other centrality measures: The above passage in your article on ego-centered decomposition was an interesting observation. I wasn't clear about how this measure is different or a theoretical/practical improvement on the Betweenness centrality (measure of brokerage) or even PageRank centrality (measure of power). Could you elaborate on that?

[linghui-wu]

Thank you for your presentation in advance. Last quarter we had a workshop discussing the interactions between different disciplines and I proposed a question pondering the feasibilities of closely combining natural science and social science. The paper "Dominating sets and ego-centered decompositions in social networks" does enlighten me. I really enjoy the way mathematical definitions and theorems are linked to social network analysis, which renders the whole article logically-rigorous.

However, I also struggled with reading the paper since I am not quite familiar with this particular field. I am really interested in what you mentioned in the Conclusion that the methodologies are able to be applied in bibliometric citation networks and social media mining. So my questions include (a) what do you think should be the main intuitive takeaway of the paper and (b) could you elaborate more on how the algorithms would play a role in empirical network studies?

[goldengua]

Thank you very much for this presentation. I am not very familiar with this area, and as a social science student, I am interested in how the model could be applied to social science problems? Also, I would appreciate it if there is more background knowledge.

[ShuyanHuang]

Thanks for presenting. The Friedkin–Johnsen model of social influence on graph is very inspiring to social science researchers. I am wondering whether this kind of model can involve probability, agents' decision making and feedback processes.

[WMhYang]

Thank you very much for your papers. Although I am not familiar with this field, I find the paper Dominating sets and ego–centered decompositions in social networks interesting because it makes me realized that a social network could be simplified with proper mathematical equations and graphic analysis. However, I had a tough time when following the whole theory and induction. Would you mind give me some intuitive explanation of them? Moreover, in the end of your paper, you mentioned that the methodology could be extended to accommodate empirical networks like bibliometric citation networks and networks mined from Twitter data. Since the cases you provided in the paper only involve a relatively small size of data, would you please give us some caveats on dealing with this kind of big data?

[KenChenCompEcon]

Thanks for your presentation and your great contributions in the realm of social science graph theory. The work of decomposing ego-centered networks is inspiring and I am wondering if there is a test on the robustness of the decomposition? And what are the threatening factors if ego-centered subpopulations can be extracted from online networks in terms of social influence?

[dhruvalb]

Looking forward to your presentation tomorrow! In your paper, "Dominating Sets and Ego-Centered Decompositions in Social Networks", you mention in that applying the method to decompose into ego-centric networks on directed graphs will require modifications. Could you please share some considerations? How would we apply such a method to a import-export trade network?

[YuxinNg]

Thanks for the articles! Just like many people have already mentioned, Not coming from a Math background, it is not easy for me to understand all the models in your paper. Hopefully after your speech tomorrow, I will have a clear picture about your article. But I still have one question about the limitation of your models. The topic you were dealing with was "social network, formed by a group of persons, who are assumed to hold an opinion or an attitude". What if the social network is more complex, lets say, a group of groups (thinking about International relationship), do all the models still apply? Thanks!

[ruixili]

Thank you very much for this presentation. In the abstract of the first paper, you mentioned the opinion propagation inside of a social network. And in the second paper, "Dominating Sets and Ego-Centered Decompositions in Social Networks", you brought up the notion of ego-centered decomposition. I wonder how do these two papers relate. Does it mean if we find the ego-centered decomposition, which is an opinion leader in social media context, we can spread our ideas faster? Is there any other application for the decomposition technique?

[ShanglunLi]

Thank you for providing such an interesting paper to read! When you split a whole social network into small networks, do you have any assumptions to check? If we split the network without any assumption check, will the result of the research become inaccurate to some extent?

[nswxin]

Thank you so much for your presentation. I am particularly interested in bringing the network science into schools of mathematics, and I am really looking forward to learning about the examples in the US. My question is (perhaps I will get the answer directly from your presentation tomorrow), if we want to do similar things in China, what kind of preparation should we do and also, what kind of outcomes can we prospect at this stage?

[TianxinZheng]

Thanks for presenting these intriguing papers. I was wondering, in your paper of decomposing ego-centered networks, how do you make sure the robustness of the decomposition especially when scaling up to larger and more complex networks?

[SiyuanPengMike]

Thanks a lot for your interesting and inspiring papers. I'm wondering that is there any other way to visualize all your results and methods better. Even though line charts is a traditional and widely used way to represent relationships in networks, I do believe there should be other charts to visualize the results better with the help of new functions in python or R. Thanks again for your paper and looking forward to your representation tomorrow.

[Leahjl]

Thanks for your presentation. It is fascinating to interpret network science based on mathematics. I wonder how do you test your model you mentioned at the last part of the paper.

[bjcliang-uchi]

Your papers offer some inspiring perspectives on how to understand social networks from a quantitative background. I am wondering 1) are you going to develop certain R/ Python packages to help social scientists apply your methodology and 2) It seems that in your "Boundary Simulation of Social Influence Networks" paper, you assume that the layers are independent to each other. This is not common in the real world, where, say, investment network and alumni network are often correlated. How do you think this correlation may affect the model?

[yongfeilu]

Thank you for the presentation! Both the topic and the quantitative method used are amazing. However, could you please give more explanation on the math side of your theory? Do you think using so complex math can really reach the results you expect? Will the validation of your theory be impaired by the accurate math thing?

[di-Tong]

Thank you for sharing these interesting projects and looking forward to learning the epistemic development of the network science field! As the Dominating Set paper mentions at the end that you planned to generalize your approach to the case of directed graphs, I wonder if you have any subsequent updates on this direction. If so, could you share with us?

[harryx113]

Thank you for the presentation. Could you please elaborate on the assumption that the layers are independent of each other and what implications would the assumption have when generalizing the model to other scenarios?

[weijiexu-charlie]

Thanks for the presentation. Unfamiliar with background knowledge such as graph theory, I found myself quite struggling to understand the math definitions and proofs. Could you please explain a little bit about the relevant background knowledge in the workshop tomorrow? Furthermore, I really appreciate it if you could provide some intuitive explanations of your models and what are the appropriate scenarios to apply these models?

[liu431]

Thank you for the talk. Network science is getting increasingly important in data science. However, it's not part of the curriculum at most of the data science programs. Also, most of the network courses are not business-oriented.

Do you have suggestions for aspiring data scientists on carrying out an insightful project on network analysis?

Moreover, what do you think is the biggest challenge for the data scientists at social media firms, such as Twitter, Linkedin, and Facebook, to make robust predictions and inference from the large user networks?

[chiayunc]

Thank you for the wonderful paper. In the introduction, you mentioned that "the dominating set problem is NP-complete ". By finding out the domination number for each network, you are able to reduce the NP-complete problem to be solved in polynomial time. My question is that the determination of the domination number seems unrelated to the social scientific aspects, and this could potentially lead to limiting the scope to sets that are not necessarily social scientifically important. I wonder what is your take on this. Thank you.

[dongchengecon]

Thank you so much for presenting such an inspiring topic! In some biomedical research, we may face similar questions as you proposed in the paper. For example, metabolic network is a network of all the biochemical reactions in cells or organisms. It has been well characterized by extensive experiments. With the advent of advancement in technology, we are now able to measure the global profile of metabolites in tissues. However, due to technical limitations, there are many missing values in the network. The general research question revolves around the possibility that we could understand the states of cells based on the incomplete data in those pathways. Could this research question be solved with the some revised versions of the theory in your paper?

[HaowenShang]

Really interesting topic! Thanks for your presentation! For the paper talking about ‘Boundary Simulations of Social Influence Network’, I am quite confused on how to abstract the social influence network into graph and how to decide the layers of the graph?

[yutianlai]

Thank you for the presentation.I'm not familiar with this topic and lack enough math training. Could you elaborate in a more detailed way of the models and how they could be applied to specific situations we are more familiar with?

[ChivLiu]

Thank you for the presentation! I didn't completely understand the math concepts, but I could follow the coding part. Could you explain how multi-dimensional machine learning models such as SVM combine the layers and get more precise results?

[YanjieZhou]

Thank you for your presentation! To compare the propagation of social influence with heat diffusion is a really impressive method of enhancing our understanding of abstract and complex social influence. But I am still wondering what enlightened you to begin this kind of comparison and what role those differences between these two concepts play in using this method to explain the real world.

[skanthan95]

Thank you for your presentation! Coming from a purely psychology-based background, I didn't fully follow the methodology in your papers. Most undergraduate psychology programs don't stress the importance of learning about social network theory or the mathematical theory underlying it; how would you recommend integrating this into undergraduate social science curricula?

[rkcatipon]

Thank you for sharing your research. I'm a novice when it comes to social networks so forgive me if this question is answered in your text!

With respect to the characteristics of social diffusion within your model of social networks, I wondered if aggregating the various susceptibility coefficients of each person would be an appropriate way to measure the overall susceptibility of a network? Of course, your construction of boundaries is dependent on the distribution of the coefficients, but are there any dangers in trying to extrapolate meaning from an aggregate view?

For example, I am interested in determining what kinds of social media groups are more likely to be susceptible to propaganda about geopolitical events? If I know that there are users in an identified community that have been "infected"? Is it mathematically sound to then take an aggregate view?

[policyglot]

Thank you for condensed explanation of what would clearly correspond to an entire semester of Network Theory. Like many of my classmates, I confess I haven't completely understood the content. That being said, I had a mathematics-oriented question:

You mentioned PDE (Partial Differential Equations) while laying out how the matrices for a graph would be configured. Could you provide a social science application where PDEs could be combined with network theory?

[MegicLF]

Thank you for the presentation! In Dominating sets and ego-centered decompositions in social networks, the concepts of dominating vertices and multiplicity remind me of the k-coloring problem, and I wonder if there exists a relationship between ego-centered subgraph and the chromatic number of the graph. In Boundary Stimulation of Social Influence Networks, I wonder if the social influence network is a simple graph. If so, did you assume it to be simple or did you do extra work to reduce it? If not, how do you identify the impact of loops, cycles, and parallel edges? Moreover, are there any special cases in which the analysis mentioned in this paper cannot be implemented?

[bakerwho]

Network analysis, like data science, seems to be developing into an excellent tool for interdisciplinary researchers. In my research with networks, I've often encountered problems that seem to require the data science equivalent of 'data cleaning'.

For example, consider a network of co-starring of actors in films

• several pairs will occur only once
• several actors may be named only once (presumably less influential in the field)
• several big stars may dominate the network statistics, making it harder to understand relationships amongst mid-tier actors
• collaborations may stem from common acquaintances, but may also be erroneously attributed to these

Filtering or pruning a network in some quantitative way may be necessary to explore some of these qualitative questions. What has your experience been in this regard? Are there any tips or tricks you can share?

[hesongrun]

Thank you so much for your presentation! What do you think are the most important mathematical tools we should understand in order to grasp the essence of network analysis?

[keertanavc]

Thank you for coming over to talk about your work! I particularly liked the paper that combines graph theory and PDEs to model information diffusion in networks. I wanted to know if this model is suitable to model the formation of echo chambers in discussion forums? Looking forward to your presentation tomorrow!