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Is it the case that MO is actually split into several communities which only communicate with each other through meta-activity but have no actual mathematical interests in common?

This is not sheer curiosity since

  • personally I skip lots of questions and it would be convenient to restrict myself to fewer topics, although I have no heart to filter any tags out as it might happen that this way I never see something which might be still interesting for me; however if I would know that I am actually firmly placed inside a clearly cut out connected component, I would be more confident to filter the rest out;

  • on the other hand if there indeed are some symptoms of disconnectedness, this might be interesting generally, indicating some lack of communication in the MO slice of the mathematical community, and maybe something should be done about it.

So could one e. g. use the data explorer to somehow measure connectivity of MO?

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    $\begingroup$ The correct question would be not whether or not MO is connected, but what is the average of neighbors of MO regulars in this graph (to exclude the mass of transient users, lurkers, and otherwise people who don't participate much). $\endgroup$ – Asaf Karagila Sep 9 '14 at 6:44
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    $\begingroup$ I find the phrasing of your dichotomy unfortunate. Could you clarify what you mean by "mathematical interests in common"? $\endgroup$ – Yemon Choi Sep 9 '14 at 11:52
  • $\begingroup$ @YemonChoi sorry, I saw your question long ago and did not answer. This is in fact a painful spot for me - I work at a research institute where once in few years we try to organize a common seminar where groups of ODE people, probabilists, physicists, topologists, algebraists try to contaminate each other with their favorite topics, and so far such seminars have been constant failure. It is really bugging me and I keep thinking about ways to improve communication between us. We simply do not understand each other. $\endgroup$ – მამუკა ჯიბლაძე Oct 1 '14 at 5:46
  • $\begingroup$ This post looks at tags rather than users - but perhaps it is still a bit interesting in connection with this question: An interactive graph of MathOverflow tags. $\endgroup$ – Martin Sleziak Feb 11 at 8:38
  • $\begingroup$ a geometer can not resist: is MO irreducible? $\endgroup$ – user137767 Apr 8 at 17:30
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There is some recent research related to clustering and the role of centrality on MathOverflow.

Leydi Viviana Montoya, Athen Ma, Raul J. Mondragón, Social achievement and centrality in MathOverflow, Complex Networks IV, Studies in Computational Intelligence Volume 476, 2013, 27-38. DOI:10.1007/978-3-642-36844-8_3 (PDF)

Abstract. This paper presents an academic web community, MathOverflow, as a network. Social network analysis is used to examine the interactions among users over a period of two and a half years. We describe relevant aspects associated with its behaviour as a result of the dynamics arisen from users participation and contribution, such as the existence of clusters, rich–club and collaborative properties within the network. We examine, in particular, the relationship between the social achievements obtained by users and node centrality derived from interactions through posting questions, answers and comments. Our study shows that the two aspects have a strong direct correlation; and active participation in the forum seems to be the most effective way to gain social recognition.

Page 10 has a description of the clustering that can be observed on MathOverflow.

Most of the clusters are quite small given that 61% of the clusters has just 2 users, see fig. 3(a). The map representing the 105 clusters in the network displayed its 6 biggest groups (denominated as G1, G2, . . . , G6) and the small box in the bottom right corner contains 99 clusters with a total of 297 nodes. Also, the 6 clusters have 97.5% of the total users in the MathOverflow network. The subgraphs (clusters) diameter, average geodesic distance and density were calculated for the 6 clusters, in order to characterise them. Cluster G2 has the same diameter than the whole network (7 edges). Clusters G6 and G3 have a diameter of 11. The six clusters show a density lower than 0.006 which is bigger than the density of the whole network (0.0014), although they are significantly low given that the density provides the ratio of direct ties in the network to the total of possible direct ties [28]. The 6 biggest clusters have a small proportion of users with the highest degree values and the highest upvotes counts, with a relevant proportion of users with low degree value and upvotes as followers. The users with a degree higher than 500 or upvotes higher than 750 or with the highest reputations are located only on the 6 biggest clusters (see fig. 3(b)). In contrast, users who have achieved a reputation of 1 (which is given when users input their personal details on the community web page) are located in the biggest clusters as followers of the main users and in the small clusters, Fig. 3(c).

MO Clustering


This is a comment that's a bit too long. It looks like the author did try to correlate clusters with tags:

Specific subgroups in the network were identified based on the tags (topics) the users marked their questions with. When analysing the 3 subgroups with highest number of users (AG–Algebraic Geometry, SQ–Soft Question and NT–Number Theory) they appear to have similar network characteristics as the whole network. These subgroups contain 20%, 19% and 18% of the total users in the network respectively. The subgroups AG and NT have a diameter larger than the original network, which means the farthest two nodes in AG and NT are more distant; whereas the SQ subgroup has the same diameter as the original network (see Tab. 2).

It may seem unusual that the authors identified as a subgroup but note that their methods are purely algorithmic and not based on any predefined mathematical taxonomy. On the other hand, it is not surprising that the SQ graph is similar to the whole graph while AG and NT graphs are somewhat different.

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    $\begingroup$ I assume that the six groups correspond with various math subject areas, but can we find out which? $\endgroup$ – Joel David Hamkins Sep 9 '14 at 20:27
  • $\begingroup$ @JoelDavidHamkins The analysis did not take subject area into account. This is presumably the case but it could also be that G1 is the soft-question cluster or something similar. $\endgroup$ – François G. Dorais Sep 9 '14 at 21:10
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    $\begingroup$ Yes, I assumed that the topic affiliation would ride upon the connectivity information in the graph. It would be interesting to know which tags have high correlations with the six groups, which would presumably be possible to compute for someone with the data. It would give more semantic content to the analysis than just "there are six groups". $\endgroup$ – Joel David Hamkins Sep 9 '14 at 21:49
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    $\begingroup$ @JoelDavidHamkins: I will contact the authors. Since these are clusters of users, my guess is that classification would require more than 'computation'. It's hard to put people in boxes and I strongly suspect that most of these six groups are amalgams of related ideas that don't correspond to typical mathematical classification. (See, for example, how Netflix's movie clustering differs from human-made movie classifications.) $\endgroup$ – François G. Dorais Sep 9 '14 at 23:27
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    $\begingroup$ Great! You may be very right, but it will be interesting if they are able to report any tag correlations or another manner of describing these various groups. $\endgroup$ – Joel David Hamkins Sep 10 '14 at 0:27
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It would be relatively straightforward to build the 'coauthorship graph' (treating each page as a work, including or not including comments according to preference). Are there then standard ways to answer your question based on this graph?

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  • $\begingroup$ IIRC, this has already been done somewhere on tea. $\endgroup$ – François G. Dorais Sep 9 '14 at 4:38

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