Networks seminar

Welcome to the homepage of the Networks seminars, a weekly seminar series on networks, complex systems, and related topics held in the Mathematical Institute.  In this year's series, we will alternate between regular talks and "fresh from the arXiv" talks (FFTA) in which we invite the author of a recently published (pre)print to discuss their work. Suggestions are always welcome!

The Networks seminar usually takes place on Tuesdays at 14:00-15:00 virtually on Zoom and a link to the event will be made available in the schedule of upcoming talks below (for logged-in users) and via the mailing list.

To sign up to our mailing list simply send an empty email to the following address:
oxford_networks_seminar-subscribe@maillist.ox.ac.uk

If you would like to give a presentation at our seminar, please do not hesitate to contact the organisers Karel Devriendt or Rodrigo Leal Cervantes. The presentation can be either about your own work or on some (recent) interesting article on networks or on complex systems in general.

In case you missed any of the talks, we will also make recordings of the talks available on our youtube channel.

 

Upcoming Seminars

Tomorrow
14:00
Abstract

We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of graphs with extensive numbers of triangles and other network motifs commonly observed in many real world networks. More specifically we focus on maximum entropy ensembles under constraints placed on the counts and distributions of atomic subgraphs and derive general expressions for the entropy of such models. We also present a procedure for combining distributions of multiple atomic subgraphs that enables the construction of models with fewer parameters. Expanding the model to include atoms with edge and vertex labels we obtain a general class of models that can be parametrized in terms of basic building blocks and their distributions that includes many widely used models as special cases. These models include random graphs with arbitrary distributions of subgraphs, random hypergraphs, bipartite models, stochastic block models, models of multilayer networks and their degree corrected and directed versions. We show that the entropy for all these models can be derived from a single expression that is characterized by the symmetry groups of atomic subgraphs.

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

3 November 2020
14:00
Mattie Landman
Abstract

Here we propose a new method to compare the modular structure of a pair of node-aligned networks. The majority of current methods, such as normalized mutual information, compare two node partitions derived from a community detection algorithm yet ignore the respective underlying network topologies. Addressing this gap, our method deploys a community detection quality function to assess the fit of each node partition with respect to the other network's connectivity structure. Specifically, for two networks A and B, we project the node partition of B onto the connectivity structure of A. By evaluating the fit of B's partition relative to A's own partition on network A (using a standard quality function), we quantify how well network A describes the modular structure of B. Repeating this in the other direction, we obtain a two-dimensional distance measure, the bi-directional (BiDir) distance. The advantages of our methodology are three-fold. First, it is adaptable to a wide class of community detection algorithms that seek to optimize an objective function. Second, it takes into account the network structure, specifically the strength of the connections within and between communities, and can thus capture differences between networks with similar partitions but where one of them might have a more defined or robust community structure. Third, it can also identify cases in which dissimilar optimal partitions hide the fact that the underlying community structure of both networks is relatively similar. We illustrate our method for a variety of community detection algorithms, including multi-resolution approaches, and a range of both simulated and real world networks.

10 November 2020
14:00
Michal Gnacik
Abstract

(joint work with T. Kania, Academy of Sciences of the Czech Republic, Prague)
In this talk we discuss our recent result on the inverse eigenvalue problem for symmetric doubly stochastic matrices. 
Namely, we provide a new sufficient condition for a list of real numbers to be the spectrum of a symmetric doubly stochastic matrix. 
In our construction of such matrices, we employ the eigenvectors of the transition probability matrix of a simple symmetric random walk on the circle. 
We also demonstrate a simple algorithm for generating random doubly stochastic matrices based on our construction. Examples will be provided.

You can also find a list of all talks (with abstracts) prior to 2018 here, and the former website
of the Networks journal club at the Oxford complexity center (CABDyN) here.

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