Finding network communities using modularity density

This is the author's accepted manuscript. The final published version is available from IOP Publishing via the DOI in this recordMany real-world complex networks exhibit a community structure, in which the modules correspond to actual functional units. Identifying these communities is a key challenge for scientists. A common approach is to search for the network partition that maximizes a quality function. Here, we present a detailed analysis of a recently proposed function, namely modularity density. We show that it does not incur in the drawbacks suffered by traditional modularity, and that it can identify networks without ground-truth community structure, deriving its analytical dependence on link density in generic random graphs. In addition, we show that modularity density allows an easy comparison between networks of different sizes, and we also present some limitations that methods based on modularity density may suffer from. Finally, we introduce an efficient, quadratic community detection algorithm based on modularity density maximization, validating its accuracy against theoretical predictions and on a set of benchmark networks.Engineering and Physical Sciences Research Council (EPSRC

Analysis of the communities of an urban mobile phone network

This is the final version. Available from Public Library of Science via the DOI in this record. Data Availability: Data available at: Telecom Italia Big Data Challenge 2014, https://dandelion.eu/datamine/open-big-data/.Being able to characterise the patterns of communications between individuals across different time scales is of great importance in understanding people's social interactions. Here, we present a detailed analysis of the community structure of the network of mobile phone calls in the metropolitan area of Milan revealing temporal patterns of communications between people. We show that circadian and weekly patterns can be found in the evolution of communities, presenting evidence that these cycles arise not only at the individual level but also at that of social groups. Our findings suggest that these trends are present across a range of time scales, from hours to days and weeks, and can be used to detect socially relevant events.EPSRCEuropean Commissio

Degree correlations in directed scale-free networks

Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which is a measure of the correlation between the degrees of the nodes at the end of the links. Degree correlations are known to affect both the structure of a network and the dynamics of the processes supported thereon, including the resilience to damage, the spread of information and epidemics, and the efficiency of defence mechanisms. Nonetheless, while many studies focus on undirected scale-free networks, the interactions in real-world systems often have a directionality. Here, we investigate the dependence of the degree correlations on the power-law exponents in directed scale-free networks. To perform our study, we consider the problem of building directed networks with a prescribed degree distribution, providing a method for proper generation of power-law-distributed directed degree sequences. Applying this new method, we perform extensive numerical simulations, generating ensembles of directed scale-free networks with exponents between~2 and~3, and measuring ensemble averages of the Pearson correlation coefficients. Our results show that scale-free networks are on average uncorrelated across directed links for three of the four possible degree-degree correlations, namely in-degree to in-degree, in-degree to out-degree, and out-degree to out-degree. However, they exhibit anticorrelation between the number of outgoing connections and the number of incoming ones. The findings are consistent with an entropic origin for the observed disassortativity in biological and technological networks.Comment: 10 pages, 5 figure

Upper bounds for number of removed edges in the Erased Configuration Model

Models for generating simple graphs are important in the study of real-world complex networks. A well established example of such a model is the erased configuration model, where each node receives a number of half-edges that are connected to half-edges of other nodes at random, and then self-loops are removed and multiple edges are concatenated to make the graph simple. Although asymptotic results for many properties of this model, such as the limiting degree distribution, are known, the exact speed of convergence in terms of the graph sizes remains an open question. We provide a first answer by analyzing the size dependence of the average number of removed edges in the erased configuration model. By combining known upper bounds with a Tauberian Theorem we obtain upper bounds for the number of removed edges, in terms of the size of the graph. Remarkably, when the degree distribution follows a power-law, we observe three scaling regimes, depending on the power law exponent. Our results provide a strong theoretical basis for evaluating finite-size effects in networks

The tetrazole analogue of the auxin indole-3-acetic acid binds preferentially to TIR1 and not AFB5

Auxin is considered one of the cardinal hormones in plant growth and development. It regulates a wide range of processes throughout the plant. Synthetic auxins exploit the auxin-signalling pathway and are valuable as herbicidal agrochemicals. Currently, despite a diversity of chemical scaffolds all synthetic auxins have a carboxylic acid as the active core group. By applying bio-isosteric replacement we discovered that indole-3-tetrazole was active by surface plasmon resonance (SPR) spectrometry, showing that the tetrazole could initiate assembly of the TIR1 auxin co-receptor complex. We then tested the tetrazole’s efficacy in a range of whole plant physiological assays and in protoplast reporter assays which all confirmed auxin activity, albeit rather weak. We then tested indole-3-tetrazole against the AFB5 homologue of TIR1, finding that binding was selective against TIR1, absent with AFB5. The kinetics of binding to TIR1 are contrasted to those for the herbicide picloram, which shows the opposite receptor preference as it binds to AFB5 with far greater affinity than to TIR1. The basis of the preference of indole-3-tetrazole for TIR1 was revealed to be a single residue substitution using molecular docking, and assays using tir1 and afb5 mutant lines confirmed selectivity in vivo. Given the potential that a TIR1-selective auxin might have for unmasking receptor-specific actions, we followed a rational design, lead optimisation campaign and a set of chlorinated indole-3-tetrazoles was synthesised. Improved affinity for TIR1 and the preference for binding to TIR1 was maintained for 4- and 6-chloroindole-3-tetrazoles, coupled with improved efficacy in vivo. This work expands the range of auxin chemistry for the design of receptor-selective synthetic auxins

Consistent approximation of epidemic dynamics on degree-heterogeneous clustered networks

Realistic human contact networks capable of spreading infectious disease, for example studied in social contact surveys, exhibit both significant degree heterogeneity and clustering, both of which greatly affect epidemic dynamics. To understand the joint effects of these two network properties on epidemic dynamics, the effective degree model of Lindquist et al. [28] is reformulated with a new moment closure to apply to highly clustered networks. A simulation study comparing alternative ODE models and stochastic simulations is performed for SIR (Susceptible–Infected–Removed) epidemic dynamics, including a test for the conjectured error behaviour in [40], providing evidence that this novel model can be a more accurate approximation to epidemic dynamics on complex networks than existing approaches

Mapping structural diversity in networks sharing a given degree distribution and global clustering: Adaptive resolution grid search evolution with Diophantine equation-based mutations

Methods that generate networks sharing a given degree distribution and global clustering can induce changes in structural properties other than that controlled for. Diversity in structural properties, in turn, can affect the outcomes of dynamical processes operating on those networks. Since exhaustive sampling is not possible, we propose a novel evolutionary framework for mapping this structural diversity. The three main features of this framework are: (a) subgraph-based encoding of networks, (b) exact mutations based on solving systems of Diophantine equations, and (c) heuristic diversity-driven mechanism to drive resolution changes in the MapElite algorithm.We show that our framework can elicit networks with diversity in their higher-order structure and that this diversity affects the behaviour of the complex contagion model. Through a comparison with state of the art clustered network generation methods, we demonstrate that our approach can uncover a comparably diverse range of networks without needing computationally unfeasible mixing times. Further, we suggest that the subgraph-based encoding provides greater confidence in the diversity of higher-order network structure for low numbers of samples and is the basis for explaining our results with complex contagion model. We believe that this framework could be applied to other complex landscapes that cannot be practically mapped via exhaustive sampling