### Core team:

# Jean-Gabriel Young

### Université Laval

### D´epartement de Physique, de G´enie Physique, et d’Optique, PhD Candidate

#### Most recent papers:

Network archaeology: phase transition in the recoverability of network history.

Jean-Gabriel Young, Laurent Hébert-Dufresne, Edward Laurence, Charles Murphy, Guillaume St-Onge, Patrick Desrosiers. Preprint, 2018.[pdf] [arXiv]

**Abstract:**

Network growth processes can be understood as generative models of the structure and history of complex networks. This point of view naturally leads to the problem of network archaeology: Reconstructing all the past states of a network from its structure---a difficult permutation inference problem. In this paper, we introduce a Bayesian formulation of network archaeology, with a generalization of preferential attachment as our generative mechanism. We develop a sequential importance sampling algorithm to evaluate the posterior averages of this model, as well as an efficient heuristic that uncovers the history of a network in linear time. We use these methods to identify and characterize a phase transition in the quality of the reconstructed history, when they are applied to artificial networks generated by the model itself. Despite the existence of a no-recovery phase, we find that non-trivial inference is possible in a large portion of the parameter space as well as on empirical data.

Strategic tradeoffs in competitor dynamics on adaptive networks.

Laurent Hébert-Dufresne, Antoine Allard, Pierre-André Noël, Jean-Gabriel Young, Eric Libby. Scientific Reports, , 7, 2017.[pdf] [journal page] [arXiv]

**Abstract:**

Recent empirical work highlights the heterogeneity of social competitions such as political campaigns: proponents of some ideologies seek debate and conversation, others create echo chambers. While symmetric and static network structure is typically used as a substrate to study such competitor dynamics, network structure can instead be interpreted as a signature of the competitor strategies, yielding competition dynamics on adaptive networks. Here we demonstrate that tradeoffs between aggressiveness and defensiveness (i.e., targeting adversaries vs. targeting like-minded individuals) creates paradoxical behaviour such as non-transitive dynamics. And while there is an optimal strategy in a two competitor system, three competitor systems have no such solution; the introduction of extreme strategies can easily affect the outcome of a competition, even if the extreme strategies have no chance of winning. Not only are these results reminiscent of classic paradoxical results from evolutionary game theory, but the structure of social networks created by our model can be mapped to particular forms of payoff matrices. Consequently, social structure can act as a measurable metric for social games which in turn allows us to provide a game theoretical perspective on online political debates.

Finite size analysis of the detectability limit of the stochastic block model.

Jean-Gabriel Young, Patrick Desrosiers, Laurent Hébert-Dufresne, Edward Laurence, Louis J. Dubé. Physical Review E, , 95, 2017.[pdf] [journal page] [arXiv]

**Abstract:**

It has been shown in recent years that the stochastic block model is sometimes undetectable in the sparse limit, i.e., that no algorithm can identify a partition correlated with the partition used to generate an instance, if the instance is sparse enough and infinitely large. In this contribution, we treat the finite case explicitly, using arguments drawn from information theory and statistics. We give a necessary condition for finite-size detectability in the general SBM. We then distinguish the concept of average detectability from the concept of instance-by-instance detectability and give explicit formulas for both definitions. Using these formulas, we prove that there exist large equivalence classes of parameters, where widely different network ensembles are equally detectable with respect to our definitions of detectability. In an extensive case study, we investigate the finite-size detectability of a simplified variant of the SBM, which encompasses a number of important models as special cases. These models include the symmetric SBM, the planted coloring model, and more exotic SBMs not previously studied. We conclude with three appendices, where we study the interplay of noise and detectability, establish a connection between our information-theoretic approach and random matrix theory, and provide proofs of some of the more technical results.

Growing networks of overlapping communities with internal structur.

Jean-Gabriel Young, Laurent Hébert-Dufresne, Antoine Allard, Louis J. Dubé. Physical Review E, , 94, 2016.[pdf] [journal page] [arXiv]

**Abstract:**

We introduce an intuitive model that describes both the emergence of community structure and the evolution of the internal structure of communities in growing social networks. The model comprises two complementary mechanisms: One mechanism accounts for the evolution of the internal link structure of a single community, and the second mechanism coordinates the growth of multiple overlapping communities. The first mechanism is based on the assumption that each node establishes links with its neighbors and introduces new nodes to the community at different rates. We demonstrate that this simple mechanism gives rise to an effective maximal degree within communities. This observation is related to the anthropological theory known as Dunbar's number, i.e., the empirical observation of a maximal number of ties which an average individual can sustain within its social groups. The second mechanism is based on a recently proposed generalization of preferential attachment to community structure, appropriately called structural preferential attachment (SPA). The combination of these two mechanisms into a single model (SPA+) allows us to reproduce a number of the global statistics of real networks: The distribution of community sizes, of node memberships and of degrees. The SPA+ model also predicts (a) three qualitative regimes for the degree distribution within overlapping communities and (b) strong correlations between the number of communities to which a node belongs and its number of connections within each community. We present empirical evidence that support our findings in real complex networks.

Constrained growth of complex scale-independent systems.

Laurent Hébert-Dufresne, Antoine Allard, Jean-Gabriel Young, Louis J. Dubé. Physical Review E, , 93, 2016.[pdf] [journal page] [arXiv]

**Abstract:**

Scale independence is a ubiquitous feature of complex systems that implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution, and stock actions all feature scale independence. Assuming that they simply do, we focus here on describing how this behavior emerges, in contrast to more idealized models usually considered. We arrive at the conjecture that a minimal model to explain the growth toward scale independence involves only two coupled dynamical features: the first is the well-known preferential attachment principle, and the second is a general form of delayed temporal scaling. While the first is sufficient, the second is present in all studied data and appears to maximize the speed of convergence to true scale independence. The delay in this temporal scaling acts as a coupling between population growth and individual activity. Together, these two dynamical properties appear to pave a precise evolution path, such that even an instantaneous snapshot of a distribution is enough to reconstruct the past of the system and predict its future. We validate our approach and confirm its usefulness in diverse spheres of human activities, ranging from scientific and artistic productivity to sexual relations and online traffic.

A preferential attachment approach to community structure Growing networks of overlapping communities with internal structureand the structure of communities..

Jean-Gabriel Young, Laurent Hébert-Dufresne, Antoine Allard, Louis J. Dubé. Physical Review E, , 94, 2016.[pdf] [journal page]

**Abstract:**

We introduce an intuitive model that describes both the emergence of community structure and the evolution of the internal structure of communities in growing social networks. The model comprises two complementary mechanisms: One mechanism accounts for the evolution of the internal link structure of a single community, and the second mechanism coordinates the growth of multiple overlapping communities. The first mechanism is based on the assumption that each node establishes links with its neighbors and introduces new nodes to the community at different rates. We demonstrate that this simple mechanism gives rise to an effective maximal degree within communities. This observation is related to the anthropological theory known as Dunbar's number, i.e., the empirical observation of a maximal number of ties which an average individual can sustain within its social groups. The second mechanism is based on a recently proposed generalization of preferential attachment to community structure, appropriately called structural preferential attachment (SPA). The combination of these two mechanisms into a single model (SPA+) allows us to reproduce a number of the global statistics of real networks: The distribution of community sizes, of node memberships, and of degrees. The SPA+ model also predicts (a) three qualitative regimes for the degree distribution within overlapping communities and (b) strong correlations between the number of communities to which a node belongs and its number of connections within each community. We present empirical evidence that support our findings in real complex networks.

Complex networks as an emerging property of hierarchical preferential attachment.

Laurent Hébert-Dufresne, Edward Laurence, Antoine Allard, Jean-Gabriel Young, Louis J. Dubé. Physical Review E, , 92, 2015.[pdf] [journal page]

**Abstract:**

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of complex systems can be modeled as an organization of many embedded levels (potentially infinite in number), all of them following the same universal growth principle known as preferential attachment. We give examples of such hierarchy in real systems, for instance, in the pyramid of production entities of the film industry. More importantly, we show how real complex networks can be interpreted as a projection of our model, from which their scale independence, their clustering, their hierarchy, their fractality, and their navigability naturally emerge. Our results suggest that complex networks, viewed as growing systems, can be quite simple, and that the apparent complexity of their structure is largely a reflection of their unobserved hierarchical nature.

General and exact approach to percolation on random graphs.

Antoine Allard, Laurent Hébert-Dufresne, Jean-Gabriel Young, Louis J. Dubé. Physical Review E, , 92, 2015.[pdf] [journal page]

**Abstract:**

We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative equations that solve the exact distribution of the size and composition of components in finite-size quenched or random multitype graphs. (ii) We define a very general random graph ensemble that encompasses most of the models published to this day and also makes it possible to model structural properties not yet included in a theoretical framework. Site and bond percolation on this ensemble is solved exactly in the infinite-size limit using probability generating functions [i.e., the percolation threshold, the size, and the composition of the giant (extensive) and small components]. Several examples and applications are also provided. (iii) Our approach can be adapted to model interdependent graphs—whose most striking feature is the emergence of an extensive component via a discontinuous phase transition—in an equally general fashion. We show how a graph can successively undergo a continuous then a discontinuous phase transition, and preliminary results suggest that clustering increases the amplitude of the discontinuity at the transition.

A shadowing problem in the detection of overlapping communities: Lifting the resolution limit through a cascading procedure.

Jean-Gabriel Young, Antoine Allard, Laurent Hébert-Dufresne, Louis J. Dubé. PloS one, , 10, 2015.[pdf] [journal page]

**Abstract:**

Community detection is the process of assigning nodes and links in significant communities (eg clusters, function modules) and its development has led to a better understanding of complex networks. When applied to sizable networks, we argue that most detection algorithms correctly identify prominent communities, but fail to do so across multiple scales. As a result, a significant fraction of the network is left uncharted. We show that this problem stems from larger or denser communities overshadowing smaller or sparser ones, and that this effect accounts for most of the undetected communities and unassigned links. We propose a generic cascading approach to community detection that circumvents the problem. Using real and artificial network datasets with three widely used community detection algorithms, we show how a simple cascading procedure allows for the detection of the missing communities. This work highlights a new detection limit of community structure, and we hope that our approach can inspire better community detection algorithms.

Coexistence of phases and the observability of random graphs.

Antoine Allard, Laurent Hébert-Dufresne, Jean-Gabriel Young, Louis J. Dubé. Physical Review E, , 89, 2014.[pdf] [journal page]

**Abstract:**

In a recent Letter, Yang et al. [Phys. Rev. Lett. 109, 258701 (2012)] introduced the concept of observability transitions: the percolationlike emergence of a macroscopic observable component in graphs in which the state of a fraction of the nodes, and of their first neighbors, is monitored. We show how their concept of depth- L percolation—where the state of nodes up to a distance L of monitored nodes is known—can be mapped onto multitype random graphs, and use this mapping to exactly solve the observability problem for arbitrary L . We then demonstrate a nontrivial coexistence of an observable and of a nonobservable extensive component. This coexistence suggests that monitoring a macroscopic portion of a graph does not prevent a macroscopic event to occur unbeknown to the observer. We also show that real complex systems behave quite differently with regard to observability depending on whether they are geographically constrained or not.

Percolation on random networks with arbitrary k-core structure.

Laurent Hébert-Dufresne, Antoine Allard, Jean-Gabriel Young, Louis J. Dubé. Physical Review E, , 88, 2013.[pdf] [journal page] [arXiv]

**Abstract:**

The k-core decomposition of a network has thus far mainly served as a powerful tool for the empirical study of complex networks. We now propose its explicit integration in a theoretical model. We introduce a hard-core random network (HRN) model that generates maximally random networks with arbitrary degree distribution and arbitrary k-core structure. We then solve exactly the bond percolation problem on the HRN model and produce fast and precise analytical estimates for the corresponding real networks. Extensive comparison with real databases reveals that our approach performs better than existing models, while requiring less input information.

Global efficiency of local immunization on complex networks.

Laurent Hébert-Dufresne, Antoine Allard, Jean-Gabriel Young, Louis J. Dubé. Scientific Reports, , 3, 2013.[pdf] [journal page]

**Abstract:**

Epidemics occur in all shapes and forms: infections propagating in our sparse sexual networks, rumours and diseases spreading through our much denser social interactions, or viruses circulating on the Internet. With the advent of large databases and efficient analysis algorithms, these processes can be better predicted and controlled. In this study, we use different characteristics of network organization to identify the influential spreaders in 17 empirical networks of diverse nature using 2 epidemic models. We find that a judicious choice of local measures, based either on the network's connectivity at a microscopic scale or on its community structure at a mesoscopic scale, compares favorably to global measures, such as betweenness centrality, in terms of efficiency, practicality and robustness. We also develop an analytical framework that highlights a transition in the characteristic scale of different epidemic regimes. This allows to decide which local measure should govern immunization in a given scenario.

Unveiling hidden communities through cascading detection on network structures.

Jean-Gabriel Young, Antoine Allard, Laurent Hébert-Dufresne, Louis J. Dubé. Preprint, 2012.[pdf]

**Abstract:**

Community detection is the process of assigning nodes and links in significant communities (eg clusters, function modules) and its development has led to a better understanding of complex networks. When applied to sizable networks, we argue that most detection algorithms correctly identify prominent communities, but fail to do so across multiple scales. As a result, a significant fraction of the network is left uncharted. We show that this problem stems from larger or denser communities overshadowing smaller or sparser ones, and that this effect accounts for most of the undetected communities and unassigned links. We propose a generic cascading approach to community detection that circumvents the problem. Using real network datasets with two widely used community detection algorithms, we show how cascading detection allows for the detection of the missing communities and results in a significant drop of the fraction of unassigned links.

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