arXiv subjects

Leto Peel

Publications and source records attributed to Leto Peel.

At least 19 recordsLinked to original sources

arXiv2026

Detectability of minority communities in networks

Community structure is prevalent in real-world networks, with empirical studies revealing heterogeneous distributions where a few dominant majority communities coexist with many smaller groups. These small-scale groups, which we term minority communities, are critical for understanding network organization but pose significant challenges for detection. Here, we investigate the detectability of minority communities from a theoretical perspective using the Stochastic Block Model. We identify three distinct phases of community detection: the detectable phase, where overall community structure is recoverable but minority communities are merged into majority groups; the distinguishable phase, where minority communities form a coherent group separate from the majority but remain unresolved internally; and the resolvable phase, where each minority community is fully distinguishable. These phases correspond to phase transitions at the Kesten-Stigum threshold and two additional thresholds determined by the eigenvalue structure of the signal matrix, which we derive explicitly. Furthermore, we demonstrate that spectral clustering with the Bethe Hessian exhibits significantly weaker detection performance for minority communities compared to belief propagation, revealing a specific limitation of spectral methods in identifying fine-grained community structure despite their capability to detect macroscopic structures down to the theoretical limit.

cs.SI↗

arXiv2026

Academic collaborations and movements towards successful careers in physics

Collaboration networks evolve throughout academic careers, yet few studies systematically examine how these network dynamics relate to long-term career success and mobility. Analysing 35,708 physicists' careers spanning at least 15 years, we use time series clustering to identify ten distinct evolution patterns of network size and clustering coefficient across career years 5 to 15. We report three key results. First, authors who begin with loosely connected networks and progressively tighten their networks while expanding network size during mid-career achieve the highest PI attainment rates, publication output, and citation impact. Second, despite different starting points, network evolution patterns associated with better outcomes converge toward moderate clustering by career year 15, suggesting an optimal balance between core team cohesion and diverse external connections. Third, mobility is positively associated with these successful network evolution patterns and remains positively associated with scientific outcomes even after controlling for network evolution patterns.

physics.soc-ph↗

arXiv2026

Graphs are maximally expressive for higher-order interactions

We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on "higher-order networks" that graph-based representations are fundamentally limited to "pairwise" interactions, requiring hypergraph formulations to capture richer dependencies. We clarify this issue by emphasizing two frequently overlooked facts. First, graph-based models are not restricted to pairwise interactions, as they easily accommodate interactions that depend simultaneously on multiple adjacent nodes. Second, hypergraph formulations are strict special cases of more general graph-based representations, as they impose additional constraints on the allowable interactions between adjacent elements rather than expanding the space of possibilities. We show that key phenomenology commonly attributed to hypergraphs -- such as abrupt transitions -- can, in general, be recovered exactly using graph models, even locally tree-like ones, and thus do not constitute a class of phenomena that is inherently contingent on hypergraphs models. Finally, we argue that the broad relevance of hypergraphs for applications that is sometimes claimed in the literature is not supported by evidence. Instead it is likely grounded in misconceptions that network models cannot accommodate multibody interactions or that certain phenomena can only be captured with hypergraphs. We argue that clearly distinguishing between multivariate interactions, parametrized by graphs, and the functions that define them enables a more unified and flexible foundation for modeling interacting systems.

physics.soc-ph↗

arXiv2026

Higher order trade-offs in hypergraph community detection

Extending community detection from pairwise networks to hypergraphs introduces fundamental theoretical challenges. Hypergraphs exhibit structural heterogeneity with no direct graph analogue: hyperedges of varying orders can connect nodes across communities in diverse configurations, introducing new trade-offs in defining and detecting community structure. We address these challenges by developing a unified framework for community detection in non-uniform hypergraphs under the Hypergraph Stochastic Block Model. We introduce a general signal-to-noise ratio that enables a quantitative analysis of trade-offs unique to higher-order networks, such as which hypergedges we choose to split across communities and how we choose to split them. Building on this framework, we derive a Bethe Hessian operator for non-uniform hypergraphs that provides efficient spectral clustering with principled model selection. We characterize the resulting spectral detectability threshold and compare it to belief propagation limits, showing the methods coincide for uniform hypergraphs but diverge in non-uniform settings. Synthetic experiments confirm our analytical predictions and reveal systematic biases toward preserving higher-order and balanced-shape hyperedges. Application to empirical data demonstrates the practical relevance of these higher-order detectability trade-offs in real-world systems.

cs.SI↗

arXiv2026

Inferring signed social networks from contact patterns

Social networks are typically inferred from indirect observations, such as proximity data; yet, most methods cannot distinguish between absent relationships and actual negative ties, as both can result in few or no interactions. We address the challenge of inferring signed networks from contact patterns while accounting for whether lack of interactions reflect a lack of opportunity as opposed to active avoidance. We develop a Bayesian framework with MCMC inference that models interaction groups to separate chance from choice when no interactions are observed. Validation on synthetic data demonstrates superior performance compared to natural baselines, particularly in detecting negative edges. We apply our method to French high school contact data to reveal a structure consistent with friendship surveys and demonstrate the model's adequacy through posterior predictive checks.

cs.SI↗

arXiv2024

Gender differences in collaboration and career progression in physics

We examine gender differences in collaboration networks and academic career progression in physics. We use the likelihood and time to become a principal investigator (PI) and the length of an author's career to measure career progression. Utilising logistic regression and accelerated failure time models, we examine whether the effect of collaboration behaviour varies by gender. We find that, controlling for the number of publications, the relationship between collaborative behaviour and career progression is almost the same for men and women. Specifically, we find that those who eventually reach principal investigator (PI) status, tend to have published with more unique collaborators. In contrast, publishing repeatedly with the same highly interconnected collaborators and/or larger number of co-authors per publication is characteristic of shorter career lengths and not attaining PI status. We observe that women tend to collaborate in more tightly connected and larger groups than men. Finally, we observe that women are less likely to attain the status of PI throughout their careers and have a lower survival probability compared to men, which calls for policies to close this crucial gap.

physics.soc-ph↗

arXiv2021

Network constraints on the mixing patterns of binary node metadata

We consider the network constraints on the bounds of the assortativity coefficient, which measures the tendency of nodes with the same attribute values to be interconnected. The assortativity coefficient is the Pearson's correlation coefficient of node attribute values across network edges and ranges between -1 and 1. We focus here on the assortativity of binary node attributes and show that properties of the network, such as degree distribution and the number of nodes with each attribute value place constraints upon the attainable values of the assortativity coefficient. We explore the assortativity in three different spaces, that is, ensembles of graph configurations and node-attribute assignments that are valid for a given set of network constraints. We provide means for obtaining bounds on the extremal values of assortativity for each of these spaces. Finally, we demonstrate that under certain conditions the network constraints severely limit the maximum and minimum values of assortativity, which may present issues in how we interpret the assortativity coefficient.

cs.SI↗

arXiv2020

Detectability of hierarchical communities in networks

We study the problem of recovering a planted hierarchy of partitions in a network. The detectability of a single planted partition has previously been analysed in detail and a phase transition has been identified below which the partition cannot be detected. Here we show that, in the hierarchical setting, there exist additional phases in which the presence of multiple consistent partitions can either help or hinder detection. Accordingly, the detectability limit for non-hierarchical partitions typically provides insufficient information about the detectability of the complete hierarchical structure, as we highlight with several constructive examples.

cs.SI↗

arXiv2020

Hierarchical community structure in networks

Modular and hierarchical community structures are pervasive in real-world complex systems. A great deal of effort has gone into trying to detect and study these structures. Important theoretical advances in the detection of modular have included identifying fundamental limits of detectability by formally defining community structure using probabilistic generative models. Detecting hierarchical community structure introduces additional challenges alongside those inherited from community detection. Here we present a theoretical study on hierarchical community structure in networks, which has thus far not received the same rigorous attention. We address the following questions: 1) How should we define a hierarchy of communities? 2) How do we determine if there is sufficient evidence of a hierarchical structure in a network? and 3) How can we detect hierarchical structure efficiently? We approach these questions by introducing a definition of hierarchy based on the concept of stochastic externally equitable partitions and their relation to probabilistic models, such as the popular stochastic block model. We enumerate the challenges involved in detecting hierarchies and, by studying the spectral properties of hierarchical structure, present an efficient and principled method for detecting them.

cs.SI↗

arXiv2020

Community detection in networks without observing edges

We develop a Bayesian hierarchical model to identify communities in networks for which we do not observe the edges directly, but instead observe a series of interdependent signals for each of the nodes. Fitting the model provides an end-to-end community detection algorithm that does not extract information as a sequence of point estimates but propagates uncertainties from the raw data to the community labels. Our approach naturally supports multiscale community detection as well as the selection of an optimal scale using model comparison. We study the properties of the algorithm using synthetic data and apply it to daily returns of constituents of the S&P100 index as well as climate data from US cities.

cs.SI↗

arXiv2018

Individual perception dynamics in drunk games

We study the effects of individual perceptions of payoffs in two-player games. In particular we consider the setting in which individuals' perceptions of the game are influenced by their previous experiences and outcomes. Accordingly, we introduce a framework based on evolutionary games where individuals have the capacity to perceive their interactions in different ways. Starting from the narrative of social behaviors in a pub as an illustration, we first study the combination of the prisoner's dilemma and harmony game as two alternative perceptions of the same situation. Considering a selection of game pairs, our results show that the interplay between perception dynamics and game payoffs gives rise to non-linear phenomena unexpected in each of the games separately, such as catastrophic phase transitions in the cooperation basin of attraction, Hopf bifurcations and cycles of cooperation and defection. Combining analytical techniques with multi-agent simulations we also show how introducing individual perceptions can cause non-trivial dynamical behaviors to emerge, which cannot be obtained by analyzing the system as a whole. Specifically, initial heterogeneities at the microscopic level can yield a polarization effect that is unpredictable at the macroscopic level. This framework opens the door to the exploration of new ways of understanding the link between the emergence of cooperation and individual preferences and perceptions, with potential applications beyond social interactions.

cs.GT↗

arXiv2018

Multiscale mixing patterns in networks

Assortative mixing in networks is the tendency for nodes with the same attributes, or metadata, to link to each other. It is a property often found in social networks manifesting as a higher tendency of links occurring between people with the same age, race, or political belief. Quantifying the level of assortativity or disassortativity (the preference of linking to nodes with different attributes) can shed light on the factors involved in the formation of links and contagion processes in complex networks. It is common practice to measure the level of assortativity according to the assortativity coefficient, or modularity in the case of discrete-valued metadata. This global value is the average level of assortativity across the network and may not be a representative statistic when mixing patterns are heterogeneous. For example, a social network spanning the globe may exhibit local differences in mixing patterns as a consequence of differences in cultural norms. Here, we introduce an approach to localise this global measure so that we can describe the assortativity, across multiple scales, at the node level. Consequently we are able to capture and qualitatively evaluate the distribution of mixing patterns in the network. We find that for many real-world networks the distribution of assortativity is skewed, overdispersed and multimodal. Our method provides a clearer lens through which we can more closely examine mixing patterns in networks.

cs.SI↗

arXiv2017

The ground truth about metadata and community detection in networks

Across many scientific domains, there is a common need to automatically extract a simplified view or coarse-graining of how a complex system's components interact. This general task is called community detection in networks and is analogous to searching for clusters in independent vector data. It is common to evaluate the performance of community detection algorithms by their ability to find so-called "ground truth" communities. This works well in synthetic networks with planted communities because such networks' links are formed explicitly based on those known communities. However, there are no planted communities in real world networks. Instead, it is standard practice to treat some observed discrete-valued node attributes, or metadata, as ground truth. Here, we show that metadata are not the same as ground truth, and that treating them as such induces severe theoretical and practical problems. We prove that no algorithm can uniquely solve community detection, and we prove a general No Free Lunch theorem for community detection, which implies that there can be no algorithm that is optimal for all possible community detection tasks. However, community detection remains a powerful tool and node metadata still have value so a careful exploration of their relationship with network structure can yield insights of genuine worth. We illustrate this point by introducing two statistical techniques that can quantify the relationship between metadata and community structure for a broad class of models. We demonstrate these techniques using both synthetic and real-world networks, and for multiple types of metadata and community structure.

cs.SI↗

arXiv2016

Graph-based semi-supervised learning for relational networks

We address the problem of semi-supervised learning in relational networks, networks in which nodes are entities and links are the relationships or interactions between them. Typically this problem is confounded with the problem of graph-based semi-supervised learning (GSSL), because both problems represent the data as a graph and predict the missing class labels of nodes. However, not all graphs are created equally. In GSSL a graph is constructed, often from independent data, based on similarity. As such, edges tend to connect instances with the same class label. Relational networks, however, can be more heterogeneous and edges do not always indicate similarity. For instance, instead of links being more likely to connect nodes with the same class label, they may occur more frequently between nodes with different class labels (link-heterogeneity). Or nodes with the same class label do not necessarily have the same type of connectivity across the whole network (class-heterogeneity), e.g. in a network of sexual interactions we may observe links between opposite genders in some parts of the graph and links between the same genders in others. Performing classification in networks with different types of heterogeneity is a hard problem that is made harder still when we do not know a-priori the type or level of heterogeneity. Here we present two scalable approaches for graph-based semi-supervised learning for the more general case of relational networks. We demonstrate these approaches on synthetic and real-world networks that display different link patterns within and between classes. Compared to state-of-the-art approaches, ours give better classification performance without prior knowledge of how classes interact. In particular, our two-step label propagation algorithm gives consistently good accuracy and runs on networks of over 1.6 million nodes and 30 million edges in around 12 seconds.

cs.SI↗

arXiv2015

Detectability thresholds and optimal algorithms for community structure in dynamic networks

We study the fundamental limits on learning latent community structure in dynamic networks. Specifically, we study dynamic stochastic block models where nodes change their community membership over time, but where edges are generated independently at each time step. In this setting (which is a special case of several existing models), we are able to derive the detectability threshold exactly, as a function of the rate of change and the strength of the communities. Below this threshold, we claim that no algorithm can identify the communities better than chance. We then give two algorithms that are optimal in the sense that they succeed all the way down to this limit. The first uses belief propagation (BP), which gives asymptotically optimal accuracy, and the second is a fast spectral clustering algorithm, based on linearizing the BP equations. We verify our analytic and algorithmic results via numerical simulation, and close with a brief discussion of extensions and open questions.

stat.ML↗

arXiv2015

Predicting sports scoring dynamics with restoration and anti-persistence

Professional team sports provide an excellent domain for studying the dynamics of social competitions. These games are constructed with simple, well-defined rules and payoffs that admit a high-dimensional set of possible actions and nontrivial scoring dynamics. The resulting gameplay and efforts to predict its evolution are the object of great interest to both sports professionals and enthusiasts. In this paper, we consider two online prediction problems for team sports:~given a partially observed game Who will score next? and ultimately Who will win? We present novel interpretable generative models of within-game scoring that allow for dependence on lead size (restoration) and on the last team to score (anti-persistence). We then apply these models to comprehensive within-game scoring data for four sports leagues over a ten year period. By assessing these models' relative goodness-of-fit we shed new light on the underlying mechanisms driving the observed scoring dynamics of each sport. Furthermore, in both predictive tasks, the performance of our models consistently outperforms baselines models, and our models make quantitative assessments of the latent team skill, over time.

physics.data-an↗

arXiv2014

Detecting change points in the large-scale structure of evolving networks

Interactions among people or objects are often dynamic in nature and can be represented as a sequence of networks, each providing a snapshot of the interactions over a brief period of time. An important task in analyzing such evolving networks is change-point detection, in which we both identify the times at which the large-scale pattern of interactions changes fundamentally and quantify how large and what kind of change occurred. Here, we formalize for the first time the network change-point detection problem within an online probabilistic learning framework and introduce a method that can reliably solve it. This method combines a generalized hierarchical random graph model with a Bayesian hypothesis test to quantitatively determine if, when, and precisely how a change point has occurred. We analyze the detectability of our method using synthetic data with known change points of different types and magnitudes, and show that this method is more accurate than several previously used alternatives. Applied to two high-resolution evolving social networks, this method identifies a sequence of change points that align with known external "shocks" to these networks.

cs.SI↗

arXiv2014

Active Discovery of Network Roles for Predicting the Classes of Network Nodes

Nodes in real world networks often have class labels, or underlying attributes, that are related to the way in which they connect to other nodes. Sometimes this relationship is simple, for instance nodes of the same class are may be more likely to be connected. In other cases, however, this is not true, and the way that nodes link in a network exhibits a different, more complex relationship to their attributes. Here, we consider networks in which we know how the nodes are connected, but we do not know the class labels of the nodes or how class labels relate to the network links. We wish to identify the best subset of nodes to label in order to learn this relationship between node attributes and network links. We can then use this discovered relationship to accurately predict the class labels of the rest of the network nodes. We present a model that identifies groups of nodes with similar link patterns, which we call network roles, using a generative blockmodel. The model then predicts labels by learning the mapping from network roles to class labels using a maximum margin classifier. We choose a subset of nodes to label according to an iterative margin-based active learning strategy. By integrating the discovery of network roles with the classifier optimisation, the active learning process can adapt the network roles to better represent the network for node classification. We demonstrate the model by exploring a selection of real world networks, including a marine food web and a network of English words. We show that, in contrast to other network classifiers, this model achieves good classification accuracy for a range of networks with different relationships between class labels and network links.

cs.LG↗