Knowledge graphs [1–4] represent structured knowledge using nodes and edges, where nodes signify entities and edges denote relationships between these entities. These graphs have become essential in various fields such as cultural heritage [5], life sciences [6], and encyclopedic knowledge bases, thanks to projects like Yago [7], DBpedia [8], and Wikidata [9]. These knowledge graphs have enabled significant advancements in data integration and semantic understanding, leading to more informed scientific hypotheses and enhanced data exploration.

Despite their importance, understanding the topology and dynamics of knowledge graphs remains a challenge due to their complex and often chaotic nature. Current models, like the preferential attachment mechanism, are limited to simpler networks and fail to capture the intricate interplay of diverse relationships in knowledge graphs. There is a pressing need for models that can accurately represent the structure and dynamics of knowledge graphs, allowing for better understanding, prediction, and utilisation of the knowledge contained within them.

The paper by Lhote, Markhoff, and Soulet [10] introduces a novel approach to modelling the structure and dynamics of knowledge graphs through the concept of superficiality. This model aims to control the overlap between relationships, providing a mechanism to balance the distribution of knowledge and reduce the proportion of misdescribed entities. This is the first model tailored specifically to knowledge graphs, addressing the unique challenges posed by their complexity and diverse relationship types. The innovation lies in the introduction of superficiality, a parameter that governs the probability of adding new entities versus enriching existing ones within the graph. This model not only addresses the multimodal probability distributions observed in real KGs but also offers a more granular understanding of the knowledge distribution, particularly the presence of misdescribed entities. The authors validated their model against three major knowledge graphs: BnF, ChEMBL, and Wikidata. The results demonstrated that the generative model accurately reproduces the observed distributions of incoming and outgoing degrees in these knowledge graphs. The model successfully captures the multimodal nature and the irregularities in the degree distributions, especially for entities with low connectivity, which are typically the majority in a knowledge graphs.

One significant finding is the impact of superficiality on the level of misdescribed entities. The study revealed that lower superficiality leads to a more uniform distribution of relationships across entities, thus reducing the number of entities described by few relationships. Conversely, higher superficiality results in a higher proportion of entities with minimal descriptive facts, reflecting a paradox where increasing the volume of knowledge does not necessarily reduce the level of ignorance. The authors also conducted an ablation study comparing their model to traditional models like Barabási-Albert [11] and Bollobás [12]. The results showed that the proposed multiplex model with superficiality parameters consistently outperformed these traditional models in accurately reflecting the characteristics of real-world knowledge graphs. 

This research provides a groundbreaking approach to understanding and modelling the structure and dynamics of knowledge graphs. By introducing superficiality, the authors offer a new lens through which to examine the distribution and organisation of knowledge within these complex structures. The model not only enhances our theoretical understanding of knowledge graphs but also has practical implications for improving data storage, query optimisation, and the robustness of knowledge induction processes.

The introduction of superficiality opens several avenues for future research and application. One potential direction is refining the model to account for localised perturbations in smaller knowledge graphs or specific domains within larger knowledge graphs. Additionally, longitudinal studies could further elucidate the evolution of superficiality over time and its impact on the quality of knowledge representation. Another promising area is the application of this model in real-time knowledge graphs management systems. By adjusting superficiality parameters dynamically, it may be possible to optimise the balance between entity enrichment and the introduction of new entities, leading to more robust and accurate knowledge graphs. In the broader context of knowledge engineering and data science, this model offers a framework for exploring the vulnerability of knowledge graphs and their susceptibility to various types of biases and inaccuracies. This understanding could lead to the development of more resilient knowledge systems capable of adapting to new information while maintaining a high level of accuracy and coherence.

Overall, the concept of superficiality and the associated generative model represent significant advancements in the study and application of knowledge graphs, promising to enhance both our theoretical understanding and practical capabilities in managing and utilising these complex data structures. It would be interesting to see how this can be extended to domains in social network analyses [13,14].

References

​1.     Nickel M, Murphy K, Tresp V, Gabrilovich E. 2015 A review of relational machine learning for knowledge graphs. Proceedings of the IEEE 104, 11-33. https://doi.org/10.1109/JPROC.2015.2483592

2.     Ehrlinger L, Wöß W. 2016 Towards a definition of knowledge graphs. SEMANTiCS (Posters, Demos, SuCCESS) 48, 2.

3.     Hogan A et al. 2021 Knowledge graphs. ACM Computing Surveys (Csur) 54, 1-37.

4.     Ji S, Pan S, Cambria E, Marttinen P, Philip SY. 2021 A survey on knowledge graphs: Representation, acquisition, and applications. IEEE transactions on neural networks and learning systems 33, 494-514. https://doi.org/10.1109/TNNLS.2021.3070843

5.     Bikakis A, Hyvönen E, Jean S, Markhoff B, Mosca A. 2021 Special issue on semantic web for cultural heritage. Semantic Web 12, 163-167. https://doi.org/10.3233/SW-210425

6.     Santos A et al. 2022 A knowledge graph to interpret clinical proteomics data. Nature biotechnology 40, 692-702. https://doi.org/10.1038/s41587-021-01145-6

7.     Suchanek FM, Kasneci G, Weikum G. 2007 Yago: a core of semantic knowledge. pp. 697-706. https://doi.org/10.1145/1242572.1242667

8.     Auer S, Bizer C, Kobilarov G, Lehmann J, Cyganiak R, Ives Z. 2007 Dbpedia: A nucleus for a web of open data. pp. 722-735. Springer. https://doi.org/10.1007/978-3-540-76298-0_52

9.     Mora-Cantallops M, Sánchez-Alonso S, García-Barriocanal E. 2019 A systematic literature review on Wikidata. Data Technologies and Applications 53, 250-268. https://doi.org/10.1108/DTA-12-2018-0110

10.  Lhote L, Markhoff B, Soulet A. 2023 The Structure and Dynamics of Knowledge Graphs, with Superficiality. arXiv, ver. 3 peer-reviewed and recommended by Peer Community in Network Science. https://doi.org/10.48550/arXiv.2305.08116

11.  Barabási A-L, Albert R. 1999 Emergence of scaling in random networks. science 286, 509-512. https://doi.org/10.1126/science.286.5439.509

12.  Bollobás B, Borgs C, Chayes JT, Riordan O. 2003 Directed scale-free graphs. pp. 132-139. Baltimore, MD, United States.

13.  Sueur C, King AJ, Pelé M, Petit O. 2013 Fast and accurate decisions as a result of scale-free network properties in two primate species. In Proceedings of the European conference on complex systems 2012 (eds T Gilbert, M Kirkilionis, G Nicolis), pp. 579-584. https://doi.org/10.1007/978-3-319-00395-5_71

14.  Romano V, Shen M, Pansanel J, MacIntosh AJJ, Sueur C. 2018 Social transmission in networks: global efficiency peaks with intermediate levels of modularity. Behav Ecol Sociobiol 72, 154. https://doi.org/10.1007/s00265-018-2564-9

Hypergraphs, as a framework to model higher-order interactions, have attracted a lot of attention in recent years. One particularly fruitful research direction consists of transposing well-defined notions in simple graphs to this new paradigm. A difficulty, but also an interesting opportunity, of this task is that a single concept in simple graphs might correspond to multiple ones in the domain to which it is transposed. The problem has for instance been discussed for link streams in Latapy et al. (2018), for notions as simple as node neighborhoods or the notion of shortest path. In the present article (Poda and Matias 2024), Poda and Matias focus on the concept of modularity and, indeed, they identify multiple definitions of modularity for hypergraphs in the literature (Chodrow et al., 2021, Kaminski et al., 2021). The first interesting contribution is the unification of these different representations using a common framework. They can thus compare, based solely on the definitions themselves, theoretical similarities and differences between those modularities for hypergraphs.

In the second part of their contribution, they turn towards the empirical evaluation of these methods.  Community detection has a long tradition of experimental articles, comparing on selected benchmarks the strengths and weaknesses of selected methods, from the seminal work from Lancichinetti and Fortunato (Lancichinetti et al., 2009), to recent works comparing, for instance, modularity methods in dynamic graphs (Cazabet et al., 2020). The authors thus point to existing implementations and start comparing them using existing benchmarks for hypergraphs (Brusa and Matias, 2022, Kaminski et al., 2023). This confrontation between theoretical definition and actual networks with varying properties allows them to identify methods that do not perform as expected. Furthermore, they do not solely focus on classification performance but also evaluate other factors such as scalability. Their findings reveal that all methods perform poorly in this aspect. These observations pave the way for future work.

To conclude, this work is a very relevant contribution to the field. One could say that the first empirical comparison of methods in a particular field is a sign that it has become mature, and that is maybe one of the conclusions to draw from this article.

References

Poda, V., & Matias, C. (2024). Comparison of modularity-based approaches for nodes clustering in hypergraphs. arXiv preprint. HAL, https://hal.science/hal-04414337v2
 
Chodrow, P. S., N. Veldt, and A. R. Benson (2021). Generative hypergraph clustering: From blockmodels to modularity. Science Advances 7(28), eabh1303. 
https://doi.org/10.1126/sciadv.abh1303
 
Kaminski, B., P. Pralat, and F. Theberge (2021). Community detection algorithm using hypergraph modularity. In R. M. Benito, C. Cherifi, H. Cherifi, E. Moro, L. M. Rocha, and M. Sales-Pardo (Eds.), Complex Networks & Their Applications IX, pp. 152-163. 
 
Lancichinetti, A., & Fortunato, S. (2009). Community detection algorithms: a comparative analysis. Physical review E, 80(5), 056117.
https://doi.org/10.1103/PhysRevE.80.056117
 
Latapy, M., Viard, T., & Magnien, C. (2018). Stream graphs and link streams for the modeling of interactions over time. Social Network Analysis and Mining, 8, 1-29.
https://doi.org/10.1007/s13278-018-0537-7
 
Cazabet, R., Boudebza, S., & Rossetti, G. (2020). Evaluating community detection algorithms for progressively evolving graphs. Journal of Complex Networks, 8(6), cnaa027.
https://doi.org/10.1093/comnet/cnaa027
 
Brusa, L. and C. Matias (2022). HyperSBM: Stochastic blockmodel for hypergraphs. R package, https://github.com/LB1304/HyperSBM 
 
Kaminski, B., P. Pralat, and F. Theberge (2023). Hypergraph Artificial Benchmark for Community Detection (h-ABCD). Journal of Complex Networks 11(4), cnad028 
https://doi.org/10.21203/rs.3.rs-2471638/v1

Social relationships are recognized as an important age-related mediator of health in humans and fitness-related traits in animals (Sueur et al., 2021). Vandeleest et al. (2024) is a pioneering exploration into the complex interplay between social relationships and health in rhesus macaques. It breaks new ground by differentiating between two types of affiliative relationships – multiplex (engaging in multiple types of affiliative behaviors like grooming and contact sitting) and uniplex (involving only one type of behavior, such as grooming) (Beisner et al., 2020). The study's crux lies in its novel approach to understanding how these differing social interactions correlate with biomarkers of inflammation, namely pro-inflammatory cytokines like IL-6 and TNF-alpha.

The research is innovative in its use of social network analysis (Sosa et al., 2021), allowing for a nuanced view of the rhesus macaques' social dynamics. It reveals that multiplex grooming networks, characterized by more modular structures and kin bias, are associated with lower inflammation levels. This is in contrast to uniplex grooming networks, where a stronger link to social status correlates with higher inflammation. These findings suggest that multiplex relationships could serve as supportive, health-promoting bonds, while uniplex relationships might be more transactional, with possible physiological costs.

Moreover, the study's results highlight the importance of the diversity of affiliative interactions within a dyad. It posits that relationships involving multiple types of affiliative behaviors may have different implications for health and well-being compared to those based on a single behavior type, even if interaction rates are similar. This insight opens up new avenues for understanding the health implications of social behaviors in non-human primates and potentially in humans (Sueur et al., 2021).

Furthermore, the paper provides a comprehensive analysis of the network structures, examining kin bias, clustering, modularity, and associations with dominance rank. It also evaluates the correlations between individual network positions and health markers, offering a multifaceted understanding of how social networks influence physical well-being.

In essence, this research makes a significant contribution to our understanding of the link between sociality and health. It underscores the complexity of social relationships (Moscovice et al., 2020) and their varied impacts on health, suggesting that the nature of social bonds (multiplex vs. uniplex) plays a critical role in determining their health consequences. This study not only enhances our comprehension of primate social behavior but also has broader implications for the fields of social neuroscience, behavioral ecology, and health psychology.

References

Beisner, B., Braun, N., Pósfai, M., Vandeleest, J., D’Souza, R., & McCowan, B. (2020). A multiplex centrality metric for complex social networks: Sex, social status, and family structure predict multiplex centrality in rhesus macaques. PeerJ, 8, e8712. https://doi.org/10.7717/peerj.8712

Moscovice, L. R., Sueur, C., & Aureli, F. (2020). How socio-ecological factors influence the differentiation of social relationships: An integrated conceptual framework. Biology Letters, 16(9), 20200384. https://doi.org/10.1098/rsbl.2020.0384

Sosa, S., Sueur, C., & Puga-Gonzalez, I. (2021). Network measures in animal social network analysis: Their strengths, limits, interpretations and uses. Methods in Ecology and Evolution, 12(1), 10–21. https://doi.org/10.1111/2041-210X.13366

Sueur, C., Quque, M., Naud, A., Bergouignan, A., & Criscuolo, F. (2021). Social capital: An independent dimension of healthy ageing. Peer Community Journal, 1. https://doi.org/10.24072/pcjournal.33

Vandeleest, J. J., Wooddell, L. J., Nathman, A. C., Beisner, B. A., & McCowan, B. (2024). Differential effects of multiplex and uniplex affiliative relationships on biomarkers of inflammation. bioRxiv, ver. 4 peer-reviewed and recommended by Peer Community in Network Science. https://doi.org/10.1101/2022.11.01.514247

Networks provide an ideal tool to link social behaviour and infection in animal societies (White et al. 2017). A major focus of previous research has been on the links between social centrality and infection (Briard & Ezenwa 2021). But what happens when conclusions are drawn from sampled networks in which some individuals are not observed, or when studies focus on some individuals at the expense of others (e.g. adults versus juveniles or females versus males)? Xu et al. (2022) examine how focusing on different samples of individuals in a network analysis relating centrality to parasite load in Japanese macaques Macaca fuscata influence the conclusions drawn.

Xu et al. (2022) use faecal egg counts to estimate parasite loads of three environmentally transmitted parasites Oesophagostomum aculeatum, Strongyloides fuelleborni and Trichuris trichiura in a group of macaques on Koshima Island, Japan. After showing positive associations between parasite load and strength (the sum of an individual’s connections) and eigenvector centrality (accounting for second-order connections) in a 1-metre proximity network, the authors explore how this result is impacted by focusing on only adult females, only juveniles or random sub-samples of the population. Their results indicate that the positive association persists more strongly in the adult female networks albeit with reduced statistical power to detect it. It is largely absent in juveniles (either based on their centrality in the full network or centrality in the juvenile-only network). Random removal of individuals from the network led to a rapid reduction in the ability to detect the same positive association between centrality and parasite load due to a combination of changes in individual centrality in re-sampled networks and reduced statistical power. 

The timescale of network data collection and proximity networks studied are (likely) not fully relevant for the transmission of these parasites and social transmission of the parasites studied here is likely to be limited, there remain other reasons that we may expect correlations between sociality and infection (Ezenwa et al. 2016). Nevertheless, this is a useful contribution to the literature on sampling effects in animal networks, complementing existing work (Franks et al. 2010, Silk et al. 2015, Davis et al. 2018, Silk 2018). The results from considering different sub-samples of the group show the potential importance of carefully considering whether social network effects will be equivalently important for the whole population and which interactions will contribute either to promoting health or increasing the risk of infection. The results of random sub-sampling show how in small (within-group) networks such as these even small numbers of missing individuals could have substantial impacts on testing how traits are associated with the social network position of individuals.

The findings set up some interesting questions about how best to develop effective sampling designs in single-group studies such as these, or in how best to extend these types of projects across multiple groups (see also Silk 2018). Testing the generality of these findings across taxa with different social systems and infection prevalences or loads will also be a valuable next step for behavioural disease ecology.

References

Briard L, Ezenwa VO. 2021. Parasitism and host social behaviour: a meta-analysis of insights derived from social network analysis. Anim. Behav. 172, 171-182. https://doi.org/10.1016/j.anbehav.2020.11.010

Davis GH, Crofoot MC, Farine DR. 2018. Estimating the robustness and uncertainty of animal social networks using different observational methods. Anim. Behav. 141, 29-44. https://doi.org/10.1016/j.anbehav.2018.04.012

Ezenwa VO, Ghai RR, McKay AF, Williams AE. 2016. Group living and pathogen infection revisited. Curr. Opin. Behav. Sci. 12, 66-72. https://doi.org/10.1016/j.cobeha.2016.09.006 

Franks DW, Ruxton GD, James R. 2010. Sampling animal association networks with the gambit of the group. Behav. Ecol. Sociobiol. 64, 493-503. https://doi.org/10.1007/s00265-009-0865-8

Silk MJ, Jackson AL, Croft DP, Colhoun K, Bearhop S. 2015. The consequences of unidentifiable individuals for the analysis of an animal social network. Anim. Behav. 104, 1-11. https://doi.org/10.1016/j.anbehav.2015.03.005

Silk MJ. 2018. The next steps in the study of missing individuals in networks: a comment on Smith et al. (2017). Soc. Net. 52, 37-41. https://doi.org/10.1016/j.socnet.2017.05.002

White LA, Forester JD, Craft ME. 2017. Using contact networks to explore mechanisms of parasite transmission in wildlife. Biol. Rev. 92, 389-409. https://doi.org/10.1111/brv.12236

Xu Z, MacIntosh AJJ, Castellano-Navarro A, Macanás-Martinez E, Suzumura T, Dubosq J. 2022. Linking parasitism to network centrality and the impact of sampling bias in its interpretation. bioRxiv 2021.06.07.447302, ver. 6 peer-reviewed and recommended by Peer Community in Network Science. https://doi.org/10.1101/2021.06.07.447302 

If you work, study or play in network science then chances are you have generated a network. Whether or not you have a real-world system to analyse, synthetic networks play an important role in network science. Generating networks of a chosen size can provide a null model for a statistical test, a test bed for new algorithms or the basis for studying the interplay between structure and dynamics in complex systems. Consequently network science literature contains a wide array of network models: some designed as processes to replicate observed properties and others for the purposes of statistical inference. However, these models have different parameters and constraints associated with their generative models, may or may not have the ability to control for random noise and do not always have readily available software implementations, thus making them unavailable to network science practitioners.

The article of Cazabet et al. (2023) introduces a software "zoo, " called Structify-Net, that contains a range of models that the authors have captured from the wild. The authors have focused on developing a framework that enables the generation networks of a chosen size, according to number of nodes and edges, and provides the means to control for randomness, by interpolating between the specified structure and a random graph. The article also discusses an interesting use case to examine the interplay between network structure and node attributes, which might compliment methods based on permutation tests (Bianconi et al. 2009, Ehrhardt and Wolfe 2019). 

Structify-Net presents some interesting future opportunities. For instance, the independence that Structify-Net imposes on edge ranking (defined by the model) and the expected number of edges (defined by the user) might offer a route towards exploring network growth or evolution. Like any zoo Structify-Net is not complete in that there are many more exotic "species" that the authors, or perhaps others in the network science community, may later collect. Collecting more model implementations to align with reviews of network models (Goldenberg et al. 2010) together with methods of statistical inference has the potential to lay the foundations for the ever important bridge between theory and practice in network science (Peel et al. 2022).

References

Bianconi, Ginestra, Paolo Pin, and Matteo Marsili (2009) Assessing the Relevance of Node Features for Network Structure. Proceedings of the National Academy of Sciences 106, 28: 11433–38. https://doi.org/10.1073/pnas.0811511106

Cazabet, Remy, Salvatore Citraro, and Giulio Rossetti (2023) Structify-Net: Random Graph Generation with Controlled Size and Customized Structure. arXiv, ver. 2 peer-reviewed and recommended by Peer Community in Network Science. https://doi.org/10.48550/arXiv.2306.05274

Ehrhardt, Beate, and Patrick J. Wolfe (2019) Network Modularity in the Presence of Covariates’. SIAM Review 61, 2: 261–76. https://doi.org/10.1137/17M1111528

Goldenberg, Anna, Alice X. Zheng, Stephen E. Fienberg, and Edoardo M. Airoldi (2010) A Survey of Statistical Network Models. Foundations and Trends in Machine Learning 2, 2: 129–233. https://doi.org/10.1561/2200000005

Peel, Leto, Tiago P. Peixoto, and Manlio De Domenico (2022) Statistical Inference Links Data and Theory in Network Science. Nature Communications 13, 1: 6794. https://doi.org/10.1038/s41467-022-34267-9