Map equation with metadata: Varying the role of attributes in community detection

Differential Transcriptional Programs Reveal Modular Network Rearrangements Associated with Late-Onset Alzheimer's Disease

Alzheimer's disease (AD) is a complex, genetically heterogeneous disorder. The diverse phenotypes associated with AD result from interactions between genetic and environmental factors, influencing multiple biological pathways throughout disease progression. Network-based approaches offer a way to assess phenotype-specific states. In this study, we calculated key network metrics to characterize the network transcriptional structure and organization in LOAD, focusing on genes and pathways implicated in AD pathology within the dorsolateral prefrontal cortex (DLPFC). Our findings revealed disease-specific coexpression markers associated with diverse metabolic functions. Additionally, significant differences were observed at both the mesoscopic and local levels between AD and control networks, along with a restructuring of gene coexpression and biological functions into distinct transcriptional modules. These results show the molecular reorganization of the transcriptional program occurring in LOAD, highlighting specific adaptations that may contribute to or result from cellular responses to pathological stressors. Our findings may support the development of a unified model for the causal mechanisms of AD, suggesting that its diverse manifestations arise from multiple pathways working together to produce the disease's complex clinical patho-phenotype.

Single-trajectory map equation

Community detection, the process of identifying module structures in complex systems represented on networks, is an effective tool in various fields of science. The map equation, which is an information-theoretic framework based on the random walk on a network, is a particularly popular community detection method. Despite its outstanding performance in many applications, the inner workings of the map equation have not been thoroughly studied. Herein, we revisit the original formulation of the map equation and address the existence of its "raw form," which we refer to as the single-trajectory map equation. This raw form sheds light on many details behind the principle of the map equation that are hidden in the steady-state limit of the random walk. Most importantly, the single-trajectory map equation provides a more balanced community structure, naturally reducing the tendency of the overfitting phenomenon in the map equation.

Mapping nonlocal relationships between metadata and network structure with metadata-dependent encoding of random walks

Integrating structural information and metadata, such as gender, social status, or interests, enriches networks and enables a better understanding of the large-scale structure of complex systems. However, existing approaches to augment networks with metadata for community detection only consider immediately adjacent nodes and cannot exploit the nonlocal relationships between metadata and large-scale network structure present in many spatial and social systems. Here, we develop a flow-based community detection framework based on the map equation that integrates network information and metadata of distant nodes and reveals more complex relationships. We analyze social and spatial networks and find that our methodology can detect functional metadata-informed communities distinct from those derived solely from network information or metadata. For example, in a mobility network of London, we identify communities that reflect the heterogeneity of income distribution, and in a European power grid network, we identify communities that capture relationships between geography and energy prices beyond country borders.

The minimum description length principle for pattern mining: a survey

Mining patterns is a core task in data analysis and, beyond issues of efficient enumeration, the selection of patterns constitutes a major challenge. The Minimum Description Length (MDL) principle, a model selection method grounded in information theory, has been applied to pattern mining with the aim to obtain compact high-quality sets of patterns. After giving an outline of relevant concepts from information theory and coding, we review MDL-based methods for mining different kinds of patterns from various types of data. Finally, we open a discussion on some issues regarding these methods.

Inferring functional communities from partially observed biological networks exploiting geometric topology and side information

Cellular biological networks represent the molecular interactions that shape function of living cells. Uncovering the organization of a biological network requires efficient and accurate algorithms to determine the components, termed communities, underlying specific processes. Detecting functional communities is challenging because reconstructed biological networks are always incomplete due to technical bias and biological complexity, and the evaluation of putative communities is further complicated by a lack of known ground truth. To address these challenges, we developed a geometric-based detection framework based on Ollivier-Ricci curvature to exploit information about network topology to perform community detection from partially observed biological networks. We further improved this approach by integrating knowledge of gene function, termed side information, into the Ollivier-Ricci curvature algorithm to aid in community detection. This approach identified essential conserved and varied biological communities from partially observed Arabidopsis protein interaction datasets better than the previously used methods. We show that Ollivier-Ricci curvature with side information identified an expanded auxin community to include an important protein stability complex, the Cop9 signalosome, consistent with previous reported links to auxin response and root development. The results show that community detection based on Ollivier-Ricci curvature with side information can uncover novel components and novel communities in biological networks, providing novel insight into the organization and function of complex networks.

X-Mark: a benchmark for node-attributed community discovery algorithms

Grouping well-connected nodes that also result in label-homogeneous clusters is a task often known as attribute-aware community discovery. While approaching node-enriched graph clustering methods, rigorous tools need to be developed for evaluating the quality of the resulting partitions. In this work, we present X-Mark, a model that generates synthetic node-attributed graphs with planted communities. Its novelty consists in forming communities and node labels contextually while handling categorical or continuous attributive information. Moreover, we propose a comparison between attribute-aware algorithms, testing them against our benchmark. Accordingly to different classification schema from recent state-of-the-art surveys, our results suggest that X-Mark can shed light on the differences between several families of algorithms.

Modularity in Biological Networks

Network modeling, from the ecological to the molecular scale has become an essential tool for studying the structure, dynamics and complex behavior of living systems. Graph representations of the relationships between biological components open up a wide variety of methods for discovering the mechanistic and functional properties of biological systems. Many biological networks are organized into a modular structure, so methods to discover such modules are essential if we are to understand the biological system as a whole. However, most of the methods used in biology to this end, have a limited applicability, as they are very specific to the system they were developed for. Conversely, from the statistical physics and network science perspective, graph modularity has been theoretically studied and several methods of a very general nature have been developed. It is our perspective that in particular for the modularity detection problem, biology and theoretical physics/network science are less connected than they should. The central goal of this review is to provide the necessary background and present the most applicable and pertinent methods for community detection in a way that motivates their further usage in biological research.

Community detection with node attributes in multilayer networks

Community detection in networks is commonly performed using information about interactions between nodes. Recent advances have been made to incorporate multiple types of interactions, thus generalizing standard methods to multilayer networks. Often, though, one can access additional information regarding individual nodes, attributes, or covariates. A relevant question is thus how to properly incorporate this extra information in such frameworks. Here we develop a method that incorporates both the topology of interactions and node attributes to extract communities in multilayer networks. We propose a principled probabilistic method that does not assume any a priori correlation structure between attributes and communities but rather infers this from data. This leads to an efficient algorithmic implementation that exploits the sparsity of the dataset and can be used to perform several inference tasks; we provide an open-source implementation of the code online. We demonstrate our method on both synthetic and real-world data and compare performance with methods that do not use any attribute information. We find that including node information helps in predicting missing links or attributes. It also leads to more interpretable community structures and allows the quantification of the impact of the node attributes given in input.