François Théberge

Bogumił Kamiński, Paweł Prałat, François Théberge

The Artificial Benchmark for Community Detection (ABCD) graph is a recently introduced random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs with similar properties as the well-known LFR one, and its main parameter can be tuned to mimic its counterpart in the LFR model, the mixing parameter. In this paper, we introduce hypergraph counterpart of the ABCD model, h-ABCD, which produces random hypergraph with distributions of ground-truth community sizes and degrees following power-law. As in the original ABCD, the new model h-ABCD can produce hypergraphs with various levels of noise. More importantly, the model is flexible and can mimic any desired level of homogeneity of hyperedges that fall into one community. As a result, it can be used as a suitable, synthetic playground for analyzing and tuning hypergraph community detection algorithms.

Bogumił Kamiński, Paweł Prałat, François Théberge

The Artificial Benchmark for Community Detection graph (ABCD) is a random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs with similar properties as the well-known LFR one, and its main parameter $ξ$ can be tuned to mimic its counterpart in the LFR model, the mixing parameter $μ$. In this paper, we extend the ABCD model to include potential outliers. We perform some exploratory experiments on both the new ABCD+o model as well as a real-world network to show that outliers possess some desired, distinguishable properties.

Bogumił Kamiński, Tomasz Olczak, Bartosz Pankratz et al.

In this paper, we investigate properties and performance of synthetic random graph models with a built-in community structure. Such models are important for evaluating and tuning community detection algorithms that are unsupervised by nature. We propose ABCDe, a multi-threaded implementation of the ABCD (Artificial Benchmark for Community Detection) graph generator. We discuss the implementation details of the algorithm and compare it with both the previously available sequential version of the ABCD model and with the parallel implementation of the standard and extensively used LFR (Lancichinetti--Fortunato--Radicchi) generator. We show that ABCDe is more than ten times faster and scales better than the parallel implementation of LFR provided in NetworKit. Moreover, the algorithm is not only faster but random graphs generated by ABCD have similar properties to the ones generated by the original LFR algorithm, while the parallelized NetworKit implementation of LFR produces graphs that have noticeably different characteristics.

Bogumił Kamiński, Paweł Prałat, François Théberge et al.

This paper shows how information about the network's community structure can be used to define node features with high predictive power for classification tasks. To do so, we define a family of community-aware node features and investigate their properties. Those features are designed to ensure that they can be efficiently computed even for large graphs. We show that community-aware node features contain information that cannot be completely recovered by classical node features or node embeddings (both classical and structural) and bring value in node classification tasks. This is verified for various classification tasks on synthetic and real-life networks.

Ryan DeWolfe, Paweł Prałat, François Théberge

Clustering algorithms are an essential part of the unsupervised data science ecosystem, and extrinsic evaluation of clustering algorithms requires a method for comparing the detected clustering to a ground truth clustering. In a general setting, the detected and ground truth clusterings may have outliers (objects belonging to no cluster), overlapping clusters (objects may belong to more than one cluster), or both, but methods for comparing these clusterings are currently undeveloped. In this note, we define a pragmatic similarity measure for comparing clusterings with overlaps and outliers, show that it has several desirable properties, and experimentally confirm that it is not subject to several common biases afflicting other clustering comparison measures.

Łukasz Kraiński, Michał Czuba, Piotr Bródka et al.

One of the most persistent challenges in network science is the development of various synthetic graph models to support subsequent analyses. Among the most notable frameworks addressing this issue is the Artificial Benchmark for Community Detection (ABCD) model, a random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs similar to the well-known LFR model but it is faster, more interpretable, and can be investigated analytically. In this paper, we use the underlying ingredients of ABCD and introduce its variant, mABCD, thereby addressing the gap in models capable of generating multilayer networks. The uniqueness of the proposed approach lies in its flexibility at both levels of modelling: the internal structure of individual layers and the inter-layer dependencies, which together make the network a coherent structure rather than a collection of loosely coupled graphs. In addition to the conceptual description of the framework, we provide a comprehensive analysis of its efficient Julia implementation. Finally, we illustrate the applicability of mABCD to one of the most prominent problems in the area of complex systems: spreading phenomena analysis.

Ashkan Dehghan, Paweł Prałat, François Théberge

Many real-world and artificial systems and processes can be represented as graphs. Some examples of such systems include social networks, financial transactions, supply chains, and molecular structures. In many of these cases, one needs to consider a collection of graphs, rather than a single network. This could be a collection of distinct but related graphs, such as different protein structures or graphs resulting from dynamic processes on the same network. Examples of the latter include the evolution of social networks, community-induced graphs, or ego-nets around various nodes. A significant challenge commonly encountered is the absence of ground-truth labels for graphs or nodes, necessitating the use of unsupervised techniques to analyze such systems. Moreover, even when ground-truth labels are available, many existing graph machine learning methods depend on complex deep learning models, complicating model explainability and interpretability. To address some of these challenges, we have introduced NEExT (Network Embedding Exploration Tool) for embedding collections of graphs via user-defined node features. The advantages of the framework are twofold: (i) the ability to easily define your own interpretable node-based features in view of the task at hand, and (ii) fast embedding of graphs provided by the Vectorizers library. In this paper, we demonstrate the usefulness of NEExT on collections of synthetic and real-world graphs. For supervised tasks, we demonstrate that performance in graph classification tasks could be achieved similarly to other state-of-the-art techniques while maintaining model interpretability. Furthermore, our framework can also be used to generate high-quality embeddings in an unsupervised way, where target variables are not available.

Bogumił Kamiński, Paweł Misiorek, Paweł Prałat et al.

In this paper, we propose a scalable community detection algorithm using hypergraph modularity function, h-Louvain. It is an adaptation of the classical Louvain algorithm in the context of hypergraphs. We observe that a direct application of the Louvain algorithm to optimize the hypergraph modularity function often fails to find meaningful communities. We propose a solution to this issue by adjusting the initial stage of the algorithm via carefully and dynamically tuned linear combination of the graph modularity function of the corresponding two-section graph and the desired hypergraph modularity function. The process is guided by Bayesian optimization of the hyper-parameters of the proposed procedure. Various experiments on synthetic as well as real-world networks are performed showing that this process yields improved results in various regimes.

Stan Matwin, Aristides Milios, Paweł Prałat et al.

This survey draws a broad-stroke, panoramic picture of the State of the Art (SoTA) of the research in generative methods for the analysis of social media data. It fills a void, as the existing survey articles are either much narrower in their scope or are dated. We included two important aspects that currently gain importance in mining and modeling social media: dynamics and networks. Social dynamics are important for understanding the spreading of influence or diseases, formation of friendships, the productivity of teams, etc. Networks, on the other hand, may capture various complex relationships providing additional insight and identifying important patterns that would otherwise go unnoticed.

Bogumił Kamiński, Łukasz Kraiński, Paweł Prałat et al.

Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes themselves. If these objectives are achieved, an embedding is a meaningful, understandable, and often compressed representation of a network. Unfortunately, selecting the best embedding is a challenging task and very often requires domain experts. In this paper, we extend the framework for evaluating graph embeddings that was recently introduced by the authors. Now, the framework assigns two scores, local and global, to each embedding that measure the quality of an evaluated embedding for tasks that require good representation of local and, respectively, global properties of the network. The best embedding, if needed, can be selected in an unsupervised way, or the framework can identify a few embeddings that are worth further investigation. The framework is flexible, scalable, and can deal with undirected/directed, weighted/unweighted graphs.

Arash Dehghan-Kooshkghazi, Bogumił Kamiński, Łukasz Kraiński et al.

Graph embedding is a transformation of nodes of a graph into a set of vectors. A~good embedding should capture the graph topology, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes. If these objectives are achieved, an embedding is a meaningful, understandable, compressed representations of a network that can be used for other machine learning tools such as node classification, community detection, or link prediction. The main challenge is that one needs to make sure that embeddings describe the properties of the graphs well. As a result, selecting the best embedding is a challenging task and very often requires domain experts. In this paper, we do a series of extensive experiments with selected graph embedding algorithms, both on real-world networks as well as artificially generated ones. Based on those experiments we formulate two general conclusions. First, if one needs to pick one embedding algorithm before running the experiments, then node2vec is the best choice as it performed best in our tests. Having said that, there is no single winner in all tests and, additionally, most embedding algorithms have hyperparameters that should be tuned and are randomized. Therefore, our main recommendation for practitioners is, if possible, to generate several embeddings for a problem at hand and then use a general framework that provides a tool for an unsupervised graph embedding comparison. This framework (introduced recently in the literature and easily available on GitHub repository) assigns the divergence score to embeddings to help distinguish good ones from bad ones.

Bogumił Kamiński, Paweł Prałat, François Théberge

Most of the current complex networks that are of interest to practitioners possess a certain community structure that plays an important role in understanding the properties of these networks. Moreover, many machine learning algorithms and tools that are developed for complex networks try to take advantage of the existence of communities to improve their performance or speed. As a result, there are many competing algorithms for detecting communities in large networks. Unfortunately, these algorithms are often quite sensitive and so they cannot be fine-tuned for a given, but a constantly changing, real-world network at hand. It is therefore important to test these algorithms for various scenarios that can only be done using synthetic graphs that have built-in community structure, power-law degree distribution, and other typical properties observed in complex networks. The standard and extensively used method for generating artificial networks is the LFR graph generator. Unfortunately, this model has some scalability limitations and it is challenging to analyze it theoretically. Finally, the mixing parameter $μ$, the main parameter of the model guiding the strength of the communities, has a non-obvious interpretation and so can lead to unnaturally-defined networks. In this paper, we provide an alternative random graph model with community structure and power-law distribution for both degrees and community sizes, the Artificial Benchmark for Community Detection (ABCD). We show that the new model solves the three issues identified above and more. The conclusion is that these models produce comparable graphs but ABCD is fast, simple, and can be easily tuned to allow the user to make a smooth transition between the two extremes: pure (independent) communities and random graph with no community structure.

Valérie Poulin, François Théberge

We recently proposed a new ensemble clustering algorithm for graphs (ECG) based on the concept of consensus clustering. We validated our approach by replicating a study comparing graph clustering algorithms over benchmark graphs, showing that ECG outperforms the leading algorithms. In this paper, we extend our comparison by considering a wider range of parameters for the benchmark, generating graphs with different properties. We provide new experimental results showing that the ECG algorithm alleviates the well-known resolution limit issue, and that it leads to better stability of the partitions. We also illustrate how the ensemble obtained with ECG can be used to quantify the presence of community structure in the graph, and to zoom in on the sub-graph most closely associated with seed vertices. Finally, we illustrate further applications of ECG by comparing it to previous results for community detection on weighted graphs, and community-aware anomaly detection.

Valérie Poulin, François Théberge

We propose an ensemble clustering algorithm for graphs (ECG), which is based on the Louvain algorithm and the concept of consensus clustering. We validate our approach by replicating a recently published study comparing graph clustering algorithms over artificial networks, showing that ECG outperforms the leading algorithms from that study. We also illustrate how the ensemble obtained with ECG can be used to quantify the presence of community structure in the graph.

Valérie Poulin, François Théberge

In this paper, we propose a family of graph partition similarity measures that take the topology of the graph into account. These graph-aware measures are alternatives to using set partition similarity measures that are not specifically designed for graph partitions. The two types of measures, graph-aware and set partition measures, are shown to have opposite behaviors with respect to resolution issues and provide complementary information necessary to assess that two graph partitions are similar.