Temporal Heterogeneous Networks (THNs) are evolving networks that characterize many real-world applications such as citation and events networks, recommender systems, and knowledge graphs. Forecasting THNs involves predicting future connections within a network that evolves over time and comprises diverse types of nodes and interactions with varying temporal dynamics. Although some Graph Neural Networks (GNNs) models have been successfully applied to forecast THNs, there is a lack of a general overview of how the message-passing computation could be extended to treat THNs. Moreover, most of the current solutions exhibit pitfalls in their training and evaluation strategies. Hence, in this work, we propose a graph deep learning framework for THN forecasting. Our framework decomposes the computation of a GNN layer into multiple components and introduces two different schemes to update embedding representations for THNs. This design allows the classification of existing solutions into special instances of our framework and highlights their potential limitations. We also extend the set of benchmarks for THNs by introducing two novel high-resolution temporal heterogeneous graph datasets derived from an emerging Web3 platform and a well-established e-commerce website. Overall, we conducted the first massive evaluation of THNs solutions over four temporal heterogeneous network datasets on two different future link prediction tasks using a fair newly introduced evaluation setting that considers the evolving nature of the data. Based on the limitations of existing solutions, we develop a new model that combines working techniques from previous models and leverages a new embedding update scheme. Experiments show the prediction power of our model compared to current solutions for link prediction in temporal graphs. Moreover, the experimental evaluation highlights the strengths and weaknesses of the different solutions and shows the effectiveness of our framework design.

Blockchain technology and cryptocurrencies have garnered considerable attention over the past 15 years. The term Web3 (sometimes Web 3.0) has been coined to define a possible direction for the web based on the use of decentralisation via blockchain. Cryptocurrencies are characterised by high market volatility and susceptibility to substantial crashes, issues that require temporal analysis methodologies able to tackle the high temporal resolution, heterogeneity, and scale of blockchain data. While existing research attempts to analyse crash events, fundamental questions persist regarding the optimal timescale for analysis, differentiation between long-term and short-term trends, and the identification and characterisation of shock events within these decentralised systems. This article addresses these issues by examining cryptocurrencies traded on the Ethereum blockchain, with a spotlight on the crash of the stablecoin TerraUSD (UST) and the currency LUNA designed to stabilise it. Utilising complex network analysis and a multi-layer temporal graph allows the study of the correlations between the layers representing the currencies and system evolution across diverse timescales. The investigation sheds light on the strong interconnections among stablecoins pre-crash and the significant post-crash transformations. We identify anomalous signals before, during, and after the collapse, emphasising their impact on graph structure metrics and user movement across layers. This article is novel in its use of temporal, cross-chain graph analysis to explore a cryptocurrency collapse. It emphasises the importance of temporal analysis for studies on web-derived data. In addition, the methodology shows how graph-based analysis can enhance traditional econometric results. Overall, this research carries implications beyond its field, for example, for regulatory agencies aiming to safeguard users could use multi-layer temporal graphs as part of their suite of analysis tools.

Online social platforms for digital communication necessitate an in-depth understanding of their evolving dynamics, especially after the renewal requests brought about by new paradigms, such as Web3. The dynamics within online social networks (OSNs) are influenced by numerous factors, encompassing user behavior, content generation, platform features, and technological advancements, with triadic closure standing out as a prominent and influential element. In this study, we focus on the temporal aspects of triadic closure and its role in the evolution of OSNs, especially after the advent of the Web3 paradigm. By analyzing networks with timestamped links from diverse platforms based on different architectures, including communication, Web3-based, and trade networks, we developed a comprehensive analytical pipeline to support the study of triadic closure patterns. This pipeline includes an algorithm for the census of time-ordered triads, a vector-based model for representing growing networks (growth triadic profile), the identification of triadic closure rules (TERs), and the evaluation of the speed of the formation of closed triads. Our findings reveal significant variations in the impact of triadic closure across different OSNs, marked by diverse growth triadic profiles and varying formation speeds of closed triads as well as diversity in the predictability of evolutionary patterns based on triads. This study not only enhances the comprehension of triadic closure in the temporal evolution of OSNs but also provides valuable insights to be taken into account for the design and administration of online social platforms.

Understanding and extracting knowledge from temporal networks is crucial to understand their dynamic nature and gain insights into their evolutionary characteristics Existing approaches to network growth often rely on single-parameterized mechanisms, neglecting the diverse and heterogeneous behaviors observed in contemporary techno-social networks. To overcome this limitation, methods based on graph evolution rules (GER) mining have proven promising GERs capture interpretable patterns describing the transformation of a small subgraph into a new subgraph, providing valuable insights into evolutionary behaviors However, current approaches primarily focus on estimating subgraph frequency, neglecting the evaluation of rule significance. To address this gap, we propose a tailored null model integrated into the GERM algorithm, the first and most stable graph evolution rule mining method. Our null model preserves the graph’s static structure while shuffling timestamps, maintaining temporal distribution, and introducing randomness to event sequences By employing a z-score test, we identify statistically significant rules deviating from the null model We evaluate our methodology on three temporal networks representing co-authorship and mutual online message exchanges Our results demonstrate that the introduction of the null model affects the evaluation and interpretation of identified rules, revealing the prevalence of under-represented rules and suggesting that temporal factors and other mechanisms may impede or facilitate evolutionary paths. These findings provide deeper insights into the dynamics and mechanisms driving temporal networks, highlighting the importance of assessing the significance of the evolution patterns in understanding network evolution.

Web3, one of the novel paradigms which may drive the evolution of the future Web, is offering an invaluable volume of data stored in the supporting blockchains. Researchers from different fields such as network science, computational social science and data mining, might benefit from these large collections of temporal and heterogeneous data capturing different kinds of interaction among people and between people and the platforms. In this study we focus on a specific issue related to these modern techno-social systems, i.e. the understanding of the rules driving their growth. To reach this goal, we performed an analysis based on graph evolution rules - GERs - on different networks gathered from Web3 platforms such as Steemit or OpenSea. Graph evolution rules mining is a frequency-based method for evaluating network evolution which does not require any prior growth process for disentangling how networks evolve. By comparing the evolution rules of social network platforms and asset trading services through GER profiles, we observe that some evolution rules are common to all Web3 platforms, regardless of the system specificity. On the other hand, in specific cases, the frequency of graph evolution rules is influenced by the nature of the platform: whereas social and token-transfer networks are characterized by rules which increase network transitivity and reciprocity, NFT trading networks, especially those specialized in a specific type of digital asset, are driven by rules which form trading chains. These findings suggest that the GER approach and the GER profiles are a good starting point to get insights into the evolutionary behavior of a network and to define a classification of graph evolution rules.

Customer segmentation is a central problem in different business processes. In the last few years, it is also becoming important for banking and financial institutions given the ever-growing volume of cashless payments. When dealing with customer segmentation with transactional data, the clustering approach is widely used. In this work, we propose a different modeling approach for customer segmentation based on a graph-based representation. Specifically, we reformulate customer segmentation as a community detection problem on a similarity multi-layer network, where each layer depends on a specific cashless payment method. We introduce a vector-based representation of the cardholders' spending patterns, namely the purchase profile, to build the similarity multi-layer network. The profiles capture how customers allocate their spending capacity among merchant categories through different payment systems. From purchase profiles, we evaluate the similarity of the cardholders in terms of consumption allocation and we infer different similarity graphs based on credit and debit card payments. Different segmentation strategies based on multi-layer community detection methods have been evaluated on a large-scale dataset of credit and debit card transactions of a banking group. Since one of the main goals is verifying the feasibility of graph-based approaches for customer segmentation, we discuss the outcomes of the methods in terms of explainability of the resulting segments. Specifically, methods based on random walks, such as Infomap, return more stable and insightful results than modularity-based ones, in different settings. To sum up, we experiment with community detection algorithms to cope with the customer segmentation problem starting from a large set of credit and debit card transactions. The outcome of the solutions may support recently developed methods for bank risk assessment based on clients' behavior or targeted applications for cashless payment management.

A well-known result in social science states that, although people maintain a large number of social relationships, in practice, their interactions are concentrated mostly on a small portion of their neighbors. According to Dunbar's hypothesis, this phenomenon is due to a limited human cognitive capacity to handle too many social relationships, together with a few time for socializing. These constraints result in an organization of people's ego-network into four or five groups depending on the strength of the interactions, the so called Dunbar's circles. The verification of the Dunbar's hypothesis, the identification of social circles and their characterization are still open questions, although researchers have found evidence of its validity on different social networks, from small offline networks to online social networks, such as Twitter and Facebook. In addition, little is known about the semantic aspects of the circles, i.e. who are the members of each circle. In this paper, we cope with these issues by analyzing a mobile phone graph where people's interactions are expressed by both voice calls and text messages. We firstly compare two methods for the identification of the circles, which rely on the different definitions of strength proposed in literature. Both methods confirm the subdivision of ego-networks into four or five circles, each characterized by a specific interaction strength. Then, we validate the Dunbar's hypothesis and, by leveraging some powerful features of the mobile phone dataset in use, we provide a first semantic characterization of social circles. We show, for instance, that people maintain relationships with the members of the closest circles by combining calls and texts. In addition, by detecting home and work locations of each individual, we highlight that a semantic aspect, such as the role of the alters, impacts on the ego-network circles. In particular, family members and workmates are located in different circles: the former mainly form the closest circle, i.e. the support clique, while the latter are distributed among the outer circles.

The dichotomy between two opposite propensities, exploration and exploitation, characterizes and drives many human behaviors, from decision making to social learning. Recently, this dichotomy has been found also in human mobility where people can be divided into two basic types: returners, those who are very regular in their daily mobility; and explorers, those who are inclined to break out of their daily mobility routine and explore new places. While the former attitude has been widely studied in literature and results in the well-known tendency to frequently visit a few locations (e.g. home and workplace), the latter trait remains an unexplored aspect and deserves further investigation. In this work we focus on the characterization of the places that an individual visits when she is driven by her propensity for exploration, i.e. non-routine places which are outside her usual daily mobility patterns. To this end, we mine an anonymized mobile phone dataset which integrates call, text and data activities of about one million subscribers in Milan, to detect and characterize the non-routine places. Moreover, we complement it with Foursquare venues along with their category to semantically characterize the reasons driving the choice of the places to explore. The analysis of the non-routine places and the mobility patterns during the exploration phase brings to light some interesting findings: i) to a greater or lesser extent, all individuals are explorers since they visit a significant number of non-routine places; ii) due to the exceptionality of a visit, non-routine places are farther from home and workplace than frequently visited places; iii) we are explorers in our leisure time; iv) we get to a non-routine place leaving our home, then we return home later; and v) in Milan, shopping, in particular at fashion and clothing stores, is the main interest behind the need to explore non-routine places.

The rising attention to the spreading of fake news and unsubstantiated rumors on online social media and the pivotal role played by confirmation bias led researchers to investigate different aspects of the phenomenon. Experimental evidence shows that confirmatory information gets accepted even if containing deliberately false claims, while dissenting information is mainly ignored or might even increase group polarization. It seems reasonable that, to address misinformation problem properly, we have to understand the main determinants behind content consumption and the emergence of narratives on online social media. In this paper we address such a challenge by focusing on the discussion around the Italian Constitutional Referendum by conducting a quantitative, cross-platform analysis on both Facebook public pages and Twitter accounts. We observe the spontaneous emergence of well-separated communities on both platforms. Such a segregation is completely spontaneous, since no contents categorization was performed a priori. By exploring the dynamics behind the discussion, we find that users tend to restrict their attention to a specific set of Facebook pages/Twitter accounts. Finally, taking advantage of automatic topic extraction and sentiment analysis techniques, we are able to identify the most controversial topics inside and across both platforms. Thus, we measure the distance between how a certain topic is presented in the posts/tweets and the related users' emotional response. Our results provide interesting insights for the understanding of the evolution of the core narratives behind different echo chambers and for the early detection of massive viral phenomena around false claims.