Complex Networks & Their Applications XII

We present a novel approach for computing a variant of eigenvector centrality for multilayer networks with inter-layer constraints on node importance. Specifically, we consider a multilayer network defined by multiple edge-weighted, potentially directed, graphs over the same set of nodes with each graph representing one layer of the network and no inter-layer edges. As in the standard eigenvector centrality construction, the importance of each node in a given layer is based on the weighted sum of the importance of adjacent nodes in that same layer. Unlike standard eigenvector centrality, we assume that the adjacency relationship and the importance of adjacent nodes may be based on distinct layers. Importantly, this type of centrality constraint is only partially supported by existing frameworks for multilayer eigenvector centrality that use edges between nodes in different layers to capture inter-layer dependencies. For our model, constrained, layer-specific eigenvector centrality values are defined by a system of independent eigenvalue problems and dependent pseudo-eigenvalue problems, whose solution can be efficiently realized using an interleaved power iteration algorithm. An R package implementing this method along with example vignettes is available at https://hrfrost.host.dartmouth.edu/CMLC/.

Social media and online data pose challenges in information mining, network analysis, opinion mining, and combating misinformation. However, no previous work has been able to apply knowledge graph (KG) and contextual focal structure analysis (CFSA) on multisource data to study situational awareness in public discussion and establish information propagation such as the Belt and Road Initiative (BRI). This research uses multisource data, a knowledge graph model, and a CFSA, which we term KG-CFSA. We extract entities and topics from documents and correlate them with third-party data sources such as Wikidata and Diffbot. We establish relationships using a Cartesian product merge function to develop a graph model. The merge function uses search algorithms and pairwise matching to establish relationships. The model is divided into three instances: document-entity, document-document, and topic-topic. For the document-document instance, we used topics and entities and topic overlaps to establish a relationship while we used co-occurrence for the topic-topic instance. The study identified 276 focal sets; the top two focal sets are focal sets 275 and 276. The most important focal content comes from an Indonesian Twitter user, who operates a personal blog on opinion and story covers. The findings highlight the effectiveness of multisource KG-CFSA in establishing context for a social network analysis.

The social networks that interconnect groups of people are often “multi-layered"– comprised of a variety of relationships and interaction types. Although researchers increasingly acknowledge the presence of multiple layers and even measure them separately, little is known about whether and how different layers function differently. We conducted a field experiment in twelve villages in rural Uganda that measured real multi-layer social networks and then tracked how each layer was used to discuss new information about refugees. A majority of respondents discussed refugees with someone to whom they were connected in the social network. The connections came from all four layers, though the layer indicating regular homestead visits was used most frequently. People did not discuss refugees with every one of their network neighbors; homophily in views, homophily in level of interest, and the alter’s interest in the topic best distinguish links that were used from those that were not.

The information diffusion on social media shows no signs of stopping, and for many marketers, having influencers spread information has become a common advertising method. However, the use of social media has diversified, and the intentions behind following other users can vary greatly. Correspondingly, there are several patterns of communication on social media, and based on the density and symmetry of these communications, it is believed that one can infer the intentions of the users who follow others. In this study, we consider retweets, replies, and mentions, three types of communication in the context of follower relationships on Twitter, as a multi-layer graph. We propose multi-layer motifs by categorizing the edges, and we associate motif patterns with follower intentions to infer users’ follow intents. Through experiments using real data, we confirm that our proposed multi-layer motifs can extract link patterns leading to follow intentions that would not be detectable using traditional single-layer motifs.

Finding dense subgraphs of a large network is a fundamental problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications over the last five decades. However, most existing studies have focused on graphs with a single type of connection. In applications such as biological, social, and transportation networks, interactions between objects span multiple aspects, yielding multiplex graphs. Existing dense subgraph mining methods in multiplex graphs consider the same importance for different types of connections, while in real-world applications, one relation type can be noisy, insignificant, or irrelevant. Moreover, they are limited to the edge-density measure, unable to change the emphasis on larger/smaller degrees depending on the application. To this end, we define a new family of dense subgraph objectives, parametrized by two variables p and $$\beta $$ β , that can (1) consider different importance weights for each relation type, and (2) change the emphasis on the larger/smaller degrees, depending on the application. Due to the NP-hardness of this problem, we first extend the FirmCore, k-core counterpart in multiplex graphs, to layer-weighted multiplex graphs, and based on it, we propose two polynomial-time approximation algorithms for the generalized densest subgraph problem, when $$p \ge 1$$ p ≥ 1 and the general case. Our experimental results show the importance of considering different weights for different relation types and the effectiveness and efficiency of our algorithms.

Recent advances have focused mainly on the resilience of the monoplex network in attacks targeting random nodes or links, as well as the robustness of the network against cascading attacks. However, very little research has been done to investigate the robustness of nodes in multiplex networks against targeted attacks. In this paper, we first propose a new measure, MultiCoreRank, to calculate the global influence of nodes in a multiplex network. The measure models the influence propagation on the core lattice of a multiplex network after the core decomposition. Then, to study how the structural features can affect the influence robustness of nodes, we compare the dynamics of node influence on three types of multiplex networks: assortative, neutral, and disassortative, where the assortativity is measured by the correlation coefficient of the degrees of nodes across different layers. We found that assortative networks have higher resilience against attack than neutral and disassortative networks. The structure of disassortative networks tends to break down quicker under attack.

In this work, we propose a novel representation of complex networks, which is compact and enables very efficient network analysis. Multi-relational networks capture complex data relationships and have a wide range of applications. As they get to be used with ever larger quantities of data, it is crucial to find efficient ways to represent and analyse them. This paper introduces the concept of Prime Adjacency Matrices (PAMs), which utilize prime numbers, to represent the relations of the network. Due to the Fundamental Theorem of Arithmetic, this allows for a lossless, compact representation of a complete multi-relational graph, using a single adjacency matrix. Moreover, this representation enables the fast computation of multi-hop adjacency matrices, which can be useful for a variety of downstream tasks. We illustrate the benefits of using the proposed approach through various network analysis tasks.

Finding the $$k$$ k -median in a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. While known to be computationally challenging (NP-hard) several approximation algorithms have been proposed, most with high-order polynomial-time complexity. However, the graph topology of complex networks with heavy-tailed degree distributions present characteristics that can be exploited to yield custom-tailored algorithms. We compare eight algorithms specifically designed for complex networks and evaluate their performance based on accuracy and efficiency for problems of varying sizes and application areas. Rather than relying on a small number of problems, we conduct over 16,000 experiments covering a wide range of network sizes and $$k$$ k -median values. While individual results vary, a few methods provide consistently good results. We draw general conclusions about how algorithms perform in practice and provide general guidelines for solutions.

In the study of the behavior of centrality measures with respect to network modifications, score monotonicity means that adding an arc increases the centrality score of the target of the arc; rank monotonicity means that adding an arc improves the importance of the target of the arc relative to the remaining nodes. It is known [7, 8] that score and rank monotonicity hold in directed graphs for almost all the classical centrality measures. In undirected graphs one expects that the corresponding properties (where both endpoints of the new edge enjoy the increase in score/rank) hold when adding a new edge. However, recent results [6] have shown that in undirected networks this is not true: for many centrality measures, it is possible to find situations where adding an edge reduces the rank of one of its two endpoints. In this paper we introduce a weaker condition for undirected networks, semi-monotonicity, in which just one of the endpoints of a new edge is required to enjoy score or rank monotonicity. We show that this condition is satisfied by closeness and betweenness centrality, and that harmonic centrality satisfies it in an even stronger sense.

Rewiring of molecular interactions under different conditions causes different phenotypic responses. Differential Network Analysis (also indicated as DNA) aims to investigate the rewiring of gene and protein networks. DNA algorithms combine statistical learning and graph theory to explore the changes in the interaction patterns starting from experimental observation. Despite there exist many methods to model rewiring in networks, we propose to use age and gender factors to guide rewiring algorithms. We present a novel differential network analysis method that consider the differential expression of genes by means of sex and gender attributes. We hypothesise that the expression of genes may be represented by using a non-gaussian process. We quantify changes in non-parametric correlations between gene pairs and changes in expression levels for individual genes. We apply our method to identify the differential networks between males and females in public expression datasets related to mellitus diabetes in liver tissue. Results show that this method can find biologically relevant differential networks.

Player synergies are a salient feature of team sports. In the team game of cricket, player synergies may be reflected in batting partnerships. Batting partnerships have been analysed extensively. In this paper, we introduce and precisely define bowling partnerships. We explain their importance, and analyse ball-by-ball data from three formats of the game: 2,034 one-day international matches, 634 Test matches and 1,432 Twenty-20 international matches, in order to find such bowling partnerships (“bowlerships”). We find that bowlerships exist. We construct bowlership networks based on these pairwise synergies. We assert that these bowlership networks can be analysed for team selection before a match, and making bowling changes during the match. We present Algorithm that selects a team based on bowlerships.

We present here a critical correction of the heuristic algorithm MinimalFlipSet in [8] for the NP-hard problem of finding a minimum size subset of edges in an unbalanced signed graph G whose ‘+’/‘ $$-$$ - ’edge-labels can be flipped to balance G.

Numerous research efforts have centered on identifying the most influential players in networked social systems. This problem is immensely crucial in the research of complex networks. Most existing techniques either model social dynamics on static networks only and ignore the underlying time-serial nature or model the social interactions as temporal edges without considering the influential relationship between them. In this paper, we propose a novel perspective of modeling social interaction data as the graph on event sequence, as well as the Soft K-Shell algorithm that analyzes not only the network’s local and global structural aspects, but also the underlying spreading dynamics. The extensive experiments validated the efficiency and feasibility of our method in various social networks from real world data. To the best of our knowledge, this work is the first of its kind.

We study a distributed optimization problem which uses an undirected, unweighted hypergraph communication from a dynamical system viewpoint. The stability analysis of the dynamical system is conducted with the use of approaches relevant to non linear decentralized control where we also use the hypergraph Laplacian matrix for the decomposition of the dynamical system. Additionally, we present a Laplacian matrix for the case of a directed and weighted hypergraph and we show how this Laplacian matrix is decomposed for the stability analysis of the distributed optimization problem with the specific directed and weighted hypergraph communication structure.

We analyze a recipe stream created on a social media site dedicated to sharing homemade recipes in terms of a temporal hypergraph over a set of ingredients. Unlike the previous studies for transition analysis of temporal higher-order networks, we propose a novel analysis method based on topics and projected graphs to effectively characterize the structural transitions of the temporal hypergraph immediately before and after the occurrences of hyperedges. First, we propose a probabilistic model to extract the topics of hyperedges on the basis of the trends and seasonality of recipes, and present its Bayesian inference method. Next, we propose employing the projected graph of the entire hypergraph, and examining whether each of its main edges is present or not in the temporal hypergraph, both immediately before and after the occurrences of hyperedges for each topic. Using real data of a Japanese recipe sharing site, we empirically demonstrate the effectiveness of the proposed analysis method, and reveal several interesting properties in the evolution of Japanese homemade recipes.

For the past decade, immigration has taken center stage in the Italian public discourse, providing fertile ground for far-right parties to cultivate fear and ultimately nurturing sentiments of animosity and racism. The Russian invasion of Ukraine introduced a unique narrative as European white refugees sought shelter, diverging from the conventional refugee archetype ingrained within the Italian collective consciousness. Employing the tools of Network Science, this study aims to dissect whether the Russo-Ukrainian conflict in 2022 has triggered shifts in Italians’ viewpoints toward refugees. Specifically, we delve into whether the proximity of the conflict and the ethnic parallels between refugees and Italians have prompted changes in attitudes toward refugees. Through an exploration of the intricate interplay between international conflict, social network dynamics, and evolving sentiments, this research contributes to understanding the intricate dynamics that underlie shifts in public sentiment regarding migration.

Homophily is the social network phenomenon whereby sim-ilar individuals have a greater propensity to form ties. Motivated by concerns of risky-prescribing among older patients in the United States, we developed exponential random graph models to estimate the effect of homophily of risky prescribing net of other physician characteristics and network features in a complex network. We also developed novel network measures and associated non-parametric statistical tests that allow for greater homophily in specific triadic confgurations (“super-homophily"). Using a shared-patient network of all physicians who treated patients residing in the US state of Ohio in 2014, we found statistical evidence of physician homophily (both in level and heterogeneity across regions) and triadic homophily on risky prescribing. Our findings may explain the emergence of prescriber communities, motivate group-level prescriber interventions to directly reduce risky-prescribing, and motivate interventions that reshape physician shared-patient networks to indirectly reduce risky-prescribing.

The expansion of coordinating communities via focal information spreaders on online social networks has attained much-needed attention over the past few years. Several methods have been applied to investigate the influential communities of information spreaders in static social networks. However, investigating static social networks does not entirely reflect the activities and the dynamics of evolving communities over time. Researchers have applied advanced operational methods such as game theory and evolving complex graphs to describe the change in the regular communities in dynamic social networks. Yet, these methods need the ability to describe the focal information spreaders in dynamic social networks. For this purpose, in this research, we propose a systematic approach to measure the influence of focal information spreaders and track their evolution in social networks over time. This novel approach combines the focal structure analysis model and the adaptation algorithm to identify the coordinating communities of information spreaders in social networks and illustrate their development in the network over time, respectively. We evaluate our findings using a real-world dynamic Twitter network collected from the Saudi Arabian women’s Right to Drive campaign coordination in 2013. The outcomes of this approach allow observing, predicting, tracking, and measuring the coordination among the focal information spreaders over time. Correspondingly, this approach investigates and illustrates when the information spreaders will escalate their activities, where they concentrate their influence in the network, and what coordinating communities of spreaders are more tactical than others in the network.

Solving maze puzzles is a recreational activity with longstanding roots in human civilization dating back several thousands of years. This paper considers the problem of automated maze generation for a more recent class of maze puzzles, the logic maze, popularized by Abbott in 1990. Although there are several distinct types of logic mazes, we present a single unified generation strategy based on a state graph representation. We capture desirable features of a maze in an objective function that consists of several network science metrics on the state graph and the original maze. We then optimize this objective function through the use of local state space search and obtain high-quality results.

Exploring and comprehending the culinary heritage of a nation holds a captivating allure. It offers insights into the structure and qualities of its cuisine. The endeavor becomes more accessible with the availability of a well-organized dataset. In this paper, we present the introduction of INDoRI (Indian Dataset of Recipes and Ingredients), a compilation drawn from seven distinct online platforms, representing 18 regions within the Indian subcontinent. This comprehensive geographical span ensures a portrayal of the rich variety within culinary practices. Furthermore, we introduce a unique collection of stop words, referred to as ISW (Ingredient Stop Words), manually tuned for the culinary domain. We assess the validity of ISW in the context of global cuisines beyond Indian culinary tradition. Subsequently, an ingredient network (InN) is constructed, highlighting interconnections among ingredients sourced from different recipes. We delve into both the defining attributes of INDoRI and the communal dimensions of InN. Additionally, we outline the potential applications that can be developed leveraging this dataset. Addressing one of the applications, we demonstrated a research problem on InN with a simple weighted community detection algorithm. Furthermore, we provide a comparative analysis of the results obtained with this algorithm against those generated by two baselines.

This paper presents an approach to enhancing neonatal care through the application of artificial intelligence (AI). Utilizing network-oriented modeling methodologies, the study aims to develop a network model to improve outcomes in neonatal respiratory support. The introduction sets the stage by outlining the significance of neonatal respiratory support and the challenges faced in this domain. The literature review delves into the existing body of work, highlighting the gaps and the need for a network modeling approach. The network-oriented modeling approach provides a robust framework that captures various states, such as world states, doctors’ mental states, and AI coach states, facilitating a comprehensive understanding of the complex interactions in neonatal respiratory support. Through Matlab simulations, the study investigates multiple scenarios, from optimal conditions to deviations from standard protocol. The main contribution focuses on the introduction of an AI coach, which serves as a real-time intervention mechanism to fill in the doctor's knowledge gaps. The research serves as a seminal work in the intersection of artificial intelligence and healthcare, demonstrating the potential of network-oriented modeling in improving patient outcomes and streamlining healthcare protocols.

Network alignment is a commonly encountered problem in many applications, where the objective is to match the nodes in different networks such that the incident edges of matched nodes are consistent. Gromov-Wasserstein (GW) distance, based on optimal transport, has been shown to be useful in assessing the topological (dis)similarity between two networks, as well as network alignment. In many practical applications of network alignment, there may be “seed” nodes with known matchings. However, GW distance assumes that no matchings are known. Here, we propose Generalized GW-based Network Alignment(GGWNA), with a loss/distance function that reflects the topological similarity of known matching nodes. We test the resulting framework using a large collection of real-world social networks. Our results show that, as compared to state-of-the-art network alignment algorithms, GGWNA can deliver more accurate alignment when the seed size is small. We also perform systematic simulation studies to characterize the performance of GGWNA as a function of seed size and noise, and find that GGWNA is more robust to noise as compared to competing algorithms. The implementation of GGWNA and the Supplementary Material can be found in https://github.com/Meng-zhen-Li/Generalized-GW.git .

Navigation plays a pivotal role in the operation of real-world complex networks. In this paper, we delve into the extensive realm of the ’store and forward’ principle, comprising two fundamental components: the addressing scheme for network nodes and the routing function responsible for establishing paths between network endpoints. Particularly, we show that the hyperbolic geometry of complex networks can be used to greatly improve the orderliness of navigation patterns in complex networks implementing the store and forward principle. By using entropy-based measures applied on the forwarding tables we provide a formal assessment for the orderliness which can also be used to estimate the memory requirements of navigation directly at individual nodes and in the whole network.

Re-globalization is a currently understudied topic and previous research focuses mostly on theoretical discussion of the problem. Empirical re-globalization related research suggests that re-globalization in terms of structural changes in financial network did not start recently, but was already observed after global financial crisis. It might have been further strengthened by pandemic and recent geopolitical tensions, but these tendencies have not been tested empirically. Among possible scenarios of re-globalization, most likely are discussed to be geographical regionalization or ally-based bipolar regionalization. Therefore, we aim to test these scenarios empirically. Using 5-layer multiplex financial network data of 2009–2020 from 234 countries, we found that multiplex financial network appears to be already highly regionalized, but regionalization and globalization appears to be not contradictory processes. Geographical regionalization did not increase in terms of shifting interregional investment to intraregional territory as interregional investment network density and value also increased as well as intraregional. The world appears to have become bipolarly ally-regionalized with 2 main communities - US & Europe vs. China. However, it is worth noting that Europe’s role is still unclear as not all European countries belong to the same identified cluster. Future research could aim to explore in detail what are the main factors affecting ally-familiarity based region formation.

Network backbone extraction techniques reduce the size of networks while trying to preserve their topological features. The literature reports numerous backbone extraction algorithms. However, there are few works about their ability to highlight the network community structure, although it is an essential property of many real-world networks. This paper presents an experimental comparison of six popular backbone extraction techniques in a typical modular network (Disparity Filter, Locally Adaptive Network Sparsification (LANS), Doubly Stochastic, High Salience Skeleton, Metric Backbone, globally and locally adaptive network backbone (GLANB)). Investigations on a modular network representing the American elementary school system reveal valuable insights into how each technique influences the network’s underlying community structure. Disparity and LANS backbones exhibit multi-component structures. The Doubly Stochastic backbone maintains transitivity. Moreover, it retains a significant proportion of inter-community edges and maintains a balanced ratio of intra and inter-community links. Other methods prioritize intra-community edges. The GLANB method excels in network filtering and accurate representation of the community structure. By shedding light on these nuanced aspects of backbone extraction techniques, our study contributes to a better understanding of their effects on network topology, enabling their practical use in real-world scenarios.

Identifying the influential spreaders in complex networks has emerged as an important research challenge to control the spread of (mis)information or infectious diseases. Researchers have proposed many centrality measures to identify the influential nodes (spreaders) in the past few years. Still, most of them have not considered the importance of the edges in unweighted networks. To address this issue, we propose a novel centrality measure to identify the spreading ability of the Influential Spreaders using the Potential Edge Weight method (IS-PEW). Considering the connectivity structure, the ability of information exchange, and the importance of neighbouring nodes, we measure the potential edge weight. The ranking similarity of spreaders identified by IS-PEW and the baseline centrality methods are compared with the Susceptible-Infectious-Recovered (SIR) epidemic simulator using Kendall’s rank correlation. The spreading ability of the top-ranking spreaders is also compared for five different percentages of top-ranking node sets using six different real networks.

Understanding of real systems relies on the identification of its central elements. Over the years, a large number of centrality measures have been proposed to assess the importance of nodes in complex networks. However, most real networks are incomplete and contain incorrect data, resulting in a high sensitivity of centrality indices. In this paper, we examine the robustness of centrality to the presence of errors in the network structure. Our experiments are performed on weighted and unweighted real-world networks ranging from the criminal network to the trade food network. As a result, we discuss a sensitivity of centrality measures to different data imputation techniques.

This paper presents ATEM, a novel framework for studying topic evolution in scientific archives. ATEM employs dynamic topic modeling and dynamic graph embedding to explore the dynamics of content and citations within a scientific corpus. ATEM explores a new notion of citation context that uncovers emerging topics by analyzing the dynamics of citation links between evolving topics. Our experiments demonstrate that ATEM can efficiently detect emerging cross-disciplinary topics within the DBLP archive of over five million computer science articles.

The transparent nature of public blockchain systems allows for unprecedented access to economic community data. Examples of such communities are the fungible token networks created by the ERC-20 standard on the Ethereum protocol. In this paper we study ERC-20 token networks, where nodes represent users and edges represent fungible token transfers between them. We focus our analysis on the top 100 largest networks, including a total of about 160 million edges and 60 million nodes. After a global analysis of the size and temporal evolution of such networks, we define and study seven features describing their main topological properties. In an attempt to characterize the networks by their topologies, we use the introduced features to cluster the networks together. To evaluate our results, we manually classify each network depending on the application domain of the corresponding contract and measure the homogeneity of the obtained clusterings. Overall, the results appear to indicate a lack of relationship between the scope of a contract and the topological features of the induced networks.

Understanding the properties of anonymity networks such as the Invisible Internet Project (Garlic router) and Tor (Onion router) is critical for the future of cybersecurity, cyberwarfare and Internet freedom. In this paper, we theoretically model the Invisible Internet and provide the preliminary components for developing a theoretical lens that can be used to address its open questions. Additionally, this work lays the theoretical foundation for studying I2P’s key network properties such as resilience, anonymity and minimum attackers/routers ratio to exploit the network. The model was validated against a simulated I2P network.

The world economy is experiencing the novel adoption of distributed currencies that are free from the control of central banks. Distributed currencies suffer from extreme volatility, and this can lead to catastrophic implications during future economic crisis. Understanding the dynamics of this new type of currencies is vital for empowering supervisory bodies to behave proactively as well-informed planners rather than reactively as incident responders. Bitcoin, the first and dominant distributed cryptocurrency, is still notoriously vague, especially for a financial instrument with market value exceeding $1 trillion. Modeling the Bitcoin Overlay Network poses a number of important theoretical and methodological challenges. This drastically undermines the ability to predict key features such as network’s resilience. In this work, we developed Evolutionary Random Graph, a theoretical model that describes the network of bitcoin miners. The correctness of this model has been validated using real and simulated bitcoin data.

We propose an original density estimator built from a cloud of points $$ \mathcal {X}^{}_{ } \subset \mathbb R ^d$$ X ⊂ R d . To do this, we consider geometric graphs $$\mathcal {G}(\mathcal {X}^{}_{ }, \ r)$$ G ( X , r ) on the cloud. These graphs depend on a radius r. By varying the radius, we see the emergence of large components around certain critical radii, which is the phenomenon of continuum percolation. Percolation allows us to have both a local view of the data (through local constraints on the radius r) and a global one (the emergence of macro-structures). With this tool, we address the problem of galaxy filament extraction. The density estimator gives us a relevant graph on galaxies. With an algorithm sharing the ideas of the Fréchet mean, we extract a subgraph from this graph, the galaxy filaments.

We suggest an approach to the shape DNA of data based on a number of metric invariants introduced by Grove and Markvorsen that encode its essential global geometry of the given structure. First experiments on real life networks and on natural images are given to demonstrate the feasibility of this approach. Even this incipient test clearly demonstrate the efficiency of the proposed invariants in the classification and understanding of stochastic textures as opposed to man-made ones.

Defining accurate models for real-world social networks is essential across various research fields including sociology, epidemiology, and marketing. Such models serve as indispensable tools to capture the dynamics of phenomena ranging from disease spread to rumor dissemination, encapsulating intricate patterns of interactions among individuals within a population. To this end, a latent geometry and/or hidden degrees can be used to obtain networks that are small-world, highly clustered, and have a scale-free degree distributions.This study aims to integrate group mixing within the framework of latent geometry models. Our approach is based on conceptualizing a graph with a planted partition as the union of different mono- and bipartite subgraphs, for intra- and inter-block edges, respectively. We highlight that the hidden degree – the analogous of the radial coordinate in purely geometric hyperbolic models – must be replaced by a hidden fitness, and that all latent features must be assigned to the nodes once and for all, rather than once for each subgraph.Through extensive simulations, we show that the proposed model generates networks with a unique combination of features, that cannot be obtained with standard geometric models nor with maximum entropy degree-corrected block models.

The emergence of a complex economic system is an interesting issue that has been addressed by many economists. This paper suggests that the processes that develop network formation within economic agents could be assimilated with the same procedures used by neurons in the human brain. Furthermore, the present paper presents a heuristic proof that suggests that the previous assumption is possible since the complex economic system, as a biological one, is a self-organization that has the same properties as any ergodic random dynamical chaotically system. In particular, it has been found that both systems possess a Markov Blanket or a Markov Decision Process, economically speaking. Furthermore, the demonstration in the present paper is restricted to how coupled dynamical systems organize themselves over time. In conclusion, the present work focuses on a simple but key aspect of complex economic system self-organization, providing a behavior metaphor in a different time-scale.

Using network analysis, this paper analyzes export surges of commodities from U.S. states to examine their connectedness along industrial and inter-state ties, and how they propagate through the trade network along these ties. Our findings suggest that export surges tend to be highly skewed towards particular goods, that these surges spread according to higher-order structural dependencies in the supply chain, and that increases of export surges were defined by preferential attachment.

In economy, a major issue is the potential lack of liquidity for settling the debts generated by payment delays among companies. Since this lack may trigger cascading failures, we analyse the interconnection of debts. Settling debts means lowering the systemic risks. We analyse the data of a large economic network from an Italian invoice operator on a one-year span. We compare different methods to detect structures or communities that could be helpful for debt netting algorithms. The structure of such networks is not currently well known. We give hints on how to sort and identify the type of B2B invoice graphs. In particular, we address the possibility to identify relevant communities in such networks.

Despite its unconventional origins, Bitcoin has emerged as the predominant cryptocurrency in the modern era and has entered mainstream discourse. Transactions in the Bitcoin ecosystem are different from those of ordinary finance, because of the way in which the cryptocurrency was designed. A proper structural understanding, and model, of Bitcoin transaction flows has largely been lacking. In this paper, we propose a model (based on directed acyclic graphs) that enables us to conduct structural analysis of networked Bitcoin transaction flows. Our model includes ‘activity’ measures, analogous to liquidity measures in ordinary financial markets, that are inspired by intuitions from thermodynamics. We apply the model and the activity measures to conduct structural analysis on a large transaction dataset from the early days of Bitcoin (first five years) when it was most in flux, and its future was still uncertain. Among other findings, our structural analysis suggests that the activity measure is correlated with major news events that affected Bitcoin. Our model could potentially be used to study other cryptocurrencies for which transaction data is available, as well as more recent Bitcoin transaction data.

Financial networks can be constructed using statistical dependencies found within price series of speculative assets. Inference generally involves multivariate predictive modelling to reveal causal and correlational structures within the time series data, but difficulties frequently arise due to the highly unstable nature of these markets. The complex interplay of social and economic factors results in erratic behaviour, producing data that rarely adheres to theoretical assumptions. It remains unclear if these violations impact the constructed networks, and if so, whether robust alternatives produce more informative results. This study introduces the Rank-Vector-Autoregression model, demonstrating its capacity to produce robust cryptocurrency networks aligned with economic rationale. Our rank method achieves superior classification compared to the standard approach for various types of simulated data, particularly when including adversarial abnormalities. When applied to a dataset of 261 cryptocurrency return series, our method produces a network containing fewer, but more strongly market-correlated links, and increased connectivity within the mean-reversion subset. Applying our method to the squared deviations produces a comparatively dense volatility network, suggesting that significant price coupling occurs in higher order moments. Our results demonstrate the use of a robust and scalable technique for obtaining accurate causality networks in finance.