Detecting Core-Periphery Structures by Surprise

Detecting the presence of mesoscale structures in complex networks is of primary importance. This is especially true for financial networks, whose structural organization deeply affects their resilience to events like default cascades, shocks propagation, etc. Several methods have been proposed, so far, to detect communities, i.e. groups of nodes whose connectivity is significantly large. Communities, however do not represent the only kind of mesoscale structures characterizing real-world networks: other examples are provided by bow-tie structures, core-periphery structures and bipartite structures. Here we propose a novel method to detect statistically-signifcant bimodular structures, i.e. either bipartite or core-periphery ones. It is based on a modification of the surprise, recently proposed for detecting communities. Our variant allows for bimodular nodes partitions to be revealed, by letting links to be placed either 1) within the core part and between the core and the periphery parts or 2) just between the (empty) layers of a bipartite network. From a technical point of view, this is achieved by employing a multinomial hypergeometric distribution instead of the traditional (binomial) hypergeometric one; as in the latter case, this allows a p-value to be assigned to any given (bi)partition of the nodes. To illustrate the performance of our method, we report the results of its application to several real-world networks, including social, economic and financial ones.Comment: 11 pages, 10 figures. Python code freely available at https://github.com/jeroenvldj/bimodular_surpris

Finding core-periphery structures with node influences

Detecting core-periphery structures is one of the outstanding issues in complex network analysis. Various algorithms can identify core nodes and periphery nodes. Recent advances found that many networks from real-world data can be better modeled with multiple pairs of core-periphery nodes. In this study, we propose to use an influence propagation process to detect multiple pairs of core-periphery nodes. In this framework, we assume each node can emit a certain amount of influence and propagate it through the network. Then we identify nodes with large influences as core nodes, and we utilize a maximum influence chain to construct a node-pairing network to determine core-periphery pairs. This approach can take node interactions into consideration and can reduce noises in finding pairs. Experiments on randomly generated networks and real-world networks confirm the efficiency and accuracy of our algorithm

Bitcoin Transaction Networks: an overview of recent results

Cryptocurrencies are distributed systems that allow exchanges of native (and non-) tokens among participants. The complete historical bookkeeping and its wide availability opens up an unprecedented possibility, i.e. that of understanding the evolution of their network structure while gaining useful insight on the relationships between user' behaviour and cryptocurrency pricing in exchange markets. In this contribution we review some of the most recent results concerning the structural properties of Bitcoin Transaction Networks, a generic name referring to a set of different constructs: the Bitcoin Address Network, the Bitcoin User Network and the Bitcoin Lightning Network. The picture that emerges is that of system growing over time, which becomes increasingly sparse and whose mesoscopic structural organization is characterised by the presence of an increasingly significant core-periphery structure. Such a peculiar topology is matched by a highly uneven distribution of bitcoins, a result suggesting that Bitcoin is becoming an increasingly centralized system at different levels.Comment: 15 pages, 7 figure

An instinct for detection: psychological perspectives on CCTV surveillance

The aim of this article is to inform and stimulate a proactive, multidisciplinary approach to research and development in surveillance-based detective work. In this article we review some of the key psychological issues and phenomena that practitioners should be aware of. We look at how human performance can be explained with reference to our biological and evolutionary legacy. We show how critical viewing conditions can be in determining whether observers detect or overlook criminal activity in video material. We examine situations where performance can be surprisingly poor, and cover situations where, even once confronted with evidence of these detection deficits, observers still underestimate their susceptibility to them. Finally we explain why the emergence of these relatively recent research themes presents an opportunity for police and law enforcement agencies to set a new, multidisciplinary research agenda focused on relevant and pressing issues of national and international importance

Lightning network: a second path towards centralisation of the Bitcoin economy

The Bitcoin Lightning Network (BLN), a so-called "second layer" payment protocol, was launched in 2018 to scale up the number of transactions between Bitcoin owners. In this paper, we analyse the structure of the BLN over a period of 18 months, ranging from 12th January 2018 to 17th July 2019. Here, we consider three representations of the BLN: the daily snapshot one, the weekly snapshot one and the daily-block snapshot one. By studying the topological properties of the three representations above, we find that the total volume of transacted bitcoins approximately grows as the square of the network size; however, despite the huge activity characterising the BLN, the bitcoins distribution is very unequal: the average Gini coefficient of the node strengths (computed across the entire history of the Bitcoin Lightning Network) is, in fact, ~0.88 causing the 10% (50%) of the nodes to hold the 80% (99%) of the bitcoins at stake in the BLN (on average, across the entire period). This concentration brings up the question of which minimalist network model allows us to explain the network topological structure. Like for other economic systems, we hypothesise that local properties of nodes, like the degree, ultimately determine part of its characteristics. Therefore, we have tested the goodness of the Undirected Binary Configuration Model (UBCM) in reproducing the structural features of the BLN: the UBCM recovers the disassortative and the hierarchical character of the BLN but underestimates the centrality of nodes; this suggests that the BLN is becoming an increasingly centralised network, more and more compatible with a core-periphery structure. Further inspection of the resilience of the BLN shows that removing hubs leads to the collapse of the network into many components, an evidence suggesting that this network may be a target for the so-called split attacks.Comment: 11 pages, 7 figure

The weighted Bitcoin Lightning Network

The Bitcoin Lightning Network (BLN) was launched in 2018 to scale up the number of transactions between Bitcoin owners. Although several contributions concerning the analysis of the BLN binary structure have recently appeared in the literature, the properties of its weighted counterpart are still largely unknown. The present contribution aims at filling this gap, by considering the Bitcoin Lightning Network over a period of 18 months, ranging from 12th January 2018 to 17th July 2019, and focusing on its weighted, undirected, daily snapshot representation - each weight representing the total capacity of the channels the two involved nodes have established on a given temporal snapshot. As the study of the BLN weighted structural properties reveals, it is becoming increasingly ‘centralized’ at different levels, just as its binary counterpart: (1) the Nakamoto coefficient shows that the percentage of nodes whose degrees/strengths ‘enclose’ the 51% of the total number of links/total weight is rapidly decreasing; (2) the Gini coefficient confirms that several weighted centrality measures are becoming increasingly unevenly distributed; (3) the weighted BLN topology is becoming increasingly compatible with a core–periphery structure, with the largest nodes ‘by strength’ constituting the core of such a network, whose size keeps shrinking as the BLN evolves. Further inspection of the resilience of the weighted BLN shows that removing such hubs leads to the network fragmentation into many components, an evidence indicating potential security threats — as the ones represented by the so called ‘split attacks’

Hierarchical Models for Relational Event Sequences

Interaction within small groups can often be represented as a sequence of events, where each event involves a sender and a recipient. Recent methods for modeling network data in continuous time model the rate at which individuals interact conditioned on the previous history of events as well as actor covariates. We present a hierarchical extension for modeling multiple such sequences, facilitating inferences about event-level dynamics and their variation across sequences. The hierarchical approach allows one to share information across sequences in a principled manner---we illustrate the efficacy of such sharing through a set of prediction experiments. After discussing methods for adequacy checking and model selection for this class of models, the method is illustrated with an analysis of high school classroom dynamics