Directed Random Markets: Connectivity determines Money

Boltzmann-Gibbs distribution arises as the statistical equilibrium probability distribution of money among the agents of a closed economic system where random and undirected exchanges are allowed. When considering a model with uniform savings in the exchanges, the final distribution is close to the gamma family. In this work, we implement these exchange rules on networks and we find that these stationary probability distributions are robust and they are not affected by the topology of the underlying network. We introduce a new family of interactions: random but directed ones. In this case, it is found the topology to be determinant and the mean money per economic agent is related to the degree of the node representing the agent in the network. The relation between the mean money per economic agent and its degree is shown to be linear.Comment: 14 pages, 6 figure

Using Complex Network Analysis to Assess the Evolution of International Economic Integration: The cases of East Asia and Latin America

Over the past four decades the High Performing Asian Economies (HPAE) have followed a development strategy based on the exposure of their local markets to the presence of foreign competition and on an outward oriented production. In contrast, Latin American Economies (LATAM) began taking steps in this direction only in the late eighties and early nineties, but before this period these countries were more focused in the implementation of import substitution policies. These divergent paths have led to sharply different growth performance in the two regions. Yet, standard trade openness indicators fall short of portraying the peculiarity of the Asian experience, and to explain why other emerging markets with similar characteristics have been less successful over the last 25 years. This paper offers an alternative perspective on the issue by exploiting recently-developed indicators based on weighted network analysis. This allows us to investigate the whole structure of international trade relationships and to determine both the position of HPAE countries in the network and its evolution over time. We show that HPAE countries are more integrated into the world economy, as they have moved -over the past 25 years- from the periphery of the network towards its core. In contrast, the LATAM region seems to be loosing presence within the network or, at best, its integration process has remained stagnant.International trade, High Performing Asian Economies, Latin American Economies, Development, Growth, Networks, Complex Weighted Networks, World Trade Web, Centrality

A model for dynamic communicators

We develop and test an intuitively simple dynamic network model to describe the type of time-varying connectivity structure present in many technological settings. The model assumes that nodes have an inherent hierarchy governing the emergence of new connections. This idea draws on newly established concepts in online human behaviour concerning the existence of discussion catalysts, who initiate long threads, and online leaders, who trigger feedback. We show that the model captures an important property found in e-mail and voice call data – ‘dynamic communicators’ with sufficient foresight or impact to generate effective links and having an influence that is grossly underestimated by static measures based on snaphots or aggregated data

An Email Attachment is Worth a Thousand Words, or Is It?

There is an extensive body of research on Social Network Analysis (SNA) based on the email archive. The network used in the analysis is generally extracted either by capturing the email communication in From, To, Cc and Bcc email header fields or by the entities contained in the email message. In the latter case, the entities could be, for instance, the bag of words, url's, names, phones, etc. It could also include the textual content of attachments, for instance Microsoft Word documents, excel spreadsheets, or Adobe pdfs. The nodes in this network represent users and entities. The edges represent communication between users and relations to the entities. We suggest taking a different approach to the network extraction and use attachments shared between users as the edges. The motivation for this is two-fold. First, attachments represent the "intimacy" manifestation of the relation's strength. Second, the statistical analysis of private email archives that we collected and Enron email corpus shows that the attachments contribute in average around 80-90% to the archive's disk-space usage, which means that most of the data is presently ignored in the SNA of email archives. Consequently, we hypothesize that this approach might provide more insight into the social structure of the email archive. We extract the communication and shared attachments networks from Enron email corpus. We further analyze degree, betweenness, closeness, and eigenvector centrality measures in both networks and review the differences and what can be learned from them. We use nearest neighbor algorithm to generate similarity groups for five Enron employees. The groups are consistent with Enron's organizational chart, which validates our approach.Comment: 12 pages, 4 figures, 7 tables, IML'17, Liverpool, U

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

On dynamic breadth-first search in external-memory

We provide the first non-trivial result on dynamic breadth-first search (BFS) in external-memory: For general sparse undirected graphs of initially $n$ nodes and O(n) edges and monotone update sequences of either $\Theta(n)$ edge insertions or $\Theta(n)$ edge deletions, we prove an amortized high-probability bound of O(n/B^{2/3}+\sort(n)\cdot \log B) I/Os per update. In contrast, the currently best approach for static BFS on sparse undirected graphs requires \Omega(n/B^{1/2}+\sort(n)) I/Os. 1998 ACM Subject Classification: F.2.2. Key words and phrases: External Memory, Dynamic Graph Algorithms, BFS, Randomization