http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

/pdf/community-detection-in-graphs-34rogm3r6p.pdf

Community detection in graphs

A network is a network — be it between words (those associated with ‘bright’ in this case) or protein structures. Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of1,2,3,4. A key question is how to interpret the global organization of such networks as the coexistence of their structural subunits (communities) associated with more highly interconnected parts. Identifying these a priori unknown building blocks (such as functionally related proteins5,6, industrial sectors7 and groups of people8,9) is crucial to the understanding of the structural and functional properties of networks. The existing deterministic methods used for large networks find separated communities, whereas most of the actual networks are made of highly overlapping cohesive groups of nodes. Here we introduce an approach to analysing the main statistical features of the interwoven sets of overlapping communities that makes a step towards uncovering the modular structure of complex systems. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique for exploring overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks. Our studies of collaboration, word-association and protein interaction graphs show that the web of communities has non-trivial correlations and specific scaling properties.

/pdf/uncovering-the-overlapping-community-structure-of-complex-1f119qtsda.pdf

Uncovering the overlapping community structure of complex networks in nature and society

https://deim.urv.cat/~alexandre.arenas/publicacions/pdf/review.pdf

Synchronization in complex networks

The time dependence of the recently introduced minimum spanning tree description of correlations between stocks, called the ‘‘asset tree’’ has been studied in order to reflect the financial market taxonomy. The nodes of the tree are identified with stocks and the distance between them is a unique function of the corresponding element of the correlation matrix. By using the concept of a central vertex, chosen as the most strongly connected node of the tree, an important characteristic is defined by the mean occupation layer. During crashes, due to the strong global correlation in the market, the tree shrinks topologically, and this is shown by a low value of the mean occupation layer . The tree seems to have a scale-free structure where the scaling exponent of the degree distribution is different for ‘‘business as usual’’ and ‘‘crash’’ periods. The basic structure of the tree topology is very robust with respect to time. We also point out that the diversification aspect of portfolio optimization results in the fact that the assets of the classic Markowitz portfolio are always located on the outer leaves of the tree. Technical aspects such as the window size dependence of the investigated quantities are also discussed.

/pdf/dynamics-of-market-correlations-taxonomy-and-portfolio-1sjj6k2bg9.pdf

Dynamics of market correlations: taxonomy and portfolio analysis.

– The purpose of this paper is to decompose total customer value as perceived by department store shoppers into utilitarian, hedonic and social dimensions, and empirically test this conceptualization in a Finnish department store shopping context., – Data were collected by a questionnaire administered over three days at a department store that generates the second largest turnover in Finland. A total of 364 shoppers completed the questionnaire., – Empirical evidence supports our tripartite conceptualization of total customer value. In particular, social value is an independent construct. Further, social value varies by day‐of‐week, with a significant increase on Saturday (versus weekdays) when the store is more crowded, whereas no such differences in utilitarian and hedonic values were detected., – The principal contribution is a tripartite conceptualization of total customer value that incorporates utilitarian, social and hedonic value dimensions in a department store shopping context. Individually these dimensions are all well rooted in streams of consumer behavior literature, albeit mostly at the product or brand, not the store, level. Increasing our understanding of these softer aspects of shopping, particularly the social dimension, is important because they represent possible differentiating factors in the highly competitive and often commoditized retail markets.

Decomposing the value of department store shopping into utilitarian, hedonic and social dimensions: Evidence from Finland

This paper introduces a new methodology for constructing a network of companies called a dynamic asset graph. This is similar to the dynamic asset tree studied recently, as both are based on correlations between asset returns. However, the new modified methodology does not, in general, lead to a tree but a disconnected graph. The asset tree, due to the minimum spanning tree criterion, is forced to "accept" edge lengths that are far less optimal (longer) than the asset graph, thus resulting in higher overall length for the tree. The same criterion also causes asset trees to be more fragile in structure when measured by the single-step survival ratio. Over longer time periods, in the beginning the asset graph decays more slowly than the asset tree, but in the long run the situation is reversed. The vertex degree distributions indicate that the possible scale free behavior of the asset graph is not as evident as it is in the case of the asset tree.

/pdf/asset-trees-and-asset-graphs-in-financial-markets-29tuopzasv.pdf

Asset Trees and Asset Graphs in Financial Markets

The purpose of this study was to determine the effect of expertise on prechoice decision processes and final outcomes. By decomposing verbal protocols collected from 90 individuals who made one complex, mortgage loan decision, we could compare the frequency and type of elementary information processes evoked. We found that experts, relative to less knowledgeable decision makers, made a greater number of problem framing statements; made more references to why an option was being retained for further consideration; and used more compensatory decision rules. In addition, we found that misunderstanding externally provided information mediates the expertise‐choice relationship. Novices were significantly more likely to misunderstand information than were more knowledgeable decision makers. As a result, there was greater variance in novices’ final choices than was the case with experts’. The deleterious effect of mis‐understandings is disconcerting because consumers frequently miscomprehend print communications.

Expertise effects on prechoice decision processes and final outcomes

In this study we analyze the Standard and Poor's 500 index data of the New York Stock Exchange for more than 32 years. Using a simple random walk model we demonstrate that the proper variable to look at is the logarithmic return. In the statistical analysis we have done fittings to the Levy distribution using either the index data as such or pre-processing it with ARCH, GARCH or IGARCH methods, which tend to remove the time-dependent variance. For short times the truncated Levy distribution is found to fit the data quite well. Since this is not a stable distribution, the scaling behavior observed for short times should brake down for longer times. We demonstrate that the characteristic time where this cross-over starts is of the order of one day.

Antti J. Kanto

Papers

Dynamics of market correlations: taxonomy and portfolio analysis.

Decomposing the value of department store shopping into utilitarian, hedonic and social dimensions: Evidence from Finland

Asset Trees and Asset Graphs in Financial Markets

Expertise effects on prechoice decision processes and final outcomes

Characteristic times in stock market indices