An efficient counting method for the colored triad census

The triad census is an important approach to understand local structure in network science, providing comprehensive assessments of the observed relational configurations between triples of actors in a network. However, researchers are often interested in combinations of relational and categorical nodal attributes. In this case, it is desirable to account for the label, or color, of the nodes in the triad census. In this paper, we describe an efficient algorithm for constructing the colored triad census, based, in part, on existing methods for the classic triad census. We evaluate the performance of the algorithm using empirical and simulated data for both undirected and directed graphs. The results of the simulation demonstrate that the proposed algorithm reduces computational time many-fold over the naive approach. We also apply the colored triad census to the Zachary karate club network dataset. We simultaneously show the efficiency of the algorithm, and a way to conduct a statistical test on the census by forming a null distribution from 1,000 realizations of a mixing-matrix conditioned graph and comparing the observed colored triad counts to the expected. From this, we demonstrate the method's utility in our discussion of results about homophily, heterophily, and bridging, simultaneously gained via the colored triad census. In sum, the proposed algorithm for the colored triad census brings novel utility to social network analysis in an efficient package

Common Organizing Mechanisms in Ecological and Socio-economic Networks

Previous work has shown that species interacting in an ecosystem and actors transacting in an economic context may have notable similarities in behavior. However, the specific mechanism that may underlie similarities in nature and human systems has not been analyzed. Building on stochastic food-web models, we propose a parsimonious bipartite-cooperation model that reproduces the key features of mutualistic networks - degree distribution, nestedness and modularity -- for both ecological networks and socio-economic networks. Our analysis uses two diverse networks. Mutually-beneficial interactions between plants and their pollinators, and cooperative economic exchanges between designers and their contractors. We find that these mutualistic networks share a key hierarchical ordering of their members, along with an exponential constraint in the number and type of partners they can cooperate with. We use our model to show that slight changes in the interaction constraints can produce either extremely nested or random structures, revealing that these constraints play a key role in the evolution of mutualistic networks. This could also encourage a new systematic approach to study the functional and structural properties of networks. The surprising correspondence across mutualistic networks suggests their broadly representativeness and their potential role in the productive organization of exchange systems, both ecological and social.Comment: In F. Reed-Tsochas and N. Johnson (eds.) Complex Systems and Interdisciplinary Sciences. London: World Scientific Publishing (in press

Small-world networks and management science research: a review

This paper reviews the literature on small-world networks in social science and management. This relatively new area of research represents an unusual level of crossdisciplinary research within social science and between social science and the physical sciences. We review the findings of this emerging area with an eye to describing the underlying theory of small worlds, the technical apparatus, promising facts, and unsettled issues for future research

The Structure of the Toyota Supply Network: An Empirical Analysis

Increasing awareness of the intrinsically complex nature of supply networks has brought the field of supply chain management into the domain of network science. However, due to the difficulties of acquiring large-scale and consistent empirical data sets, a more complete picture of a real-world supply network has remained remarkably elusive. In this paper, we present novel data that characterize the Toyota supply network, and identify key structural features using measures from social network analysis and the more recent field of network science. We show that the network structure for the Toyota supply network departs widely from the simplified models on which much previous work is based. Our analysis reveals the heterogeneous composition of the network and identifies key firms. Further analysis reveals the existence of constituent sub-networks, and we show that their structures reflect various factors, such as product categorization, geographical closeness and business alignment. Mapping the topology, geography, and distribution of productive capabilities for this supply network provides a critical first step for developing a more empirically-grounded theory of distributed production

A Simple Generative Model of Collective Online Behaviour

Human activities increasingly take place in online environments, providing novel opportunities for relating individual behaviours to population-level outcomes. In this paper, we introduce a simple generative model for the collective behaviour of millions of social networking site users who are deciding between different software applications. Our model incorporates two distinct components: one is associated with recent decisions of users, and the other reflects the cumulative popularity of each application. Importantly, although various combinations of the two mechanisms yield long-time behaviour that is consistent with data, the only models that reproduce the observed temporal dynamics are those that strongly emphasize the recent popularity of applications over their cumulative popularity. This demonstrates---even when using purely observational data without experimental design---that temporal data-driven modelling can effectively distinguish between competing microscopic mechanisms, allowing us to uncover new aspects of collective online behaviour.Comment: Updated, with new figures and Supplementary Informatio

Diffusing Workers in a Multiplex World

The study of labor mobility across firms is crucial to understand economic performance, unemployment, skills reallocation and other aspects that shape the economic life of nations. Modeling labor flows between firms has been a challenge due to the complexity arising from the distributed and heterogeneous nature of labor flows. In this paper, we introduce a discrete-time model of labor flowing on a multi-layered network (i.e. a multiplex graph). By introducing multiple layers, the model accounts for different mobility patters (e.g. industries, geographies, occupations, etc.), which is important to understand the reallocation of human capital, skills and knowledge. We apply the model to UK empirical micro-data and find that our measure of regional preferences for low versus high skilled workers vary significantly from a single to a multi-layer representation of the world

Daily Rhythms in Mobile Telephone Communication

Circadian rhythms are known to be important drivers of human activity and the recent availability of electronic records of human behaviour has provided fine-grained data of temporal patterns of activity on a large scale. Further, questionnaire studies have identified important individual differences in circadian rhythms, with people broadly categorised into morning-like or evening-like individuals. However, little is known about the social aspects of these circadian rhythms, or how they vary across individuals. In this study we use a unique 18-month dataset that combines mobile phone calls and questionnaire data to examine individual differences in the daily rhythms of mobile phone activity. We demonstrate clear individual differences in daily patterns of phone calls, and show that these individual differences are persistent despite a high degree of turnover in the individuals' social networks. Further, women's calls were longer than men's calls, especially during the evening and at night, and these calls were typically focused on a small number of emotionally intense relationships. These results demonstrate that individual differences in circadian rhythms are not just related to broad patterns of morningness and eveningness, but have a strong social component, in directing phone calls to specific individuals at specific times of day.TA and JS were funded by The Academy of Finland, project No. 260427 (http://www.aka.fi) and the computational resources were provided by Aalto 379 Science-IT project. The study was funded by a grant from the UK Engineering and Physical Sciences Research Council and Economic and Social Research Council (grant No. EP/D052114/2). RD is funded by European Research Council (grant no. 295663). The 380 collection of the data by SGBR and RD was made possible by a grant from the UK 381 EPSRC and ESRC research councils. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Identifying the underlying structure and dynamic interactions in a voting network

We analyse the structure and behaviour of a specific voting network using a dynamic structure-based methodology which draws on Q-Analysis and social network theory. Our empirical focus is on the Eurovision Song Contest over a period of 20 years. For a multicultural contest of this kind, one of the key questions is how the quality of a song is judged and how voting groups emerge. We investigate structures that may identify the winner based purely on the topology of the network. This provides a basic framework to identify what the characteristics associated with becoming a winner are, and may help to establish a homogenous criterion for subjective measures such as quality. Further, we measure the importance of voting cliques, and present a dynamic model based on a changing multidimensional measure of connectivity in order to reveal the formation of emerging community structure within the contest. Finally, we study the dynamic behaviour exhibited by the network in order to understand the clustering of voting preferences and the relationship between local and global properties.Comment: 20 pages, 10 figures, 3 tables, submitted to Physica

Cooperation under Indirect Reciprocity and Imitative Trust

Indirect reciprocity, a key concept in behavioral experiments and evolutionary game theory, provides a mechanism that allows reciprocal altruism to emerge in a population of self-regarding individuals even when repeated interactions between pairs of actors are unlikely. Recent empirical evidence show that humans typically follow complex assessment strategies involving both reciprocity and social imitation when making cooperative decisions. However, currently, we have no systematic understanding of how imitation, a mechanism that may also generate negative effects via a process of cumulative advantage, affects cooperation when repeated interactions are unlikely or information about a recipient's reputation is unavailable. Here we extend existing evolutionary models, which use an image score for reputation to track how individuals cooperate by contributing resources, by introducing a new imitative-trust score, which tracks whether actors have been the recipients of cooperation in the past. We show that imitative trust can co-exist with indirect reciprocity mechanisms up to a threshold and then cooperation reverses -revealing the elusive nature of cooperation. Moreover, we find that when information about a recipient's reputation is limited, trusting the action of third parties towards her (i.e. imitating) does favor a higher collective cooperation compared to random-trusting and share-alike mechanisms. We believe these results shed new light on the factors favoring social imitation as an adaptive mechanism in populations of cooperating social actors