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arXiv2014

Dominating Scale-Free Networks Using Generalized Probabilistic Methods

We study ensemble-based graph-theoretical methods aiming to approximate the size of the minimum dominating set (MDS) in scale-free networks. We analyze both analytical upper bounds of dominating sets and numerical realizations for applications. We propose two novel probabilistic dominating set selection strategies that are applicable to heterogeneous networks. One of them obtains the smallest probabilistic dominating set and also outperforms the deterministic degree-ranked method. We show that a degree-dependent probabilistic selection method becomes optimal in its deterministic limit. In addition, we also find the precise limit where selecting high-degree nodes exclusively becomes inefficient for network domination. We validate our results on several real-world networks, and provide highly accurate analytical estimates for our methods.

physics.soc-ph↗
arXiv2016

Impact of embedding on predictability of failure-recovery dynamics in networks

Failure, damage spread and recovery crucially underlie many spatially embedded networked systems ranging from transportation structures to the human body. Here we study the interplay between spontaneous damage, induced failure and recovery in both embedded and non-embedded networks. In our model the network's components follow three realistic processes that capture these features: (i) spontaneous failure of a component independent of the neighborhood (internal failure), (ii) failure induced by failed neighboring nodes (external failure) and (iii) spontaneous recovery of a component.We identify a metastable domain in the global network phase diagram spanned by the model's control parameters where dramatic hysteresis effects and random switching between two coexisting states are observed. The loss of predictability due to these effects depend on the characteristic link length of the embedded system. For the Euclidean lattice in particular, hysteresis and switching only occur in an extremely narrow region of the parameter space compared to random networks. We develop a unifying theory which links the dynamics of our model to contact processes. Our unifying framework may help to better understand predictability and controllability in spatially embedded and random networks where spontaneous recovery of components can mitigate spontaneous failure and damage spread in the global network.

physics.soc-ph↗
arXiv2013

Assortative mixing in functional brain networks during epileptic seizures

We investigate assortativity of functional brain networks before, during, and after one-hundred epileptic seizures with different anatomical onset locations. We construct binary functional networks from multi-channel electroencephalographic data recorded from 60 epilepsy patients, and from time-resolved estimates of the assortativity coefficient we conclude that positive degree-degree correlations are inherent to seizure dynamics. While seizures evolve, an increasing assortativity indicates a segregation of the underlying functional network into groups of brain regions that are only sparsely interconnected, if at all. Interestingly, assortativity decreases already prior to seizure end. Together with previous observations of characteristic temporal evolutions of global statistical properties and synchronizability of epileptic brain networks, our findings may help to gain deeper insights into the complicated dynamics underlying generation, propagation, and termination of seizures.

physics.data-an↗
arXiv2013

Analysis of Remote Synchronization in Complex Networks

A novel regime of synchronization, called remote synchronization, where the peripheral nodes form a phase synchronized cluster not including the hub, was recently observed in star motifs. We show the existence of a more general dynamical state of remote synchronization in arbitrary networks of coupled oscillators. This state is characterized by the synchronization of pairs of nodes that are not directly connected via a physical link or any sequence of synchronized nodes. This phenomenon is almost negligible in networks of phase oscillators as its underlying mechanism is the modulation of the amplitude of those intermediary nodes between the remotely synchronized units. Our findings thus show the ubiquity and robustness of these states and bridge the gap from their recent observation in simple toy graphs to complex networks.

physics.soc-ph↗
arXiv2013

Role of social environment and social clustering in spread of opinions in co-evolving networks

Taking a pragmatic approach to the processes involved in the phenomena of collective opinion formation, we investigate two specific modifications to the co-evolving network voter model of opinion formation, studied by Holme and Newman [1]. First, we replace the rewiring probability parameter by a distribution of probability of accepting or rejecting opinions between individuals, accounting for the asymmetric influences in relationships among individuals in a social group. Second, we modify the rewiring step by a path-length-based preference for rewiring that reinforces local clustering. We have investigated the influences of these modifications on the outcomes of the simulations of this model. We found that varying the shape of the distribution of probability of accepting or rejecting opinions can lead to the emergence of two qualitatively distinct final states, one having several isolated connected components each in internal consensus leading to the existence of diverse set of opinions and the other having one single dominant connected component with each node within it having the same opinion. Furthermore, and more importantly, we found that the initial clustering in network can also induce similar transitions. Our investigation also brings forward that these transitions are governed by a weak and complex dependence on system size. We found that the networks in the final states of the model have rich structural properties including the small world property for some parameter regimes. [1] P. Holme and M. Newman, Phys. Rev. E 74, 056108 (2006).

physics.soc-ph↗
arXiv2014

Dynamics on Modular Networks with Heterogeneous Correlations

We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model. The new network ensemble generalizes existing models (e.g., the well-known configuration model and LFR networks) by allowing a heterogeneous distribution of degree-degree correlations across modules, which is important for the consideration of nonidentical interacting networks.

physics.soc-ph↗
arXiv2012

An Alternative Approach to the Calculation and Analysis of Connectivity in the World City Network

Empirical research on world cities often draws on Taylor's (2001) notion of an 'interlocking network model', in which office networks of globalized service firms are assumed to shape the spatialities of urban networks. In spite of its many merits, this approach is limited because the resultant adjacency matrices are not really fit for network-analytic calculations. We therefore propose a fresh analytical approach using a primary linkage algorithm that produces a one-mode directed graph based on Taylor's two-mode city/firm network data. The procedure has the advantage of creating less dense networks when compared to the interlocking network model, while nonetheless retaining the network structure apparent in the initial dataset. We randomize the empirical network with a bootstrapping simulation approach, and compare the simulated parameters of this null-model with our empirical network parameter (i.e. betweenness centrality). We find that our approach produces results that are comparable to those of the standard interlocking network model. However, because our approach is based on an actual graph representation and network analysis, we are able to assess cities' position in the network at large. For instance, we find that cities such as Tokyo, Sydney, Melbourne, Almaty and Karachi hold more strategic and valuable positions than suggested in the interlocking networks as they play a bridging role in connecting cities across regions. In general, we argue that our graph representation allows for further and deeper analysis of the original data, further extending world city network research into a theory-based empirical research approach.

physics.soc-ph↗
arXiv2013

Statistical detection of systematic election irregularities

Democratic societies are built around the principle of free and fair elections, that each citizen's vote should count equal. National elections can be regarded as large-scale social experiments, where people are grouped into usually large numbers of electoral districts and vote according to their preferences. The large number of samples implies certain statistical consequences for the polling results which can be used to identify election irregularities. Using a suitable data collapse, we find that vote distributions of elections with alleged fraud show a kurtosis of hundred times more than normal elections on certain levels of data aggregation. As an example we show that reported irregularities in recent Russian elections are indeed well explained by systematic ballot stuffing and develop a parametric model quantifying to which extent fraudulent mechanisms are present. We show that if specific statistical properties are present in an election, the results do not represent the will of the people. We formulate a parametric test detecting these statistical properties in election results. Remarkably, this technique produces similar outcomes irrespective of the data resolution and thus allows for cross-country comparisons.

physics.soc-ph↗
arXiv2013

From the Physics of Interacting Polymers to Optimizing Routes on the London Underground

Optimizing paths on networks is crucial for many applications, from subway traffic to Internet communication. As global path optimization that takes account of all path-choices simultaneously is computationally hard, most existing routing algorithms optimize paths individually, thus providing sub-optimal solutions. We employ the physics of interacting polymers and disordered systems to analyze macroscopic properties of generic path-optimization problems and derive a simple, principled, generic and distributed routing algorithm capable of considering simultaneously all individual path choices. We demonstrate the efficacy of the new algorithm by applying it to: (i) random graphs resembling Internet overlay networks; (ii) travel on the London underground network based on Oyster-card data; and (iii) the global airport network. Analytically derived macroscopic properties give rise to insightful new routing phenomena, including phase transitions and scaling laws, which facilitate better understanding of the appropriate operational regimes and their limitations that are difficult to obtain otherwise.

physics.soc-ph↗
arXiv2013

Understanding metropolitan patterns of daily encounters

Understanding of the mechanisms driving our daily face-to-face encounters is still limited; the field lacks large-scale datasets describing both individual behaviors and their collective interactions. However, here, with the help of travel smart card data, we uncover such encounter mechanisms and structures by constructing a time-resolved in-vehicle social encounter network on public buses in a city (about 5 million residents). This is the first time that such a large network of encounters has been identified and analyzed. Using a population scale dataset, we find physical encounters display reproducible temporal patterns, indicating that repeated encounters are regular and identical. On an individual scale, we find that collective regularities dominate distinct encounters' bounded nature. An individual's encounter capability is rooted in his/her daily behavioral regularity, explaining the emergence of "familiar strangers" in daily life. Strikingly, we find individuals with repeated encounters are not grouped into small communities, but become strongly connected over time, resulting in a large, but imperceptible, small-world contact network or "structure of co-presence" across the whole metropolitan area. Revealing the encounter pattern and identifying this large-scale contact network are crucial to understanding the dynamics in patterns of social acquaintances, collective human behaviors, and -- particularly -- disclosing the impact of human behavior on various diffusion/spreading processes.

physics.soc-ph↗
arXiv2013

Temporal motifs reveal homophily, gender-specific patterns and group talk in mobile communication networks

Electronic communication records provide detailed information about temporal aspects of human interaction. Previous studies have shown that individuals' communication patterns have complex temporal structure, and that this structure has system-wide effects. In this paper we use mobile phone records to show that interaction patterns involving multiple individuals have non-trivial temporal structure that cannot be deduced from a network presentation where only interaction frequencies are taken into account. We apply a recently introduced method, temporal motifs, to identify interaction patterns in a temporal network where nodes have additional attributes such as gender and age. We then develop a null model that allows identifying differences between various types of nodes so that these differences are independent of the network based on interaction frequencies. We find gender-related differences in communication patters, and show the existence of temporal homophily, the tendency of similar individuals to participate in interaction patterns beyond what would be expected on the basis of the network structure alone. We also show that temporal patterns differ between dense and sparse parts of the network. Because this result is independent of edge weights, it can be considered as an extension of Granovetter's hypothesis to temporal networks.

physics.soc-ph↗
arXiv2014

Principles of scientific research team formation and evolution

Research teams are the fundamental social unit of science, and yet there is currently no model that describes their basic property: size. In most fields teams have grown significantly in recent decades. We show that this is partly due to the change in the character of team-size distribution. We explain these changes with a comprehensive yet straightforward model of how teams of different sizes emerge and grow. This model accurately reproduces the evolution of empirical team-size distribution over the period of 50 years. The modeling reveals that there are two modes of knowledge production. The first and more fundamental mode employs relatively small, core teams. Core teams form by a Poisson process and produce a Poisson distribution of team sizes in which larger teams are exceedingly rare. The second mode employs extended teams, which started as core teams, but subsequently accumulated new members proportional to the past productivity of their members. Given time, this mode gives rise to a power-law tail of large teams (10-1000 members), which features in many fields today. Based on this model we construct an analytical functional form that allows the contribution of different modes of authorship to be determined directly from the data and is applicable to any field. The model also offers a solid foundation for studying other social aspects of science, such as productivity and collaboration.

physics.soc-ph↗
arXiv2013

Spectral redemption: clustering sparse networks

Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even when other algorithms such as belief propagation can do so. Here we introduce a new class of spectral algorithms based on a non-backtracking walk on the directed edges of the graph. The spectrum of this operator is much better-behaved than that of the adjacency matrix or other commonly used matrices, maintaining a strong separation between the bulk eigenvalues and the eigenvalues relevant to community structure even in the sparse case. We show that our algorithm is optimal for graphs generated by the stochastic block model, detecting communities all the way down to the theoretical limit. We also show the spectrum of the non-backtracking operator for some real-world networks, illustrating its advantages over traditional spectral clustering.

cs.SI↗
arXiv2014

Collective credit allocation in science

Collaboration among researchers is an essential component of the modern scientific enterprise, playing a particularly important role in multidisciplinary research. However, we continue to wrestle with allocating credit to the coauthors of publications with multiple authors, since the relative contribution of each author is difficult to determine. At the same time, the scientific community runs an informal field-dependent credit allocation process that assigns credit in a collective fashion to each work. Here we develop a credit allocation algorithm that captures the coauthors' contribution to a publication as perceived by the scientific community, reproducing the informal collective credit allocation of science. We validate the method by identifying the authors of Nobel-winning papers that are credited for the discovery, independent of their positions in the author list. The method can also compare the relative impact of researchers working in the same field, even if they did not publish together. The ability to accurately measure the relative credit of researchers could affect many aspects of credit allocation in science, potentially impacting hiring, funding, and promotion decisions.

physics.soc-ph↗
arXiv2014

Quantifying the benefits of vehicle pooling with shareability networks

Taxi services are a vital part of urban transportation, and a considerable contributor to traffic congestion and air pollution causing substantial adverse effects on human health. Sharing taxi trips is a possible way of reducing the negative impact of taxi services on cities, but this comes at the expense of passenger discomfort quantifiable in terms of a longer travel time. Due to computational challenges, taxi sharing has traditionally been approached on small scales, such as within airport perimeters, or with dynamical ad-hoc heuristics. However, a mathematical framework for the systematic understanding of the tradeoff between collective benefits of sharing and individual passenger discomfort is lacking. Here we introduce the notion of shareability network which allows us to model the collective benefits of sharing as a function of passenger inconvenience, and to efficiently compute optimal sharing strategies on massive datasets. We apply this framework to a dataset of millions of taxi trips taken in New York City, showing that with increasing but still relatively low passenger discomfort, cumulative trip length can be cut by 40% or more. This benefit comes with reductions in service cost, emissions, and with split fares, hinting towards a wide passenger acceptance of such a shared service. Simulation of a realistic online system demonstrates the feasibility of a shareable taxi service in New York City. Shareability as a function of trip density saturates fast, suggesting effectiveness of the taxi sharing system also in cities with much sparser taxi fleets or when willingness to share is low.

physics.soc-ph↗
arXiv2021

Evolution of cooperation with asymmetric social interactions

How cooperation emerges in human societies is both an evolutionary enigma, and a practical problem with tangible implications for societal health. Population structure has long been recognized as a catalyst for cooperation because local interactions enable reciprocity. Analysis of this phenomenon typically assumes bi-directional social interactions, even though real-world interactions are often uni-directional. Uni-directional interactions -- where one individual has the opportunity to contribute altruistically to another, but not conversely -- arise in real-world populations as the result of organizational hierarchies, social stratification, popularity effects, and endogenous mechanisms of network growth. Here we expand the theory of cooperation in structured populations to account for both uni- and bi-directional social interactions. Even though directed interactions remove the opportunity for reciprocity, we find that cooperation can nonetheless be favored in directed social networks and that cooperation is provably maximized for networks with an intermediate proportion of directed interactions, as observed in many empirical settings. We also identify two simple structural motifs that allow efficient modification of interaction directionality to promote cooperation by orders of magnitude. We discuss how our results relate to the concepts of generalized and indirect reciprocity.

q-bio.PE↗
arXiv2012

The Image of the City Out of the Underlying Scaling of City Artifacts or Locations

Two fundamental issues surrounding research on the image of the city respectively focus on the city's external and internal representations. The external representation in the context of this paper refers to the city itself, external to human minds, while the internal representation concerns how the city is represented in human minds internally. This paper deals with the first issue, i.e., what trait the city has that make it imageable? We develop an argument that the image of the city arises from the underlying scaling of city artifacts or locations. This scaling refers to the fact that, in an imageable city (a city that can easily be imaged in human minds), small city artifacts are far more common than large ones; or alternatively low dense locations are far more common than high dense locations. The sizes of city artifacts in a rank-size plot exhibit a heavy tailed distribution consisting of the head, which is composed of a minority of unique artifacts (vital and very important), and the tail, which is composed of redundant other artifacts (trivial and less important). Eventually, those extremely unique and vital artifacts in the top head, i.e., what Lynch called city elements, make up the image of the city. We argue that the ever-increasing amount of geographic information on cities, in particular obtained from social media such as Flickr and Twitter, can turn research on the image of the city, or cognitive mapping in general, into a quantitative manner. The scaling property might be formulated as a law of geography. Keywords: Scaling of geographic space, face of the city, cognitive maps, power law, and heavy tailed distributions.

nlin.AO↗
arXiv2012

Head/tail Breaks: A New Classification Scheme for Data with a Heavy-tailed Distribution

This paper introduces a new classification scheme - head/tail breaks - in order to find groupings or hierarchy for data with a heavy-tailed distribution. The heavy-tailed distributions are heavily right skewed, with a minority of large values in the head and a majority of small values in the tail, commonly characterized by a power law, a lognormal or an exponential function. For example, a country's population is often distributed in such a heavy-tailed manner, with a minority of people (e.g., 20 percent) in the countryside and the vast majority (e.g., 80 percent) in urban areas. This heavy-tailed distribution is also called scaling, hierarchy or scaling hierarchy. This new classification scheme partitions all of the data values around the mean into two parts and continues the process iteratively for the values (above the mean) in the head until the head part values are no longer heavy-tailed distributed. Thus, the number of classes and the class intervals are both naturally determined. We therefore claim that the new classification scheme is more natural than the natural breaks in finding the groupings or hierarchy for data with a heavy-tailed distribution. We demonstrate the advantages of the head/tail breaks method over Jenks' natural breaks in capturing the underlying hierarchy of the data. Keywords: data classification, head/tail division rule, natural breaks, scaling, and hierarchy

physics.data-an↗