Mesoscopic structure and social aspects of human mobility

The individual movements of large numbers of people are important in many contexts, from urban planning to disease spreading. Datasets that capture human mobility are now available and many interesting features have been discovered, including the ultra-slow spatial growth of individual mobility. However, the detailed substructures and spatiotemporal flows of mobility - the sets and sequences of visited locations - have not been well studied. We show that individual mobility is dominated by small groups of frequently visited, dynamically close locations, forming primary "habitats" capturing typical daily activity, along with subsidiary habitats representing additional travel. These habitats do not correspond to typical contexts such as home or work. The temporal evolution of mobility within habitats, which constitutes most motion, is universal across habitats and exhibits scaling patterns both distinct from all previous observations and unpredicted by current models. The delay to enter subsidiary habitats is a primary factor in the spatiotemporal growth of human travel. Interestingly, habitats correlate with non-mobility dynamics such as communication activity, implying that habitats may influence processes such as information spreading and revealing new connections between human mobility and social networks.Comment: 7 pages, 5 figures (main text); 11 pages, 9 figures, 1 table (supporting information

Which friends are more popular than you? Contact strength and the friendship paradox in social networks

The friendship paradox states that in a social network, egos tend to have lower degree than their alters, or, “your friends have more friends than you do”. Most research has focused on the friendship paradox and its implications for information transmission, but treating the network as static and unweighted. Yet, people can dedicate only a finite fraction of their attention budget to each social interaction: a high-degree individual may have less time to dedicate to individual social links, forcing them to modulate the quantities of contact made to their different social ties. Here we study the friendship paradox in the context of differing contact volumes between egos and alters, finding a connection between contact volume and the strength of the friendship paradox. The most frequently contacted alters exhibit a less pronounced friendship paradox compared with the ego, whereas less-frequently contacted alters are more likely to be high degree and give rise to the paradox. We argue therefore for a more nuanced version of the friendship paradox: “your closest friends have slightly more friends than you do”, and in certain networks even: “your best friend has no more friends than you do”. We demonstrate that this relationship is robust, holding in both a social media and a mobile phone dataset. These results have implications for information transfer and influence in social networks, which we explore using a simple dynamical model.James P. Bagrow, Christopher M. Danforth and Lewis Mitchel

Modularity measure of networks with overlapping communities

In this paper we introduce a non-fuzzy measure which has been designed to rank the partitions of a network's nodes into overlapping communities. Such a measure can be useful for both quantifying clusters detected by various methods and during finding the overlapping community-structure by optimization methods. The theoretical problem referring to the separation of overlapping modules is discussed, and an example for possible applications is given as well

Evaluating Local Community Methods in Networks

We present a new benchmarking procedure that is unambiguous and specific to local community-finding methods, allowing one to compare the accuracy of various methods. We apply this to new and existing algorithms. A simple class of synthetic benchmark networks is also developed, capable of testing properties specific to these local methods.Comment: 8 pages, 9 figures, code included with sourc

Phase transition in the rich-get-richer mechanism due to finite-size effects

The rich-get-richer mechanism (agents increase their ``wealth'' randomly at a rate proportional to their holdings) is often invoked to explain the Pareto power-law distribution observed in many physical situations, such as the degree distribution of growing scale free nets. We use two different analytical approaches, as well as numerical simulations, to study the case where the number of agents is fixed and finite (but large), and the rich-get-richer mechanism is invoked a fraction r of the time (the remainder of the time wealth is disbursed by a homogeneous process). At short times, we recover the Pareto law observed for an unbounded number of agents. In later times, the (moving) distribution can be scaled to reveal a phase transition with a Gaussian asymptotic form for r < 1/2 and a Pareto-like tail (on the positive side) and a novel stretched exponential decay (on the negative side) for r > 1/2.Comment: 9 pages, 1 figure, code and data included with source. Update corrects typos, adds journal-re

Comparing community structure identification

We compare recent approaches to community structure identification in terms of sensitivity and computational cost. The recently proposed modularity measure is revisited and the performance of the methods as applied to ad hoc networks with known community structure, is compared. We find that the most accurate methods tend to be more computationally expensive, and that both aspects need to be considered when choosing a method for practical purposes. The work is intended as an introduction as well as a proposal for a standard benchmark test of community detection methods.Comment: 10 pages, 3 figures, 1 table. v2: condensed, updated version as appears in JSTA

The role of caretakers in disease dynamics

One of the key challenges in modeling the dynamics of contagion phenomena is to understand how the structure of social interactions shapes the time course of a disease. Complex network theory has provided significant advances in this context. However, awareness of an epidemic in a population typically yields behavioral changes that correspond to changes in the network structure on which the disease evolves. This feedback mechanism has not been investigated in depth. For example, one would intuitively expect susceptible individuals to avoid other infecteds. However, doctors treating patients or parents tending sick children may also increase the amount of contact made with an infecteds, in an effort to speed up recovery but also exposing themselves to higher risks of infection. We study the role of these caretaker links in an adaptive network models where individuals react to a disease by increasing or decreasing the amount of contact they make with infected individuals. We find that pure avoidance, with only few caretaker links, is the best strategy for curtailing an SIS disease in networks that possess a large topological variability. In more homogeneous networks, disease prevalence is decreased for low concentrations of caretakers whereas a high prevalence emerges if caretaker concentration passes a well defined critical value.Comment: 8 pages, 9 figure

Spatiotemporal correlations of handset-based service usages

We study spatiotemporal correlations and temporal diversities of handset-based service usages by analyzing a dataset that includes detailed information about locations and service usages of 124 users over 16 months. By constructing the spatiotemporal trajectories of the users we detect several meaningful places or contexts for each one of them and show how the context affects the service usage patterns. We find that temporal patterns of service usages are bound to the typical weekly cycles of humans, yet they show maximal activities at different times. We first discuss their temporal correlations and then investigate the time-ordering behavior of communication services like calls being followed by the non-communication services like applications. We also find that the behavioral overlap network based on the clustering of temporal patterns is comparable to the communication network of users. Our approach provides a useful framework for handset-based data analysis and helps us to understand the complexities of information and communications technology enabled human behavior.Comment: 11 pages, 15 figure

A network-specific approach to percolation in networks with bidirectional links

Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine the connectivity of nodes below the percolation threshold and offer an estimate to the percolation threshold in networks with bidirectional links. Our analysis does not require the assumption that a network belongs to a specific ensemble and can at the same time easily handle arbitrary removal strategies (previously an open problem for undirected networks). In validating our analysis, we find that it predicts the effects of many known complex structures (e.g., degree correlations) and may be used to study both probabilistic and deterministic attacks.Comment: 6 pages, 8 figure

Genetic algorithm with a local search strategy for discovering communities in complex networks

In order to further improve the performance of current genetic algorithms aiming at discovering communities, a local search based genetic algorithm GALS is here proposed. The core of GALS is a local search based mutation technique. In order to overcome the drawbacks of traditional mutation methods, the paper develops the concept of marginal gene and then the local monotonicity of modularity function Q is deduced from each nodes local view. Based on these two elements, a new mutation method combined with a local search strategy is presented. GALS has been evaluated on both synthetic benchmarks and several real networks, and compared with some presently competing algorithms. Experimental results show that GALS is highly effective and efficient for discovering community.Thanks are due to the referees for helpful comments. This work was supported by National Natural Science Foundation of China (60873149, 60973088, 61133011, 61202308), Scholarship Award for Excellent Doctoral Student granted by Ministry of Education (450060454018), Program for New Century Excellent Talents in University (NCET-11-0204), and Jilin University Innovation Project (450060481084)