Coexistence of opposite opinions in a network with communities

The Majority Rule is applied to a topology that consists of two coupled random networks, thereby mimicking the modular structure observed in social networks. We calculate analytically the asymptotic behaviour of the model and derive a phase diagram that depends on the frequency of random opinion flips and on the inter-connectivity between the two communities. It is shown that three regimes may take place: a disordered regime, where no collective phenomena takes place; a symmetric regime, where the nodes in both communities reach the same average opinion; an asymmetric regime, where the nodes in each community reach an opposite average opinion. The transition from the asymmetric regime to the symmetric regime is shown to be discontinuous.Comment: 14 pages, 4 figure

Bloggers Behavior and Emergent Communities in Blog Space

Interactions between users in cyberspace may lead to phenomena different from those observed in common social networks. Here we analyse large data sets about users and Blogs which they write and comment, mapped onto a bipartite graph. In such enlarged Blog space we trace user activity over time, which results in robust temporal patterns of user--Blog behavior and the emergence of communities. With the spectral methods applied to the projection on weighted user network we detect clusters of users related to their common interests and habits. Our results suggest that different mechanisms may play the role in the case of very popular Blogs. Our analysis makes a suitable basis for theoretical modeling of the evolution of cyber communities and for practical study of the data, in particular for an efficient search of interesting Blog clusters and further retrieval of their contents by text analysis

Fitness-driven deactivation in network evolution

Individual nodes in evolving real-world networks typically experience growth and decay --- that is, the popularity and influence of individuals peaks and then fades. In this paper, we study this phenomenon via an intrinsic nodal fitness function and an intuitive aging mechanism. Each node of the network is endowed with a fitness which represents its activity. All the nodes have two discrete stages: active and inactive. The evolution of the network combines the addition of new active nodes randomly connected to existing active ones and the deactivation of old active nodes with possibility inversely proportional to their fitnesses. We obtain a structured exponential network when the fitness distribution of the individuals is homogeneous and a structured scale-free network with heterogeneous fitness distributions. Furthermore, we recover two universal scaling laws of the clustering coefficient for both cases, $C(k) \sim k^{-1}$ and $C \sim n^{-1}$, where $k$ and $n$ refer to the node degree and the number of active individuals, respectively. These results offer a new simple description of the growth and aging of networks where intrinsic features of individual nodes drive their popularity, and hence degree.Comment: IoP Styl

Self-similar correlation function in brain resting-state fMRI

Adaptive behavior, cognition and emotion are the result of a bewildering variety of brain spatiotemporal activity patterns. An important problem in neuroscience is to understand the mechanism by which the human brain's 100 billion neurons and 100 trillion synapses manage to produce this large repertoire of cortical configurations in a flexible manner. In addition, it is recognized that temporal correlations across such configurations cannot be arbitrary, but they need to meet two conflicting demands: while diverse cortical areas should remain functionally segregated from each other, they must still perform as a collective, i.e., they are functionally integrated. Here, we investigate these large-scale dynamical properties by inspecting the character of the spatiotemporal correlations of brain resting-state activity. In physical systems, these correlations in space and time are captured by measuring the correlation coefficient between a signal recorded at two different points in space at two different times. We show that this two-point correlation function extracted from resting-state fMRI data exhibits self-similarity in space and time. In space, self-similarity is revealed by considering three successive spatial coarse-graining steps while in time it is revealed by the 1/f frequency behavior of the power spectrum. The uncovered dynamical self-similarity implies that the brain is spontaneously at a continuously changing (in space and time) intermediate state between two extremes, one of excessive cortical integration and the other of complete segregation. This dynamical property may be seen as an important marker of brain well-being both in health and disease.Comment: 14 pages 13 figures; published online before print September 2

Effects of time window size and placement on the structure of aggregated networks

Complex networks are often constructed by aggregating empirical data over time, such that a link represents the existence of interactions between the endpoint nodes and the link weight represents the intensity of such interactions within the aggregation time window. The resulting networks are then often considered static. More often than not, the aggregation time window is dictated by the availability of data, and the effects of its length on the resulting networks are rarely considered. Here, we address this question by studying the structural features of networks emerging from aggregating empirical data over different time intervals, focussing on networks derived from time-stamped, anonymized mobile telephone call records. Our results show that short aggregation intervals yield networks where strong links associated with dense clusters dominate; the seeds of such clusters or communities become already visible for intervals of around one week. The degree and weight distributions are seen to become stationary around a few days and a few weeks, respectively. An aggregation interval of around 30 days results in the stablest similar networks when consecutive windows are compared. For longer intervals, the effects of weak or random links become increasingly stronger, and the average degree of the network keeps growing even for intervals up to 180 days. The placement of the time window is also seen to affect the outcome: for short windows, different behavioural patterns play a role during weekends and weekdays, and for longer windows it is seen that networks aggregated during holiday periods are significantly different.Comment: 19 pages, 11 figure

Random hypergraphs and their applications

In the last few years we have witnessed the emergence, primarily in on-line communities, of new types of social networks that require for their representation more complex graph structures than have been employed in the past. One example is the folksonomy, a tripartite structure of users, resources, and tags -- labels collaboratively applied by the users to the resources in order to impart meaningful structure on an otherwise undifferentiated database. Here we propose a mathematical model of such tripartite structures which represents them as random hypergraphs. We show that it is possible to calculate many properties of this model exactly in the limit of large network size and we compare the results against observations of a real folksonomy, that of the on-line photography web site Flickr. We show that in some cases the model matches the properties of the observed network well, while in others there are significant differences, which we find to be attributable to the practice of multiple tagging, i.e., the application by a single user of many tags to one resource, or one tag to many resources.Comment: 11 pages, 7 figure

Local variation of hashtag spike trains and popularity in Twitter

We draw a parallel between hashtag time series and neuron spike trains. In each case, the process presents complex dynamic patterns including temporal correlations, burstiness, and all other types of nonstationarity. We propose the adoption of the so-called local variation in order to uncover salient dynamics, while properly detrending for the time-dependent features of a signal. The methodology is tested on both real and randomized hashtag spike trains, and identifies that popular hashtags present regular and so less bursty behavior, suggesting its potential use for predicting online popularity in social media.Comment: 7 pages, 7 figure

Generalized Master Equations for Non-Poisson Dynamics on Networks

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Consequently, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that the equation reduces to the standard rate equations when the underlying process is Poisson and that the stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature

Line Graphs of Weighted Networks for Overlapping Communities

In this paper, we develop the idea to partition the edges of a weighted graph in order to uncover overlapping communities of its nodes. Our approach is based on the construction of different types of weighted line graphs, i.e. graphs whose nodes are the links of the original graph, that encapsulate differently the relations between the edges. Weighted line graphs are argued to provide an alternative, valuable representation of the system's topology, and are shown to have important applications in community detection, as the usual node partition of a line graph naturally leads to an edge partition of the original graph. This identification allows us to use traditional partitioning methods in order to address the long-standing problem of the detection of overlapping communities. We apply it to the analysis of different social and geographical networks.Comment: 8 Pages. New title and text revisions to emphasise differences from earlier paper

Interplay between telecommunications and face-to-face interactions - a study using mobile phone data

In this study we analyze one year of anonymized telecommunications data for over one million customers from a large European cellphone operator, and we investigate the relationship between people's calls and their physical location. We discover that more than 90% of users who have called each other have also shared the same space (cell tower), even if they live far apart. Moreover, we find that close to 70% of users who call each other frequently (at least once per month on average) have shared the same space at the same time - an instance that we call co-location. Co-locations appear indicative of coordination calls, which occur just before face-to-face meetings. Their number is highly predictable based on the amount of calls between two users and the distance between their home locations - suggesting a new way to quantify the interplay between telecommunications and face-to-face interactions