Records of social interactions provide us with new sources data for understanding how interaction patterns affect collective dynamics. Such human activity are often bursty, i.e., they consist short periods intense followed by long silence. This burstiness has been shown to spreading phenomena; it accelerates epidemic in some cases and slows down other cases. We investigate a model history-dependent contagion. In our model, repeated between susceptible infected individuals period time is...

Many dynamical systems can be successfully analyzed by representing them as networks. Empirically measured networks and dynamic processes that take place in these situations show heterogeneous, non-Markovian, intrinsically correlated topologies dynamics. This makes their analysis particularly challenging. Randomized reference models (RRMs) have emerged a general versatile toolbox for studying such systems. Defined random with given features constrained to match those of an input (empirical)...

Recent developments in sensing technologies have enabled us to examine the nature of human social behavior greater detail. By applying an information-theoretic method spatiotemporal data cell-phone locations, [C. Song et al., Science 327, 1018 (2010)] found that mobility patterns are remarkably predictable. Inspired by their work, we address a similar predictability question different kind activity: conversation events. The sequence one's partners is defined as degree which next partner can...

Structure of networks constructed from mentioning relationships between posts in online media may be valuable for understanding how information and opinions spread these media. We crawled Twitter to collect tweets replies construct a large number so-called reply trees, each which was rooted at tweet joined by replies. Consistent with the previous literature, we found that empirical trees were characterized some long path-like star-like irregular although their frequencies not high. tested...

Structure of real networked systems, such as social relationship, can be modeled temporal networks in which each edge appears only at the prescribed time. Understanding structure requires quantifying importance a vertex, is pair vertex index and In this paper, we define two centrality measures based on fastest paths use vertex. The definition free from parameters robust against change time scale focus. addition, efficiently compute these values for all vertices. Using measures, reveal that...

In many data sets, crucial information on the structure and temporality of a system coexists with noise non-essential elements. networked systems, for instance, some edges might be or exist only by chance. Filtering them out extracting set relevant connections, "network backbone", is non-trivial task, methods put forward until now do not address time-resolved networks, whose availability has strongly increased in recent years. We develop here such method, defining an adequate temporal...

Recent analysis of social communications among humans has revealed that the interval between interactions for a pair individuals and an individual often follows long-tail distribution. We investigate effect such non-Poissonian nature human behavior on dynamics opinion formation. use variant voter model numerically compare time to consensus all voters with different distributions interevent intervals networks. Compared exponential distribution (i.e., standard model), power-law slows down...

Records of time-stamped social interactions between pairs individuals (e.g., face-to-face conversations, e-mail exchanges, and phone calls) constitute a so-called temporal network. A remarkable difference networks conventional static is that events rather than links are the unit elements generating collective behavior nodes. We propose an importance measure for single interaction events. By generalizing concept advance event proposed by [Kossinets G, Kleinberg J, Watts D J (2008) Proceeding...

To control infection spreading on networks, we investigate the effect of observer nodes that recognize in a neighboring node and make rest neighbor immune. We numerically show random placement works better networks with clustering than locally treelike implying our model is promising for realistic social networks. The efficiency several heuristic schemes also examined synthetic empirical In parallel numerical simulations epidemic dynamics, can be assessed by size largest connected component...

Relationship lending is broadly interpreted as a strong partnership between lender and borrower. Nevertheless, we still lack consensus regarding how to quantify the strength of relationship, while simple statistics such frequency volume loans have been used proxies in previous studies. Here, propose statistical tests identify relationship significant tie banks. Application proposed method Italian interbank networks reveals that fraction among all bilateral trades has quite stable lenders...

Some temporal networks, most notably citation are naturally represented as directed acyclic graphs (DAGs). To detect communities in DAGs, we propose a modularity for DAGs by defining an appropriate null model (i.e., randomized network) respecting the order of nodes. We implement spectral method to approximately maximize proposed measure and test on networks other DAGs. find that attained values similar partitions obtain maximizing (designed DAGs), undirected general networks. In words, if...

We study the dynamical properties of human communication through different channels, i.e., short messages, phone calls, and emails, adopting techniques from neuronal spike train analysis in order to characterize temporal fluctuations successive inter-event times. first measure so-called local variation (LV) incoming outgoing event sequences users, find that these in- out- LV values are positively correlated for uncorrelated calls emails. Second, we analyze response-time distribution after...

The global financial crisis in 2007-2009 demonstrated that systemic risk can spread all over the world through a complex web of linkages, yet we still lack fundamental knowledge about evolution web. In particular, interbank credit networks shape core system, which time-varying interconnected emerges from massive number temporal transactions between banks. current understanding mechanics makes it difficult to evaluate and control risk. Here, uncover dynamics by seeking patterns daily...

When we represent real-world systems as networks, the directions of links often convey valuable information. Finding module structures that respect link is one most important tasks for analysing directed networks. Although many notions a have been proposed, no consensus has reached. This lack results partly because there might exist distinct types modules in single network, whereas previous studies focused on an independent criterion modules. To address this issue, propose generic notion...

Yang, Wang, and Motter [Phys. Rev. Lett. 109, 258701 (2012)] analyzed a model for network observability transitions in which sensor placed on node makes the adjacent nodes observable. The size of connected components comprising observable is major concern model. We analyze this random heterogeneous networks with degree correlation. With numerical simulations analytical arguments based generating functions, we find that negative correlation more This result holds true both when sensors are...

We provide a general framework for analyzing degree correlations between nodes separated by more than one step (i.e., beyond nearest neighbors) in complex networks. One probability and four conditional probabilities are introduced to fully describe long-range with respect $k$ $k'$ of two shortest path length $l$ them. present relations among these clarify the relevance nearest-neighbor correlations. Unlike correlations, some meaningful only finite-size Furthermore, as baseline determine...

Epidemic outbreaks of new pathogens, or known pathogens in populations, cause a great deal fear because they are hard to predict. For theoretical models disease spreading, on the other hand, quantities characterizing outbreak converge deterministic functions time. Our goal this paper is shed some light apparent discrepancy. We measure diversity (and, thus, predictability of) sizes and extinction times as time given different scenarios amount information available. Under assumption perfect --...

There is recent evidence that the $XY$ spin model on complex networks can display three different macroscopic states in response to topology of network underpinning interactions spins. In this work, we present a novel way characterise based spectral decomposition time series using topological information about underlying networks. We use classes generate spins for possible states. then temporal Graph Signal Transform technique decompose eigenbasis Laplacian. From decomposition, produce...

Analysis and modeling of networked objects are fundamental pieces modern data mining. Most real-world networks, from biological to social ones, known have common structural properties. These properties allow us model the growth processes networks develop useful algorithms. One remarkable example is fractality which suggests self-similar organization global network structure. To determine a network, we need solve so-called box-covering problem, where preceding algorithms not feasible for...

A temporal network consists of a time series interaction events, each which is defined by triplet composed the indices two nodes and event. Mapping to more tractable static often useful. mapping method was recently proposed on basis so-called transfer entropy (G. V. Steeg A. Galstyan, in Proc. 21st Int. Conf. WWW, p.509, 2012). In method, one generates directed influence link represents causal relationship between activity patterns at nodes. However, significance inferred links sensitivity...