Jari Saramäki

Small But Slow World: How Network Topology and Burstiness Slow Down Spreading

While communication networks show the small-world property of short paths, the spreading dynamics in them turns out slow. Here, the time evolution of information propagation is followed through communication networks by using empirical data on contact sequences and the susceptible-infected model. Introducing null models where event sequences are appropriately shuffled, we are able to distinguish between the contributions of different impeding effects. The slowing down of spreading is found to be caused mainly by weight-topology correlations and the bursty activity patterns of individuals.

Characterizing the Community Structure of Complex Networks

Background Community structure is one of the key properties of complex networks and plays a crucial role in their topology and function. While an impressive amount of work has been done on the issue of community detection, very little attention has been so far devoted to the investigation of communities in real networks. Methodology/Principal Findings We present a systematic empirical analysis of the statistical properties of communities in large information, communication, technological, biological, and social networks. We find that the mesoscopic organization of networks of the same category is remarkably similar. This is reflected in several characteristics of community structure, which can be used as “fingerprints” of specific network categories. While community size distributions are always broad, certain categories of networks consist mainly of tree-like communities, while others have denser modules. Average path lengths within communities initially grow logarithmically with community size, but the growth saturates or slows down for communities larger than a characteristic size. This behaviour is related to the presence of hubs within communities, whose roles differ across categories. Also the community embeddedness of nodes, measured in terms of the fraction of links within their communities, has a characteristic distribution for each category. Conclusions/Significance Our findings, verified by the use of two fundamentally different community detection methods, allow for a classification of real networks and pave the way to a realistic modelling of networks evolution.

Path lengths, correlations, and centrality in temporal networks

In temporal networks, where nodes interact via sequences of temporary events, information or resources can only flow through paths that follow the time ordering of events. Such temporal paths play a crucial role in dynamic processes. However, since networks have so far been usually considered static or quasistatic, the properties of temporal paths are not yet well understood. Building on a definition and algorithmic implementation of the average temporal distance between nodes, we study temporal paths in empirical networks of human communication and air transport. Although temporal distances correlate with static graph distances, there is a large spread, and nodes that appear close from the static network view may be connected via slow paths or not at all. Differences between static and temporal properties are further highlighted in studies of the temporal closeness centrality. In addition, correlations and heterogeneities in the underlying event sequences affect temporal path lengths, increasing temporal distances in communication networks and decreasing them in the air transport network.

Emergence of communities in weighted networks.

Topology and weights are closely related in weighted complex networks and this is reflected in their modular structure. We present a simple network model where the weights are generated dynamically and they shape the developing topology. By tuning a model parameter governing the importance of weights, the resulting networks undergo a gradual structural transition from a module-free topology to one with communities. The model also reproduces many features of large social networks, including the weak links property.

Persistence of social signatures in human communication

Significance We combine cell phone data with survey responses to show that a person’s social signature, as we call the pattern of their interactions with different friends and family members, is remarkably robust. People focus a high proportion of their communication efforts on a small number of individuals, and this behavior persists even when there are changes in the identity of the individuals involved. Although social signatures vary between individuals, a given individual appears to retain a specific social signature over time. Our results are likely to reflect limitations in the ability of humans to maintain many emotionally close relationships, both because of limited time and because the emotional “capital” that individuals can allocate between family members and friends is finite. The social network maintained by a focal individual, or ego, is intrinsically dynamic and typically exhibits some turnover in membership over time as personal circumstances change. However, the consequences of such changes on the distribution of an ego’s network ties are not well understood. Here we use a unique 18-mo dataset that combines mobile phone calls and survey data to track changes in the ego networks and communication patterns of students making the transition from school to university or work. Our analysis reveals that individuals display a distinctive and robust social signature, captured by how interactions are distributed across different alters. Notably, for a given ego, these social signatures tend to persist over time, despite considerable turnover in the identity of alters in the ego network. Thus, as new network members are added, some old network members either are replaced or receive fewer calls, preserving the overall distribution of calls across network members. This is likely to reflect the consequences of finite resources such as the time available for communication, the cognitive and emotional effort required to sustain close relationships, and the ability to make emotional investments.

Temporal motifs in time-dependent networks

Temporal networks are commonly used to represent systems where connections between elements are active only for restricted periods of time, such as telecommunication, neural signal processing, biochemical reaction and human social interaction networks. We introduce the framework of temporal motifs to study the mesoscale topological–temporal structure of temporal networks in which the events of nodes do not overlap in time. Temporal motifs are classes of similar event sequences, where the similarity refers not only to topology but also to the temporal order of the events. We provide a mapping from event sequences to coloured directed graphs that enables an efficient algorithm for identifying temporal motifs. We discuss some aspects of temporal motifs, including causality and null models, and present basic statistics of temporal motifs in a large mobile call network.

Temporal motifs reveal homophily, gender-specific patterns, and group talk in call sequences

Significance Social ties are more common between individuals with similar traits, a feature known as homophily. Ties are also known to be stronger between individuals with multiple common acquaintances. Both of these two properties constrain the flow of information and ideas in social networks. We study time-dependent communication patterns in a large mobile phone communication dataset and show that both of these two properties are in fact stronger than can be observed in any static snapshot of a communication network. The methods developed to obtain these results can be used more generally to study various time-dependent networks. Recent studies on electronic communication records have shown that human communication has complex temporal structure. We study how communication patterns that involve multiple individuals are affected by attributes such as sex and age. To this end, we represent the communication records as a colored temporal network where node color is used to represent individuals’ attributes, and identify patterns known as temporal motifs. We then construct a null model for the occurrence of temporal motifs that takes into account the interaction frequencies and connectivity between nodes of different colors. This null model allows us to detect significant patterns in call sequences that cannot be observed in a static network that uses interaction frequencies as link weights. We find sex-related differences in communication patterns in a large dataset of mobile phone records and show the existence of temporal homophily, the tendency of similar individuals to participate in communication patterns beyond what would be expected on the basis of their average interaction frequencies. We also show that temporal patterns differ between dense and sparse neighborhoods in the network. Because also this result is independent of interaction frequencies, it can be seen as an extension of Granovetter’s hypothesis to temporal networks.

Exploring temporal networks with greedy walks

AbstractTemporal networks come with a wide variety of heterogeneities, from burstiness of eventnsequences to correlations between timings of node and link activations. In this paper, wenset to explore the latter by using temporal greedy walks as probes ofntemporal network structure. Given a temporal network (a sequence of contacts), temporalngreedy walks proceed from node to node by always following the first available contact.nBecause of this, their structure is particularly sensitive to temporal-topologicalnpatterns involving repeated contacts between sets of nodes. This becomes evident in theirnsmall coverage per step taken as compared to a temporal reference model – in empiricalntemporal networks, greedy walks often get stuck within small sets of nodes because ofncorrelated contact patterns. While this may also happen in static networks that havenpronounced community structure, the use of the temporal reference model takes thenunderlying static network structure out of the equation and indicates that there is anpurely temporal reason for the observations. Further analysis of the structure of greedynwalks indicates that burst trains, sequences of repeated contacts between node pairs, arenthe dominant factor. However, there are larger patterns too, as shown withnnon-backtracking greedy walks. We proceed further to study the entropy rates of greedynwalks, and show that the sequences of visited nodes are more structured and predictable innoriginal data as compared to temporally uncorrelated references. Taken together, thesenresults indicate a richness of correlated temporal-topological patterns in temporalnnetworks.

Multiscale analysis of spreading in a large communication network

In temporal networks, both the topology of the underlying network and the timings of interaction events can be crucial in determining how a dynamic process mediated by the network unfolds. We have explored the limiting case of the speed of spreading in the SI model, set up such that an event between an infectious and a susceptible individual always transmits the infection. The speed of this process sets an upper bound for the speed of any dynamic process that is mediated through the interaction events of the network. With the help of temporal networks derived from large-scale time-stamped data on mobile phone calls, we extend earlier results that indicate the slowing-down effects of burstiness and temporal inhomogeneities. In such networks, links are not permanently active, but dynamic processes are mediated by recurrent events taking place on the links at specific points in time. We perform a multiscale analysis and pinpoint the importance of the timings of event sequences on individual links, their correlations with neighboring sequences, and the temporal pathways taken by the network-scale spreading process. This is achieved by studying empirically and analytically different characteristic relay times of links, relevant to the respective scales, and a set of temporal reference models that allow for removing selected time-domain correlations one by one. Our analysis shows that for the spreading velocity, time-domain inhomogeneities are as important as the network topology, which indicates the need to take time-domain information into account when studying spreading dynamics. In particular, results for the different characteristic relay times underline the importance of the burstiness of individual links.

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.