spreading processes on temporal networks

Spreading phenomena on temporal networks

Petter Holme

Temporal networks

network

Temporal networksHow can we measure them?

sociopatterns.org

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Step 1: Compartmental models

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Rocha, Liljeros, Holme, 2010. PNAS 107: 5706-5711.

Escort/sex-buyer contacts: 16,730 individuals 50,632 contacts 2,232 days

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Rocha, Liljeros, Holme, 2011. PLoS Comp Biol 7: e1001109.

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Understanding Complex Systems

Petter HolmeJari Saramäki Editors

Temporal Networks

Physics Reports 519 (2012) 97–125

Contents lists available at SciVerse ScienceDirect

Physics Reports

journal homepage: www.elsevier.com/locate/physrep

Temporal networksPetter Holmea,b,c,⇤, Jari Saramäki da IceLab, Department of Physics, Umeå University, 901 87 Umeå, Swedenb Department of Energy Science, Sungkyunkwan University, Suwon 440–746, Republic of Koreac Department of Sociology, Stockholm University, 106 91 Stockholm, Swedend Department of Biomedical Engineering and Computational Science, School of Science, Aalto University, 00076 Aalto, Espoo, Finland

a r t i c l e i n f o

Article history:Accepted 1 March 2012Available online 6 March 2012editor: D.K. Campbell

a b s t r a c t

A great variety of systems in nature, society and technology – from the web of sexualcontacts to the Internet, from the nervous system to power grids – can be modeled asgraphs of vertices coupled by edges. The network structure, describing how the graph iswired, helps us understand, predict and optimize the behavior of dynamical systems. Inmany cases, however, the edges are not continuously active. As an example, in networksof communication via e-mail, text messages, or phone calls, edges represent sequencesof instantaneous or practically instantaneous contacts. In some cases, edges are active fornon-negligible periods of time: e.g., the proximity patterns of inpatients at hospitals canbe represented by a graph where an edge between two individuals is on throughout thetime they are at the same ward. Like network topology, the temporal structure of edgeactivations can affect dynamics of systems interacting through the network, from diseasecontagion on the network of patients to information diffusion over an e-mail network. Inthis review, we present the emergent field of temporal networks, and discuss methodsfor analyzing topological and temporal structure and models for elucidating their relationto the behavior of dynamical systems. In the light of traditional network theory, one cansee this framework as moving the information of when things happen from the dynamicalsystem on the network, to the network itself. Since fundamental properties, such as thetransitivity of edges, do not necessarily hold in temporal networks, many of thesemethodsneed to be quite different from those for static networks. The study of temporal networks isvery interdisciplinary in nature. Reflecting this, even the object of study has many names—temporal graphs, evolving graphs, time-varying graphs, time-aggregated graphs, time-stamped graphs, dynamic networks, dynamic graphs, dynamical graphs, and so on. Thisreview covers different fields where temporal graphs are considered, but does not attemptto unify related terminology—rather, we want to make papers readable across disciplines.

© 2012 Elsevier B.V. All rights reserved.

Contents

1. Introduction.......................................................................................................................................................................................... 982. Types of temporal networks................................................................................................................................................................ 100

2.1. Person-to-person communication.......................................................................................................................................... 1002.2. One-to many information dissemination............................................................................................................................... 1012.3. Physical proximity ................................................................................................................................................................... 1012.4. Cell biology............................................................................................................................................................................... 101

⇤ Corresponding author at: IceLab, Department of Physics, Umeå University, 901 87 Umeå, Sweden.E-mail address: [email protected] (P. Holme).

0370-1573/$ – see front matter© 2012 Elsevier B.V. All rights reserved.doi:10.1016/j.physrep.2012.03.001

Holme, Scientific Reports, 2015.

Time matters

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HistoryNetwork

1. Laszlo Barabási discovers a power-law.

2. It makes a difference for spreading dynamics.

3. It helps us to understand real epidemics.

Time

1. Laszlo Barabási discovers a power-law.

2. It makes a difference for spreading dynamics.

3. It helps us to understand real epidemics.

Fat-tailed interevent time distributions

Slowing down of spreading.

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Min, Goh, Vazquez, 2011. PRE 83, 036102.

But both the cell phone and the prostitution data are bursty. So why are they different w.r.t. spreading?

Interevent times

Europhys. Lett., 64 (3), pp. 427–433 (2003)

EUROPHYSICS LETTERS 1 November 2003

Network dynamics of ongoing social relationships

P. Holme(∗)Department of Physics, Umea University - 901 87 Umea, Sweden

(received 21 July 2003; accepted in final form 22 August 2003)

PACS. 89.65.-s – Social and economic systems.PACS. 89.75.Hc – Networks and genealogical trees.PACS. 89.75.-k – Complex systems.

Abstract. – Many recent large-scale studies of interaction networks have focused on networksof accumulated contacts. In this letter we explore social networks of ongoing relationships withan emphasis on dynamical aspects. We find a distribution of response times (times betweenconsecutive contacts of different direction between two actors) that has a power law shape over alarge range. We also argue that the distribution of relationship duration (the time between thefirst and last contacts between actors) is exponentially decaying. Methods to reanalyze the datato compensate for the finite sampling time are proposed. We find that the degree distributionfor networks of ongoing contacts fits better to a power law than the degree distribution ofthe network of accumulated contacts do. We see that the clustering and assortative mixingcoefficients are of the same order for networks of ongoing and accumulated contacts, and thatthe structural fluctuations of the former are rather large.

Introduction. – The recent development in database technology has allowed researchersto extract very large data sets of human interaction sequences. These large data sets aresuitable to the methods and modeling techniques of statistical physics, and thus, the last yearshave witnessed the appearance of an interdisciplinary field between physics and sociology [1–3].More specifically, these studies have focused on network structure —in what ways the networksof social interaction deviate from completely random networks, and how this structure canemerge from individual behavior. Most [4] of these recent large-scale social-network studieshave focused on networks of accumulated relationships. In many cases, the social network ofinterest is rather the network of ongoing social relationships: The dynamics of the spreadingof diseases [5], opinion formation [6], and fads [7] are often rather fast compared to theevolution of the network —in such cases, inactive relationships have no relevance. In socialsearch processes [8], distant acquaintances can be helpful, but not all acquaintances a personhas ever had. We also believe that the network of ongoing contacts lies conceptually closerto the colloquial idea of a network of friends than what the network of actors and theiraccumulated contacts do. Furthermore, traditional social-network studies (e.g., refs. [9–11])based on interviews or field surveys have mapped out ongoing contacts. The complication,and probably the reason why earlier studies have focused on the network of accumulated

(∗) E-mail: [email protected]

c⃝ EDP Sciences

Limited communication capacity unveilsstrategies for human interactionGiovanna Miritello1,2, Ruben Lara2, Manuel Cebrian3,4 & Esteban Moro1,5

1Departamento de Matematicas & GISC, Universidad Carlos III de Madrid, 28911 Leganes, Spain, 2Telefonica Research, 28050Madrid, Spain, 3NICTA, Melbourne, Victoria 3010, Australia, 4Department of Computer Science & Engineering, University ofCalifornia at San Diego, La Jolla, CA 92093, USA, 5Instituto de Ingenierıa del Conocimiento, Universidad Autonoma de Madrid,28049 Madrid, Spain.

Connectivity is the key process that characterizes the structural and functional properties of social networks.However, the bursty activity of dyadic interactions may hinder the discrimination of inactive ties from largeinterevent times in active ones. We develop a principled method to detect tie de-activation and apply it to alarge longitudinal, cross-sectional communication dataset (<19 months, <20 million people). Contrary tothe perception of ever-growing connectivity, we observe that individuals exhibit a finite communicationcapacity, which limits the number of ties they can maintain active in time. On average men display highercapacity than women, and this capacity decreases for both genders over their lifespan. Separatingcommunication capacity from activity reveals a diverse range of tie activation strategies, from stable toexploratory. This allows us to draw novel relationships between individual strategies for human interactionand the evolution of social networks at global scale.

Many different forces govern the evolution of social relationships making them far from random. In recentyears, the understanding of what mechanisms control the dynamics of activating or deactivating socialties have uncovered forces ranging from geography to structural positions in the social network (e.g.

preferential attachment, triadic closure), to homophily1. These finding are pervasive in empirical analyses acrosscultures, communication technologies and interaction environments2–11.

However, the incorrect assumption that time, attention and cognition are elastic resources has blurred thestudy of how individuals manage their social interactions over time12–14. Understanding such social strategies isnot only of paramount importance to make progress in the characterization of human behavior, but also toimprove our current description of social networks as evolutionary objects against the (aggregated) ever-growingor static pictures of the social structure.

Several reasons have hampered the observation of tie activation/deactivation dynamics in social networks atlarge scale: on the one hand, studies of diffusion based on datasets from pre-electronic eras have safely assumedthat tie activation/deactivation is a much slower process than interactions within a tie, and thus their dynamicsmight be safely neglected15–17. However, the current ability to communicate faster and further than ever accel-erates tie dynamics in an unprecedented manner to the point that tie activation/deactivation may rival in timewith processes like information spreading. On the other hand, available data about how ties form or decay wererestricted to egocentric, small social networks and/or short periods of time which made it difficult to assess theuniversality of the results obtained and their extension to other situations5. Finally, although in some online socialnetworks there are explicit rules for the establishment of social ties, in most cases activity is the only way to assessthe existence of the tie18,19. Online social networks are plagued with this problem due to the cheap cost ofmaintaining ‘‘friends’’ which are in fact already deactivated relationships20. However, using activity as proxyfor tie presence is a problem in most communication channels like mobile phone calls, emails, electronic socialnetworks etc., since tie activity is very bursty21 and so far there is no clear method to discriminate those social tiesthat are already inactive from large-inter even times within active relationships42.

ResultsDetection of tie activation/deactivation. To study the formation and decay of communication ties, we study theCall Detail Records (CDRs) from a single mobile phone operator over a period of 19 months. The data consists ofthe anonymized voice calls of about 20 million users that form 700 million communication ties. After filtering outall the incoming or outgoing calls that involve other operators, we only consider users that are active across thewhole time period and retain only ties which are reciprocated. We refer to Methods Section and the Supplementary

SUBJECT AREAS:SCIENTIFIC DATA

COMPLEX NETWORKS

APPLIED MATHEMATICS

STATISTICAL PHYSICS

Received

15 January 2013

Accepted

2 May 2013

Published

6 June 2013

Correspondence andrequests for materials

should be addressed toE.M. (emoro@math.

uc3m.es)

SCIENTIFIC REPORTS | 3 : 1950 | DOI: 10.1038/srep01950 1

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Holme, Liljeros, 2014. Scientific Reports 4: 4999.

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…a no-brain (low-brain?) approach

but what about yet other structures?

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Network structuresavg. fraction of nodes present when 50% of contact happenedavg. fraction of links present when 50% of contact happenedavg. fraction of nodes present at 50% of the sampling timeavg. fraction of links present at 50% of the sampling timefrac. of nodes present 1st and last 10% of the contactsfrac. of links present 1st and last 10% of the contactsfrac. of nodes present 1st and last 10% of the sampling timefrac. of links present 1st and last 10% of the sampling time

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link duration, meanlink duration, s.d.link duration, coefficient of variationlink duration, skewlink interevent time, meanlink interevent time, s.d.link interevent time, coefficient of variationlink interevent time, skew

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Node activitynode duration, meannode duration, s.d.node duration, coefficient of variationnode duration, skewnode interevent time, meannode interevent time, s.d.node interevent time, coefficient of variationnode interevent time, skew

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Reality

Vaccination

Assume we can vaccinate a fraction f, then how can we choose the people to vaccinate? Using only local info?

Vaccination

Chose a person at random.

Neighborhood vaccination Cohen, Havlin, ben Avraham, 2002.

Ask her to name a friend.


Vaccinate the friend.


Lee, Rocha, Liljeros, Holme, 2012. PLoS ONE 7:e36439.

Vaccination

Vaccination

Other temporal networks results

Spreading by threshold dynamics Takaguchi, Masuda, Holme, 2013. Bursty communication patterns facilitate spreading in a threshold-based epidemic dynamics. PLoS ONE 8:e68629. Karimi, Holme, 2013. Threshold model of cascades in empirical temporal networks. Physica A 392:3476– 3483.

Random walks Holme, Saramäki, 2015. Exploring temporal networks with greedy walks. Eur J Phys B 88:334.

Review papers Masuda, Holme, 2013. Predicting and controlling infectious disease epidemics using temporal networks. F1000Prime Rep. 5:6. Holme, 2015. Modern temporal network theory: A colloquium. Eur J Phys B 88:234. Holme, 2014. Analyzing temporal networks in social media, Proc. IEEE 102:1922–1933.

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Thank you! Спасибо!

Collaborators:

Jari Saramäki

Naoki Masuda

Luis Rocha

Sungmin Lee

Fredrik Liljeros

Fariba Karimi

Illustrations by:

Mi Jin Lee