This document discusses temporal networks and how temporal structures can impact dynamical processes on networks. It begins by describing different types of temporal networks including person-to-person communication, information dissemination, physical proximity, and cellular biology networks. It then discusses methods for analyzing temporal network structures like inter-event times and how bursty or heavy-tailed distributions can slow spreading compared to memory-less processes. The document also presents examples of how neutralizing temporal structures like inter-event times or beginning/end times can impact spreading simulations. Finally, it discusses how different temporal network datasets exhibit diverse temporal structures.
23. History
Network
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.
24. Fat-tailed interevent time distributions
Slowing down of spreading.
10-12
10
-10
10
-8
10-6
10
-4
10
-2
10
0
10
2
10
4
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
Poisson
Power-law
Time
Incidence/N
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
25.
26.
27. Europhys. Lett., 64 (3), pp. 427–433 (2003)
EUROPHYSICS LETTERS 1 November 2003
Network dynamics of ongoing social relationships
P. Holme(∗
)
Department of Physics, Ume˚a University - 901 87 Ume˚a, 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 networks
of accumulated contacts. In this letter we explore social networks of ongoing relationships with
an emphasis on dynamical aspects. We find a distribution of response times (times between
consecutive contacts of different direction between two actors) that has a power law shape over a
large range. We also argue that the distribution of relationship duration (the time between the
first and last contacts between actors) is exponentially decaying. Methods to reanalyze the data
to compensate for the finite sampling time are proposed. We find that the degree distribution
for networks of ongoing contacts fits better to a power law than the degree distribution of
the network of accumulated contacts do. We see that the clustering and assortative mixing
coefficients are of the same order for networks of ongoing and accumulated contacts, and that
the structural fluctuations of the former are rather large.
Introduction. – The recent development in database technology has allowed researchers
to extract very large data sets of human interaction sequences. These large data sets are
suitable to the methods and modeling techniques of statistical physics, and thus, the last years
have 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 networks
28. Limited communication capacity unveils
strategies for human interaction
Giovanna Miritello1,2
, Rube´n Lara2
, Manuel Cebrian3,4
& Esteban Moro1,5
1
Departamento de Matema´ticas & GISC, Universidad Carlos III de Madrid, 28911 Legane´s, Spain, 2
Telefo´nica Research, 28050
Madrid, Spain, 3
NICTA, Melbourne, Victoria 3010, Australia, 4
Department of Computer Science & Engineering, University of
California at San Diego, La Jolla, CA 92093, USA, 5
Instituto de Ingenierı´a del Conocimiento, Universidad Auto´noma 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 large
interevent times in active ones. We develop a principled method to detect tie de-activation and apply it to a
large longitudinal, cross-sectional communication dataset (<19 months, <20 million people). Contrary to
the perception of ever-growing connectivity, we observe that individuals exhibit a finite communication
capacity, which limits the number of ties they can maintain active in time. On average men display higher
capacity than women, and this capacity decreases for both genders over their lifespan. Separating
communication capacity from activity reveals a diverse range of tie activation strategies, from stable to
exploratory. This allows us to draw novel relationships between individual strategies for human interaction
and the evolution of social networks at global scale.
any different forces govern the evolution of social relationships making them far from random. In recent
years, the understanding of what mechanisms control the dynamics of activating or deactivating social
SUBJECT AREAS:
SCIENTIFIC DATA
COMPLEX NETWORKS
APPLIED MATHEMATICS
STATISTICAL PHYSICS
Received
15 January 2013
Accepted
2 May 2013
Published
6 June 2013
Correspondence and
requests for materials
should be addressed to
E.M. (emoro@math.
32. SIR on prostitution data
0
0.1
0.2
0.3
0.1 0.2 0.90.8 10.70.60.50.40.3
0.1
1
0.01
0.001
per-contact transmission probability
durationofinfection
Ω
33. SIR on prostitution data
0
0.1
0.2
0.3
0.1 0.2 0.90.8 10.70.60.50.40.3
0.1
1
0.01
0.001
per-contact transmission probability
durationofinfection
Ω
Interevent times neutralized
34. SIR on prostitution data
0
0.1
0.2
0.3
0.1 0.2 0.90.8 10.70.60.50.40.3
0.1
1
0.01
0.001
per-contact transmission probability
durationofinfection
Ω
Beginning times neutralized
35. SIR on prostitution data
0
0.1
0.2
0.3
0.1 0.2 0.90.8 10.70.60.50.40.3
0.1
1
0.01
0.001
per-contact transmission probability
durationofinfection
Ω
End times neutralized
44. Network structures
avg. fraction of nodes present when 50% of contact happened
avg. fraction of links present when 50% of contact happened
avg. fraction of nodes present at 50% of the sampling time
avg. fraction of links present at 50% of the sampling time
frac. of nodes present 1st and last 10% of the contacts
frac. of links present 1st and last 10% of the contacts
frac. of nodes present 1st and last 10% of the sampling time
frac. of links present 1st and last 10% of the sampling time
Time evolution
degree distribution, mean
degree distribution, s.d.
degree distribution, coefficient of variation
degree distribution, skew
Degree distribution
link duration, mean
link duration, s.d.
link duration, coefficient of variation
link duration, skew
link interevent time, mean
link interevent time, s.d.
link interevent time, coefficient of variation
link interevent time, skew
Link activity
Node activity
node duration, mean
node duration, s.d.
node duration, coefficient of variation
node duration, skew
node interevent time, mean
node interevent time, s.d.
node interevent time, coefficient of variation
node interevent time, skew
Other network structure
number of nodes
clustering coefficient
assortativity
45. Network structures
0 10.5
average life time of nodes
0.10 0.2 0.3
average life time of links
fraction of nodes present after half of the contacts
0.5 10.6 0.7 0.8 0.9
x = 0.392
x = 0.418
x = 0.487
Prostitution Conference Hospital
Gallery 2Gallery 1School 1 School 2
Reality
57. 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.