Daily Rhythms in Mobile Telephone Communication
Daily Rhythms in Mobile Telephone Communication
Talayeh Aledavood talayeh.aledavood@aalto 0 1
Eduardo López 0 1
Sam G. B. Roberts 0 1
Felix Reed-Tsochas 0 1
Esteban Moro 0 1
Robin I. M. Dunbar 0 1
Jari Saramäki 0 1
0 1 Department of Computer Science, Aalto University School of Science , Espoo , Finland , 2 CABDyN Complexity Center, Saïd Business School, University of Oxford , Oxford , United Kingdom , 3 Department of Psychology, University of Chester, Chester, United Kingdom, 4 Department of Sociology, University of Oxford , Oxford , United Kingdom , 5 Departamento de Matemáticas & GISC, Universidad Carlos III de Madrid , Leganós , Spain , 6 Department of Experimental Psychology, University of Oxford , Oxford , United Kingdom
1 Editor: Renaud Lambiotte, University of Namur , BELGIUM
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 morninglike 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 18month 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.
Funding: TA and JS were funded by The Academy
of Finland, project No. 260427 (http://www.aka.fi) and
the computational resources were provided by Aalto
379 Science-IT project. The study was funded by a
grant from the UK Engineering and Physical
Sciences Research Council and Economic and
Social Research Council (grant No. EP/D052114/2).
RD is funded by European Research Council (grant
Human activity follows a circadian rhythm that is reflected at the psychological, physiological
and biochemical levels [1–3]. This rhythm is mainly driven by endogenous cellular
mechanisms, but it may be modulated by exogenous factors. Circadian rhythms are in general
synchronized to the day-night cycle. However, within this cycle, there are differences between
individuals, and individuals’ levels of alertness vary following different trajectories throughout
the day. Notably, there are morning and evening types, those who tend to wake up early and
those who prefer to sleep late. This may result from intrinsic differences in the circadian
pacemaker circuit, possibly of genetic origin. Morningness and eveningness of individuals have also
Competing Interests: The authors have declared
that no competing interests exist.
been associated with gender and personality traits [4–6]; typically, these studies have been
conducted with the traditional methods of surveys and questionnaires. In studies of statistics
aggregated over large numbers of individuals, circadian patterns and daily cycles have been
observed in a wide range of phenomena: in human suicidal acts, in times of exhibiting
unethical behaviour, in times of sexual activity, and in times of heart attacks [7–10].
Aggregate-level daily rhythms are also known to appear in electronic records of human
activity, from mobility  to Wikipedia and OpenStreetMap edits [12, 13], activity on Twitter ,
and the number of mobile phone calls per hour [15, 16]. In addition to the day-night cycle,
these patterns are modulated by a number of endogenous factors such as the daily work
schedule, commuting patterns , the activity patterns of one’s social circles, and even one’s life
circumstances such as employment or unemployment . In general, in such studies of daily
rhythms inferred from electronic records, the focus has typically remained at the aggregate level.
In this paper, we use a unique longitudinal dataset [18, 19] that combines questionnaire
data with mobile phone records, allowing us to take an individual-centric point of view instead
of focusing on aggregates. In particular, since the activity levels of individuals are known to
display individual differences, in particular morningness and eveningness, we want to see whether
there are also clear individual differences in daily call frequency patterns. Further, we want to
address the persistence of these differences. First, this is to guarantee that individual differences
are real and not only because of random fluctuations giving rise to diversity. Second, we also
use the concept of persistence to address the issue of intrinsic versus exogenous drivers. Our
data set has been collected during a period of high network turnover for the individuals, and
thus if daily patterns are seen to persist, they cannot be purely driven by one’s social network.
In addition, we want to uncover details of the observed patterns and to look for “patterns
within patterns”: are certain times of day reserved for calling certain alters, or are calls typically
placed to random individuals? Do the properties of callers and callees, such as gender, explain
some features of the observed patterns?
To this end, we employ a data set that comprises the exact times and recipients of all
outgoing mobile phone calls of 24 individuals (“egos” in the following) for 18 months. This data set
consists of 74,124 phone calls altogether. This set was originally collected for the purpose of
studying social network turnover over time : during the study, the participants finish high
school and go to work or university (often in another city), which gives rise to major turnover
in their personal networks. At the beginning of the study, the students are still at high school.
Thereafter, they begin their first university year or go to work at around month 6 of the study
(after the summer holiday period). This gives rise to turnover, and in general, should result in
rather different exogenous factors affecting the daily patterns from the beginning to the end of
the study. This is also reflected in an increase in the total number of calls made by the
participants from around month 6 (see Fig 1 in ). The mobile phone call data set is accompanied
by 3 surveys on the contacts who were called (“alters” in the following), including their gender
and information on kinship.
Together, these data allow us to study the daily rhythms of calls in terms of numbers and in
terms of recipients (who is called and when). We find that in terms of call frequency at each
hour of day, each individual has their distinct, persistent pattern. These daily patterns persist
for individuals despite a high degree of network turnover, and thus appear to be characteristics
of individual egos, rather than dependent on the identify of specific alters. Within these
patterns, there are clear variations in the entropy of called alters, indicating that certain times of
day (evening and night, typically) are reserved for calling specific alters, whereas at other times
the recipients of calls are more diverse. For female egos, there is an additional increase in the
average duration of calls towards the night—these long calls are typically made to friends
instead of family members.
We begin by computing the daily call patterns for all 24 egos. The data time span is divided to
three consecutive 6-month intervals I1, I2, and I3. For each ego and each 6-month interval, we
compute the average fraction of calls placed at each hour of the day. Considering 6-month
intervals separately allows investigation of the persistence of any observed differences: were
specific features of individual patterns due to random fluctuations alone, they would not persist
over all intervals.
The resulting daily call patterns for 8 representative egos (4 male, 4 female) for all intervals
are displayed in Fig 1. Two features clearly stand out: First, while the call patterns of all egos
follow the day-night cycle and calls at night are infrequent, there are significant differences
between individuals. As an example, the ego whose pattern is displayed in panel a) makes more
calls in the morning than others, whereas for the ego of panel g) there are frequent calls at late
hours. Second, it appears that each individual’s specific patterns are rather similar in all
6-month intervals. Both observations hold for all 24 egos. This persistence is noteworthy, since
it is known that at the same time, the social networks of these individuals undergo major
turnover . Because of this, the observed persistence points towards intrinsic driving forces
behind the daily patterns, as these do not strongly depend on an ego’s personal network
The persistence of individual daily patterns is confirmed with a more detailed analysis. Here
we use the approach of Ref.  to show that the daily call patterns of an individual in different
time intervals are more similar than the patterns of different egos within one time interval. We
use the Jensen-Shannon divergence (JSD) (see Materials and Methods for details) to measure
the difference between daily call patterns. For each ego, we calculate two different distances:
self (dself) and reference (dref). The self-distance dself for an individual i is the average JSD
between the call patterns in (I1, I2) and (I2, I3): di;self ¼ 12 d1i;2self þ d2i;3self . The reference distance
measures the divergence of patterns of different egos in one time interval. For each time
interval we calculate JSD between daily patterns of egos i and j: drijef ¼ 31 d1ij1 þ d2ij2 þ d3ij3 . As seen in
Fig 2, dself takes on average lower values than dref, meaning that there is more similarity
between an ego’s consecutive daily patterns than between the patterns of different egos in one
interval. The motivation behind this approach is as follows: while an ego’s consecutive patterns
Fig 1. The daily call patterns of 8 individuals (a-h). The red lines denote the average fraction of calls
placed at the corresponding hour for each of the three intervals I1 (solid line), I2 (dashed line), and I3
(dashdotted line). The black line is the average call pattern of all 24 individuals over all intervals. Areas shaded
green show where an individual’s fraction of calls exceeds the average, while areas shaded red show where
it falls below the average.
Fig 2. Histogram of dself and dref calculated for each ego. This plot shows the results for all egos and all time intervals.
retain their overall shapes well (Fig 1), they are not exactly similar and there are a lot of
fluctuations. Therefore, the aim is to look for persistence by checking whether consecutive patterns of
an ego show a high level of similarity; however, to assess whether similarity is high or low a
scale is required. The natural scale to use is that given by the similarities between patterns of all
egos; if one ego’s pattern remains more similar to itself than it is to others, we call it persistent.
On average, for each ego, 87% ± 12% of reference distances are higher than self-distances.
Comparing average values of distances over all egos we get hdrefi = 0.083 ± 0.28 while hdselfi =
0.05 ± 0.22 (hdselfi < hdrefi with t = 6.98 and p 10−6, two-sample unequal variance t-test). To
validate these results with another method, we have used the ℓ2 norm (see Methods), and the
results qualitatively agree with JSD: hdselfi = 0.11 ± 0.02 and hdrefi = 0.14 ± 0.03 with t = 6.11,
p < 10−5. We also used the Kolmogorov-Smirnov test on each ego’s successive patterns, and
found that the null hypothesis of patterns being similar cannot be rejected in 44 out of 48 cases
with confidence level p = 0.01.
As an alternative to the above, we have verified the persistence of patterns with
coarsegrained daily patterns and a distance measure whose values are easier to interpret directly. To
this end, we begin by coarse-graining the patterns and compute the fraction of calls placed in
6-hour bins (night: 0AM–6AM, morning: 6AM–12AM, afternoon: 12AM–6PM, evening:
6PM–12PM) for each ego and each 6-month interval. Then, using all egos, we generate a
common reference pattern by computing the median fraction of calls in each 6-hour bin, either a)
for the whole 18-month interval or b) separately for each 6-month interval. We then take each
ego’s pattern in each interval, and for each 6-hour bin, check whether the fraction of calls is
above the median (‘+’) or below the median (‘−’). This yields a string of four characters for
each ego and interval, e.g. ‘++−−’ denotes that for the focal ego and interval, the fraction of
calls is above median at night and in the morning, but below median in the afternoon and
evening. Then, we compute the Hamming distances between each ego’s strings in different
intervals, where a distance of 0 means that the strings are identical and a distance of 4 means
that all characters differ. For both a) and b), i.e. 18-month or interval-specific median
references, the outcome is that the average Hamming distance is dH = 1.1 characters, which is low
(note that the fraction of calls in a bin is categorized as above median (‘+’) even if it exceeds the
median by a vanishingly small amount, so we do not expect zero distances). Were the patterns
changing randomly independently of one another, this average distance would be dH,ref = 2.0;
taking the distributions of Hamming distances for the observed patterns and the multinomial
distribution centered around 2.0, the difference in means is significant with p < 10−5.
Alter-specificity in call patterns
We next turn to the question of where the individual daily patterns come from, and study the
extent of a social component -that is, alter-specificity- in the call patterns. One can conceive of
two extreme cases: 1) The patterns are entirely endogenous and the rate of call activity at each
hour of the day is intrinsic to the ego. In this case, the called alters are picked at random
(however, with a weight proportional to the time-averaged fraction of calls to each alter). 2) The
patterns are alter-specific, that is, calls to certain alters are placed at certain hours, and the daily
pattern is a superposition of the alter-specific patterns.
To assess the extent of alter-specificity, we again divide the day into 6-hour time spans
(night: 0AM–6AM, morning: 6AM–12AM, afternoon: 12AM–6PM, evening: 6PM–12PM),
and for each alter and each time span, compute the relative call entropies Hrel. First, call
entropies Horig are calculated from the original data for each 6-hour span. To get the relative
entropies Hrel, these values are then divided by average entropies hHrefi calculated for a reference
model where the times of calls to all alters are shuffled on a weekly basis for each ego (see
Methods). If for a given 6-hour span Hrel < 1, calls to certain alters are emphasized within that
time span, whereas if Hrel 1, there is no alter-specificity. Note that the relative entropies can
be Hrel > 1. This can happen because of the following: suppose that for some hour, calls are
placed evenly on a number of alters in the original data, resulting in high entropy. At the same
time, some other alter (‘A’) receives very many calls outside this hour. Then, when the data are
shuffled, this alter ‘A’ replaces many of the alters of the high-entropy hour, i.e. now several of
the calls during that hour are directed at ‘A’. Because of this, the average entropy of this hour is
then lower in the shuffled data, and subsequently, Hrel > 1.
The relative entropies Hrel for the same 8 individuals as in Fig 1 are displayed in Fig 3,
together with averaged relative entropy for all 24 individuals over all three intervals. The
average relative entropy is at its highest in the afternoon, with hHreli 1, indicating large diversity
of called alters. hHreli has its lowest point at night, when the number of calls is also low (see Fig
1). This indicates that the few calls made at night are typically directed to specific alters. As
with the call frequency patterns, Fig 1 clearly points out that the entropy patterns of different
egos are different (compare, e.g., panels d and e). Likewise, each ego’s patterns appear fairly
Fig 3. The relative entropies for the same 8 individuals as in Fig 1, calculated for 6-hour intervals (M: morning 6AM-12AM, A: afternoon 12AM-6PM,
E: evening 6PM-0AM, N: night 0AM-6AM). (ο): interval I1, (◻): interval I2, (^): interval I3. The black line indicates the average relative entropy for all 24
individuals over all three intervals.
persistent; however, there is more variation here, especially in the morning and at night when
the call frequency is low and the entropy measures are as a result noisy. However, in general,
deviations of the original entropies from the reference model’s mean are statistically significant;
as the reference model’s standard deviation is fairly small, the typical deviation is > 2 std’s.
We next focus on the specific alters behind the low-entropy times of day. For this, we first
count the total number of calls by each ego to each alter in each interval, and rank the alters of
each ego according to this number. Alter ranks based on number of calls are known to reflect
both the level of emotional closeness between ego and alter (as indexed on a standard
psychological 1–10 emotional closeness scale), and the frequency face-to-face contact between ego
and alter: in  it was shown that the number of calls significantly predicts emotional
closeness, for the same data set as studied in the present manuscript.
Then, for each 6-hour interval (morning, afternoon, evening, and night) we calculate the
fraction of calls directed at the two top-ranked alters (in the respective interval). These
fractions are shown in Fig 4, again for the same individuals as in Fig 1. On average, it appears that
the fraction of calls to two top-ranked alters of each ego increases towards late hours and is
often the highest at night, when there is in general only a small number of calls and low relative
entropy. The high fractions indicate that decrease of entropy towards night often comes from
calls to top-ranked alters (note that we cannot rule out that this particular behaviour might be
associated with the cohort’s age group and their general circumstances instead of being a
general feature of human communication). Also, there is individual variation and although the
top-alter fractions are often similar across intervals, in some cases, interval I1 behaves
differently. This interval corresponds to the participants finishing high school and the following
summer holidays, so differences in call behavior can be expected.
Fig 4. The fractions of calls to the two top-ranked alters for the same 8 individuals as in Fig 1, calculated for the same 6-hour intervals as in Fig 3
(M, A, E, N). (ο): interval I1, (◻): interval I2, (^): interval I3.
Because Figs 3 and 4 point towards a correlation between low entropy and calls to
topranked alters, we next quantify this as follows: As the baseline levels and slopes of Fig 4 have a
lot of variation, we take each ego and their relative entropies and fractions of calls to
topranked alters at each 6-hour interval. Then, we compute the Pearson correlation coefficient
between entropies and top-alter fractions for all egos. Out of the resulting 24 correlation
coefficients, 14 were significant with p < 0.05, with three positive coefficients and 11 negative
averaging at r −0.71. Thus for more than half of the egos, low entropy is clearly associated with a
high fraction of calls to top alters, while for almost all the rest, no conclusive results can be
drawn (note that taking a very conservative approach regarding false positives and applying
the Bonferroni correction as if we were dealing with a multiple comparison test would result in
4 significant negative coefficients and 1 significant positive coefficient, with the majority of the
few surviving coefficients still negative).
Since there are alter-specific communication patterns and the nature of communication
depends on the time of day, we also look at call durations at different times. Here, we use data
on ego and alter attributes from the conducted surveys. Previous studies have looked at gender
differences in talkativeness as well as differences in usage of phones(both for landlines and
mobile phones) [20–22], using data from different countries and age groups. Most of the recent
studies of talkativeness suggest that men and women are similar [20, 23]. However in most
studies which compare phone usage difference between men and women, women have been
reported to have longer calls [24, 25]. The differences in phone usage of males and females
have been linked to their different social roles [26–28]; it has also been observed that the
temporal communication patterns formed by groups of male or female participants differ .
Here, we add two more dimensions and look at call durations at different times of the day, as
well as durations of calls to different types of social links (kin or friend/acquaintance).
Fig 5. Average duration of calls made by males and females to their kin, friends, and all social contacts.
Fig 5 shows that overall, the average durations of calls by females are longer than those of calls
by males, and that the difference largely depends on the time of day such that it increases towards
the evening and is highest at night. A closer look shows that this difference arises mostly from
calls to friends. Male and female call durations to kin are fairly similar and do not depend much
on the time of day. When the gender of the called alters is analysed (Fig 6), it is seen that by far
the longest calls are by female egos to male alters at night; again the differences are the smallest
in the afternoon, i.e. when all egos are typically in a similar social setting (at school, work, or
university). The finding agrees with previous studies which suggest that females have different
bonding strategies and use phones for different purposes compared to men [27, 30]. Since nighttime
calls are often targeted at top-ranking alters (who typically are emotionally close ), and the
egos are in their late teens and are possibly experiencing emotionally intense relationships with
their romantic partners, it is likely that these long calls often relate to romantic relationships.
Since we have a relatively small sample of individuals (24 total), one might think that the
high values for call durations for females in afternoons and nights might only be caused by one
Fig 6. Comparison of the average duration of calls to social contacts of the same and opposite gender, separately for females and males.
or few females who make very long calls in those hours. To rule out this possibility, for each
individual we compare call durations made in the morning or afternoon with duration of calls
made in the afternoon or night, using two-sample unequal variance t-test. We see that for 9 out
of 12 females p-values for this test are less than 10−6, whereas only for 2 males out of 12 we
have such small p-values. These results are also consistent with findings of Dong et al. ,
who have analysed a dataset of 3.9 million call records over a timespan of 2 months and have
found that young females make longer calls especially in the evening.
In contrast to conventional studies on daily patterns and circadian rhythms in social networks
that focus on aggregates of very large numbers of individuals, here we focused on a small but
rich sample that combined questionnaire and mobile phone data in order to be able to explore
in much greater detail features that characterise individuals’ circadian rhythms. Our focus has
been on three specific issues, namely (1) whether there are individual-specific patterns of
calling that mirror previously demonstrated individual patterns in the way individuals allocate
their social capital to their alters; (2) whether the individual-specific patterns of calling are
persistent in light of network turnover and (3) whether there are gender differences in calling
patterns. We show that individuals do indeed have different daily patterns of call activity. These
patterns vary beyond simple morningness/eveningness, as measured in questionnaire studies,
and appear to be characteristic of the individual, in much the same way as their characteristic
way of distributing their social capital among their alters . Thus these individual patterns
are persistent, in that the pattern of distributing calls across the day is consistent across the
three time periods, despite the high degree of network turnover in the 18 months of the study,
associated with leaving school and entering work or University [18, 19]. Note, however, that
persistence despite social network turnover does not necessarily mean that egos’ daily patterns
are entirely independent of those of their alters. Rather, it may well be that the patterns are
dominated by characteristics intrinsic to egos (such as morningness/eveningness), while there
is still some synchronization taking place at the same time. Our entropy results point towards
this possibility: for a number of egos, closest friends are called around certain hours, and very
probably, this behaviour is reciprocated (but not detectable in our data since we only have
details on outgoing calls). In studies with big data—millions of anonymized call records—it is
clearly seen that incoming calls trigger returned calls, which is clear evidence of
synchronization [32–34]. In general, studying the synchrony of the daily patterns of connected individuals
would be an interesting problem.
We also showed that there are gender differences in call duration pattern across the day:
while women’s calls are generally longer than men’s calls, this was especially true during the
evening and at night. Evening calls to males and to friends by female egos were especially long,
and often involved calls to specific individuals, usually the top-ranked alters, who may be
Given that humans naturally spend the night asleep, the tendency for calls to exhibit a
striking diurnal periodicity is not, of itself, especially surprising, of course. However, in our sample,
the vast majority of calls were made between midday and late evening, with the bulk of these
occurring in the 6-hour slot between 12AM-6PM Fig 1. It is notable that, despite our essentially
diurnal nature, rather few calls were made before midday. Therefore, it is possible that most
calls made by our cohort of subjects are social rather than functional (i.e. work or
leisure-activity related). Interestingly, for many egos, communication at late evening and night frequently
involves their closest friends. One could ask whether our social behaviour is in general different
at night and during daylight hours. Wiessner  reported that certain types of conversations
(notably story-telling and social conversations) are much more common during the evening
than during the day among !Kung San hunter gatherers, with conversations involving
economic matters or social criticism taking place mainly during daylight hours. In her sample,
81% of evening fireside conversations involved storytelling (relaying of adventures or
experiences, especially in far off places, or tales about myths, social conventions and rituals,
experiences during trance states or real life travels).
Within this broad pattern, the individual differences in the distribution of calling, and
particularly the persistence of these individual differences in the light of social network turnover,
are strongly suggestive of some kind of personality characteristic. It is possible that these
differences in personal style simply reflect individual differences in circadian pattern [4–6], and are a
consequence of the fact that some individuals are more active in the morning and others more
active in the evening. It is perhaps less likely that the calling patterns are due to differences in
individual sleep/wake cycles, since the demands of the working day are likely to have required
everyone to be active in the morning and even early risers are unlikely to have gone to bed by
6PM (note that circumstances such as unemployment do have effects on daily cycles of
individuals, see ). However, it could be that, physiologically, morning people are more likely to
feel motivated to be socially engaged in the daytime and evening people more likely to be so in
the evening. The fact that some individuals find the evening hours particularly attractive, while
others prefer the day, remains intriguing in this context and obviously merits more detailed
Notwithstanding the fact that some individuals are night-oriented and others day-oriented,
it seems that many (though not all) egos prefer to call certain alters at night. These are typically
the one or two individuals (mainly males and friends) that have special status for the ego (Fig
4). We know from our detailed questionnaire data that the individuals that egos call most often
are those to whom they are emotionally closest, and those they have the most frequent
face-toface contact with . It seems that this is especially characteristic of female egos, and much
less so of male egos. Unlike women, men do not call either their girlfriends or their same-sex
best friends for long chats in the evenings (even though their girlfriends may call them). This
striking sex difference in who actively makes the effort to call is reminiscent of the finding
reported by Palchykov et al. , for a very large cellphone dataset, that younger women (in
particular) are much more proactive in calling their primary male contact than are men. This
striking difference between the two sexes may reflect women’s more intensely social nature
compared to men.
For both sexes, it was much less common to call kin during the evening. This would
reinforce the claim that relationships with kin are less fragile than those with friends, and hence
require less persistent and less special servicing . Reserving calls to these individuals for
times of the day when they are, or might seem to be, more intimate may reinforce the sense
that the relationship is special. In effect, kin relationships come for free by virtue of the fact
that they are kin and ego is embedded in a densely interconnected web of relationships with
them, and therefore require less active maintenance. In contrast, the quality of friendships
deteriorates rapidly (within months) in the absence of sufficiently frequent contact [18, 37, 38].
A strength of our study was that it combined detailed mobile phone records with
questionnaire data. Thus we have information on the nature of the relationship between egos and the
alters they are calling, in terms of gender, kinship and emotional intensity. Further, we know
from previous findings that the number and duration of phone calls relates to the emotional
intensity of the relationship, as well as the level of social activity [18, 19]. This dataset therefore
allows for analysis of the social nature of circadian rhythms, rather than simply examining
aggregate analyses of mobile phone activity or broad scale questionnaire data. Even though the
sample size is relatively small due to the intensive, longitudinal data collection, the nature of
the data allows us to add a level of individual detail on identity of the callers and callees. Our
results may help interpreting the results of big data studies (e.g. on related themes of
information propagation and temporal communication motifs [29, 32, 33, 39].
Materials and Methods
Our data and its use
Our dataset includes 18 months of outgoing call and text records of the 24 individuals. In this
study we have only used the call records (both to mobile phones and landlines). In addition to
this mobile phone data, participants completed 3 questionnaires about the people in their social
network at the beginning (month 0), in the middle (month 9) and at the end (month 18) of the
study. They identified each contact (alter) as kin or non-kin, and provided all the different
phone numbers that one contact might possibly have. Therefore these records are very
comprehensive and do not miss calls or texts because an alter has several phone numbers (with
multiple phone providers) and/ or uses a landline. In the social network questionnaires,
participants provided information about each alter, including gender, how emotionally close they are
to the person and the frequency of face-to-face contact with the person. The data on phone
calls was obtained from the fully time-stamped, itemised monthly bills. These itemised bills
were accessed by one of the researchers (S.G.B.R.) from the individual online accounts the
participants had with the mobile telephone operator, with the written consent of the participants.
As compensation for taking part in the study, the participants were given a mobile phone with
an 18 month contract from a major UK mobile telephone operator. The line rental for the
mobile phone was paid for and included 500 monthly free voice minutes (to landlines or
mobiles) and unlimited text messages. The participants, questionnaire and mobile phone
datasets are described fully in previous publications [18, 19]. Anonymized, aggregated data is
available online and the detailed time-stamped data used in this study is available on request. This
study was approved by the Ethics Review Committee of the University of Liverpool (the
institution at which the data collection phase of this project was originally initiated). Written
informed consent was obtained from all participants prior to data collection.
To calculate daily patterns of each ego, we have taken data from all days in the time interval of
interest and have allocated each call to a 6-hour time bin based on its time stamp. We then
count total number of events of each hour and divide it by total number of events (of that ego)
during the the time interval, to get the fraction of calls in that hour. In each time interval, we
only used data of complete weeks in that time interval.
Measuring similarity of patterns
The Jensen-Shannon divergence is a measure of the difference of two probability distributions.
It is a form of Kullback-Leibler divergence (KLD); unlike KLD, it works for probability
distributions that contain zero-valued elements. The JSD for two discrete probability distributions
P1 and P2 follows the formula JSD ðP1; P2Þ ¼ H 12 P1 þ 21 P2 12 ½H ðP1Þ H ðP2Þ , where Pi =
pi(t) and pi(t) is the fraction of calls at each (binned) time of the day, and H is the Shannon
entropy (H(P) = −∑p(t)logp(t)).
We have also used the l2-norm as a way to verify our results calculated using JSD. ℓ2-norm
is a similarity measure of two distributions, which is defined as: ‘2 ¼ qffiPffiffiffiffiffijffiffipffiffi1ffiffiðffitffiffiÞffiffiffiffiffiffiffiffipffiffi2ffiffiðffiffitffiÞffiffijffi2ffiffi.
Entropy patterns and relative entropies
We calculate the call entropy for a given hour (or range of hours) as follows: first, the fraction
of calls out of all calls to each alter a, pa, is counted for the specified hour (range of hours).
Then, the call entropy for this hour (range of hours) is computed as Horig = −∑a pa logpa. In
order to obtain the relative entropy, we repeatedly shuffle the original data as follows: for each
week, the times and recipient alters of all calls are randomly shuffled. This reference model
corresponds to a situation where the original call frequency pattern and the number of calls to
each alter are the same, but no preference is shown to any specific alter at any specific time.
Then, for each shuffled set of data, we calculate call entropy similarly as for the original data,
and average over N = 1,000 realizations to get the average reference entropy hHrefi. Finally, the
relative entropy is obtained as Hrel = Horig/hHrefi. The shuffling for the reference model is done
on a weekly basis in order to minimize the effects of long-term dynamics, such as declining
numbers of calls to alters, or alters appearing for the first time within the studied 6-month
TA would like to thank Juan Perotti and Hang-Hyun Jo for useful discussions at different
stages of the work. TA and JS acknowledge support from the Academy of Finland, project No.
260427 and the computational resources provided by Aalto Science-IT project. RD’s research
is supported by an ERC Advanced grant. The collection of the data by SGBR and RD was made
possible by a grant from the UK EPSRC and ESRC research councils.
Conceived and designed the experiments: TA JS SGBR RD EM EL FRT. Performed the
experiments: SGBR RD. Analyzed the data: TA JS. Contributed reagents/materials/analysis tools: TA
JS EM RD. Wrote the paper: TA JS RD SGBR EM.
1. Kerkhof GA . Inter-individual differences in the human circadian system: a review . Biological Psychology . 1985 ; 20 : 83 - 112 . doi: 10. 1016/0301-0511(85)90019-5 PMID: 3888298
2. Czeisler CA , Duffy JF , Shanahan TL , Brown EN , Mitchell JF , Rimmer DW , et al. Stability, Precision, and Near-24-Hour Period of the Human Circadian Pacemaker. Science . 1999 ; 284 ( 5423 ): 2177 - 2181 . doi: 10.1126/science.284.5423.2177 PMID: 10381883
3. Panda S , Hogenesch JB , Kay SA . Circadian rhythms from flies to humans . Nature . 2002 ; 417 : 329 - 335 . doi: 10.1038/417329a PMID: 12015613
4. Zhao R , Li D , Zuo P , Bai R , Zhou Q , Fan J , et al. Influences of Age , Gender, and Circadian Rhythm on Deceleration Capacity in Subjects without Evident Heart Diseases . Annals of Noninvasive Electrocardiology . 2014 ;.
5. Tsaousis I. Circadian preferences and personality traits: A meta-analysis . European Journal of Personality . 2010 ; 24 ( 4 ): 356 - 373 .
6. Keren H , Boyer P , Mort J , Eilam D. Pragmatic and idiosyncratic acts in human everyday routines: The counterpart of compulsive rituals . Behavioural Brain Research . 2010 ; 212 ( 1 ): 90 - 95 . doi: 10.1016/j.bbr. 2010 . 03.051 PMID: 20363260
7. Preti A , Miotto P. Diurnal variations in suicide by age and gender in Italy . Journal of Affective Disorders . 2001 ; 65 ( 3 ): 253 - 261 . doi: 10.1016/ S0165-0327(00)00232-9 PMID: 11511405
8. Kouchaki M , Smith IH . The morning morality effect: The influence of time of day on unethical behavior . Psychological Science . 2014 ; 25 ( 1 ): 95 - 102 . doi: 10.1177/0956797613498099 PMID: 24166855
9. Refinetti R. Time for sex: nycthemeral distribution of human sexual behavior . Journal of Circadian Rhythms . 2005 ; 3 ( 0 ). PMID: 15790406
10. Hu K , Ivanov PC , Hilton MF , Chen Z , Ayers RT , Stanley HE , et al. Endogenous circadian rhythm in an index of cardiac vulnerability independent of changes in behavior . Proceedings of the National Academy of Sciences . 2004 ; 101 ( 52 ): 18223 - 18227 . doi: 10.1073/pnas.0408243101
11. Song C , Qu Z , Blumm N , Barabási AL . Limits of predictability in human mobility . Science . 2010 ; 327 ( 5968 ): 1018 - 1021 . doi: 10.1126/science.1177170 PMID: 20167789
12. Yasseri T , Sumi R , Kertész J. Circadian Patterns of Wikipedia Editorial Activity: A Demographic Analysis . PLoS One . 2012 ; 7 :e30091. doi: 10.1371/journal. pone.0030091 PMID: 22272279
13. Yasseri T , Quattrone G , Mashhadi A. Temporal analysis of activity patterns of editors in collaborative mapping project of OpenStreetMap . In: Proceedings of the 9th International Symposium on Open Collaboration. ACM; 2013 . p. 13 .
14. ten Thij M , Bhulai S , Kampstra P. Circadian Patterns in Twitter . In: DATA ANALYTICS 2014 , The Third International Conference on Data Analytics; 2014 . p. 12 - 17 .
15. Jo HH , Karsai M , Karikoski J , Kaski K. Spatiotemporal correlations of handset-based service usages . EPJ Data Sci . 2012 ; 1 ( 1 ): 10 . doi: 10.1140/epjds10
16. Louail T , Lenormand M , García Cantú O , Picornell M , Herranz R , Frias-Martinez E , et al. From mobile phone data to the spatial structure of cities . Sci Rep . 2014 ; 4. doi: 10.1038/srep05276 PMID: 24923248
17. Llorente A , Garcia-Herranz M , Cebrian M , Moro E. Social media fingerprints of unemployment . arXiv: 14113140 [physicssoc-ph]. 2014 ;.
18. Roberts SGB , Dunbar RIM . The costs of family and friends: an 18-month longitudinal study of relationship maintenance and decay . Evolution and Human Behavior . 2011 ; 32 ( 3 ): 186 - 197 . doi: 10.1016/j. evolhumbehav. 2010 .08.005
19. Saramäki J , Leicht EA , López E , Roberts SGB , Reed-Tsochas F , Dunbar RIM . Persistence of social signatures in human communication . Proc Natl Acad Sci USA . 2014 ; 111 ( 3 ): 942 - 947 . doi: 10.1073/ pnas.1308540110 PMID: 24395777
20. Onnela JP , Waber BN , Pentland A , Schnorf S , Lazer D. Using sociometers to quantify social interaction patterns . Sci Rep . 2014 ; 4. doi: 10.1038/srep06278
21. Stoica A , Smoreda Z , Prieur C , Guillaume JL. Age , Gender and Communication Networks . NetMobAnanlysis of Mobile Phone Networks 2010 -Communication Proposal. 2010 ;.
22. Zainudeen A , Iqbal T , Samarajiva R. Who 's got the phone? Gender and the use of the telephone at the bottom of the pyramid . New Media and Society . 2010 ; 12 : 549 - 566 . doi: 10.1177/1461444809346721
23. Mehl MR , Vazire S , Ramírez-Esparza N , Slatcher RB , Pennebaker JW . Are Women Really More Talkative Than Men? Science . 2007 ; 317 ( 5834 ): 82 . PMID: 17615349
24. Smoreda Z , Licoppe C. Gender-specific Use of the Domestic Telephone . Social Psychology Quarterly . 2010 ; 63 ( 3 ): 238 - 252 . doi: 10.2307/2695871
25. Ling R . “ She calls, but it is for both of us you know”: The use of traditional fixed and mobile telephony for social networking among Norwegian parents . Telenor R&D; 1998 .
26. Rakow L. Gender on the line: women, the telephone , and community life / Lana F. Rakow. University of Illinois Press Urbana ; 1992 .
27. DeBaillon L , Rockwell P. Gender and student-status differences in cellular telephone use . International Journal of Mobile Communications . 2005 ; 3 ( 1 ): 82 - 98 . doi: 10.1504/IJMC. 2005 .005876
28. Ling R. The Mobile Connection: The Cell Phone's Impact on Society . Morgan Kaufmann; 2004 .
29. Kovanen L , Kaski K , Kertész J , Saramäki J. Temporal motifs reveal homophily, gender-specific patterns, and group talk in call sequences . Proceedings of the National Academy of Sciences . 2013 ; 110 ( 45 ): 18070 - 18075 . doi: 10.1073/pnas.1307941110
30. Sarch A. Making the Connection: Single Women's Use of the Telephone in Dating Relationships With Men . Journal of Communication . 1993 ; 43 ( 2 ): 128 - 144 . doi: 10.1111/j.1460- 2466 . 1993 .tb01266.x
31. Dong Y , Tang J , Lou T , Wu B , Chawla NV . How Long Will She Call Me ? Distribution, Social Theory and Duration Prediction . In: Blockeel H, Kersting K , Nijssen S , Zelezný F, editors. ECML/PKDD (2) . vol. 8189 of Lecture Notes in Computer Science. Springer; 2013 . p. 16 - 31 .
32. Karsai M , Kivelä M , Pan RK , Kaski K , Kertész J , Barabási AL , et al. Small but slow world: How network topology and burstiness slow down spreading . Physical Review E . 2011 ; 83 ( 2 ): 025102 . doi: 10.1103/ PhysRevE.83.025102
33. Miritello G , Moro E , Lara R. Dynamical strength of social ties in information spreading . Physical Review E . 2011 ; 83 ( 4 ): 045102 . doi: 10.1103/PhysRevE.83.045102
34. Backlund VP , Saramäki J , Pan RK . Effects of temporal correlations on cascades: Threshold models on temporal networks . Physical Review E . 2014 ; 89 ( 6 ): 062815 . doi: 10.1103/PhysRevE.89.062815
35. Wiessner PW . Embers of society: Firelight talk among the Ju/'hoansi Bushmen . Proc Natl Acad Sci USA . 2014 ; 111 ( 39 ): 14027 - 14035 . doi: 10.1073/pnas.1404212111 PMID: 25246574
36. Palchykov V , Kaski K , Kertész J , Barabási AL , Dunbar RIM . Sex differences in intimate relationships . Sci Rep . 2012 ; 2. doi: 10.1038/srep00370 PMID: 22518274
37. Oswald DL , Clark EM . Best friends forever?: High school best friendships and the transition to college . Personal Relationships . 2003 ; 10 ( 2 ): 187 - 196 . doi: 10.1111/ 1475 - 6811 . 00045
38. Cummings J , Lee J , Kraut R. Communication technology and friendship during the transition from high school to college . Oxford University Press.; 2006 .
39. Peruani F , Tabourier L , et al. Directedness of information flow in mobile phone communication networks . PloS one . 2011 ; 6 ( 12 ) :e28 . doi: 10.1371/journal.pone. 0028860