Journal of Service Science and Management, 2011, 4, 132-140
doi:10.4236/jssm.2011.42017 Published Online June 2011 (http://www.SciRP.org/journal/jssm)
Applying Zipf’s Power Law over Population
Density and Growth as Network Deployment
Indicator
Vagia Kyriakidou*, Christos Michalakelis, Dimitris Varoutas
Department of Informatics and Telecommunications, University of Athens, Athens, Greece.
Received February 25th, 2011; revised May 13th, 2011; accepted May 17th, 2011.
ABSTRACT
Population distribution analysis contains useful information regarding decision making of networks’ deployment.
However, both the public and the private sector should decide the development of networks based on qualitative and
quantitative criteria, such as the application of power laws. In this work, one of the most widely used power laws ap-
plied in demographics, the Zipf’s law, is tested over urban cities in Greece. Apart from the examination of Zipf’s law
validation over population, this study provides further results according the distribution of population density as far as
an analysis based on population differentiations in the last decades. According to the results, it is proved that the con-
sidered sample plays a crucial role to the final conclusions, since the acceptance or the rejection of the law depends on
it. Moreover, important information regarding the deployment of networks are revealed and discussed.
Keywords: Population Distribution, Zipf’s Law, Population Density, Network Deployment, Population Growth
1. Introduction
Urbanization and the process of a city growth have been
widely studied and questioned. Apart from important
economic and political conclusions, useful information
regarding telecommunications/networks development
could also be drawn. For example, the deployment of
telecommunications networks is usually decided after
conducting business models based on estimating the po-
tential users of the offered services. Thus, the analysis of
population distribution and growth provides crucial in-
formation to decision makers. Initial investments are the
main obstacle for operators in order to provide services
equally in all areas. Although, despite the increasingly
demand for such services e.g. broadband, a digital divide
gap between big and smaller cities is still evidence, due
to the lack of the required infrastructures.
The European Commission (EC) addressed the prob-
lem of these inequalities and in line with its decision for
an “Information Society for all” [1] subsidized a number
of initiatives aiming to the deployment of telecommuni-
cations networks, especially to no-metropolitan areas.
The e-Europe 2005 was additionally supported by the
action plan i2010 [2], which promoted the advantages of
ICT technologies in economical and social aspects. The
successor of this action plan is the “Digital Agenda” ini-
tiative which will be completed in 2020 and aims to ex-
pand ICT benefits [3]. The US government has also con-
fronted the same problem and as Pigg and Clark pre-
sented in [4] a number of initiatives are applied by the
US Department of Agriculture, targeting to the elimina-
tion of technological exclusion in rural areas.
Yet, apart from the total number of population in an
area, population density together with population growth
should also be included in analyses regarding network
development as they contain important information. On
the one hand, population density could offer significant
economies of scales regarding networks’ deployment. On
the other hand, the rate of population growth determines
the growth of potential users.
The stability regarding cities’ size over long time pe-
riods in developed countries was investigated among
others by [5,6]. These works concluded to equal propor-
tions between big and smaller cities. Henderson [7]
stated that urbanization process in developing countries
releases a number of political and societal challenges.
Among others, population agglomeration in urban areas
and the change from agriculture to a service-provided
economy will raise opportunities for these countries.

Applying Zipf’s Power Law over Population Density and Growth as Network Deployment Indicator 133
However, it is very likely for policy makers to address
income, technological and cognitive diversification be-
tween big and smaller cities. These differences are
caused mainly because of the distinct policy followed in
some areas that favored over others.
Hence, the compliance of a country’s population on
specific laws provides useful information to decision
makers from both the public and the private sector. The
evolution of the size distribution seems to be complied
with Zipf’s law in most cases [8]. According to this rule
and in the case of cities size, the second largest city (rank
= 2) should have half of the size of the largest one, which
is ranked as first (rank = 1), the third largest city (rank =
3) should have one third of the 1st ranked city, and so on.
Thus, this relation, which depends on the population and
the rank of each city, can be described by the following
equation:
Rank PopulationConstant (1)
The aim of this work is neither the examination of a
new regression method for the validation of Zipf’s law
nor the critic for the existing models. The paper aims to
investigate the compliance of Greek urban areas with the
Zipf’s law, not only in a population basis but also ac-
cording to density and Δ(Population) which represents
population differences among last censuses.
The rest of the paper is structured as follows. In Sec-
tion II the corresponding literature is reviewed and in
Section III, the considered sample and the methodology
of the analysis are presented. In Section III, the evalua-
tion results are presented and discussed. Finally, in Sec-
tion IV discussion of the results takes place, while Sec-
tion V concludes the analysis and proposes additional
applications.
2. Literature Review
According to Zipf there is an inversely proportional rela-
tionship between the frequency of words in a large cor-
pus and the rank-size of these words. His suggestion is
known as the “Zipf’s law” [8] and since then it has been
applied to several fields of study. The Zipf’s law or the
“rank-size rule” is one of the most famous rules–among
linguists, economists, geographers etc., although it is not
based on a clear theoretical basis [9]. Ha et al. [10]
investigated the validation of the law between English
and Mandarin corpora and Adamic and Huberman [11]
proved that web sites’ popularity follows the Zipf’s law.
Lu et al. [12] claimed that the majority of expressed
genes exhibit a power law distribution similar to Zipf’s
one etc..
Nowadays, the Zipf’s law and its applications have at-
tracted the interest of many researchers worldwide and
the factors which may affect its validation test are under
investigation. According to many researchers, concentra-
tion of population and urbanization are related to the
Zipf’s law. Kosmopoulou [13] studied the distribution in
both metro and urban areas in US cities. She concluded
that metro areas comply with Zipf’s law, while urban
areas tend to not follow the law, especially in recent
years. Nitsch [14] claimed that the law cannot be valid
for urban areas due to the evolution of the modern coun-
tries and cities. In addition, an international research
showed that the regression method may significantly
affect the results of validation tests [15]. Furthermore,
Gabaix and Ioannides [16] proposed that city size distri-
bution can be better justified through dynamic models,
than by Zipf’s law which belongs to power laws.
Sato and Yamamoto [17] investigated the relation be-
tween urbanization and demographic transition and they
suggested that urbanization plays a crucial role in the
process of economic development. In addition, Lucas
suggested in [18] that there is a positive relationship be-
tween economic development and human capital growth.
Thus, public policies have been strongly influenced by
the urban growth and population concentration [19].
Cunningham et al. [20] studied the network growth in
mobile telephony and concluded, among others, that
demographic factors affect the development of this mar-
ket. Not surprisingly, population density has a positive
impact on mobile demand. In addition, income and the
distribution of GDP on population, e.g. income inequal-
ity, are considered as driving factors regarding the adop-
tion of mobile services. Moreover, Moutafides and
Economides [21] showed that income is positively varied
with demand for broadband services.
The compliance of population under certain rules, such
as the Zipf’s law, is strongly depended on the sample size
[22]. For this reason, the following analysis is separated
in two cases. On the one hand, urban cities with popula-
tion more than 5 K inhabitants are studied and on the
other hand cities with more than 10 K are included in the
analysis. For both cases, the analysis is conducted with
and without the two main urban areas of Greece, which
are the capital city of Athens and Thessalonica.
3. The Methodology
The data sample used in this analysis were drawn from
the official Hellenic Statistical Authority [23], corre-
spond to years 1971, 1981, 1991 and 2001 and they are
the only data digitally available from corresponding
censuses. Before the explanation of the exact following
methodology, it must be clear that the dataset was de-
fined based on cities which were characterized as urban
by the National Census in 2001 (approximately ≥ 5 K
inhabitants). However, a decade has almost passed from
the last census and so data from 2011 are also included in

Applying Zipf’s Power Law over Population Density and Growth as Network Deployment Indicator 134
analysis based on forecasted values. Though, a well
known model used to forecast population i.e. Gompertz
model is applied to the observed data so as to estimate
population for 2011 2[24].
The total population of Greece is about 10 million,
from which more than 40% lives in the wider area of the
capital city of Athens. According to the last census, con-
ducted in 2001, 63 cities, including Athens and Thessa-
lonica, concentrate about 70% of the entire population of
the country. However, despite the high concentration in
the two main metro areas, more than 6 M citizens have
chosen to live in smaller cities. In addition, given the fact
that the total growth of population from 1971 to 2001
was about 40%, interesting implications for decision
makers regarding network development could be raised.
The following Table 1 shows the basic statistical meas-
ures of the dataset with and without the two main urban
areas (numbers are rounded up to the next largest integer
number):
As Zipf’s law cannot hold except for a certain sample
size 2[25], in case of initially rejection it would be useful
to put some limits and test the results again. The limits
set in a similar analysis refer to the median of the dataset
2[26]. This approach is akin to two-sided Zipf’s law that
Ripeanu et al. 2[27] and Adamic and Huberman 2[11] sug-
gested. According to this assumption, there is a notice-
able differentiation in results between bigger and smaller
cities.
The first test was applied on populations observations,
the second one on density and, finally, the third test was
applied on Δ(Population), which is the change of popula-
tion between subsequent censuses. Hence, a linear re-
gression over the dataset, using the ordinary least squares
(OLS) has been applied. The parameters of the following
equation were estimated based on the afore-mentioned
dataset:
 
ln ln
it it
PR

   (2)
where Pit is the population of the city i in time period t.
Table 1. Basic statistic measures of urban cities (observed
data).
2001 1991 1981 1971
3.644 K 3.442 K 3.313 K 2.758 K
Max (161 K)* (153 K)*(143 K)* (112 K)*
Min 5.009 2.336 1.111 636
49.614 45.766 43.007 35.945
Average (18.542)* (16.686)*(15.207)* (12.965)*
8.004 7.193 6.891 6.444
Median (7.967)* (7.191)* (6.828)* (6.326)*
146 146 146 146
N (144)* (144)* (144)* (144)*
*measures without the two main urban areas (Athens and Thessalonica)
and Rit is the rank of city i during the same time period.
Through that model the slope beta. β, and the intercept
alpha, α, were estimated.
In order to validate the accuracy of the regression,
standard statistical measures have been adopted, such as
Standard Error of the Estimate (SEE) and coefficient of
determination (COD or R-square) which should be more
than 90% for acceptable results, as Kamecke suggested
2[30].
4. The Results
4.1. Zipf’s Law Validation Test for Ranks and
Populations
In the first validation test of the Zipf’s law, the compli-
ance of population is tested using Ordinary Least Squares
(OLS). The results from the first test are presented in
Table 2 and in Figure 1.
According to this test, it can be concluded that the first
dataset, where Athens and Thessalonica included, tends
to comply with the Zipf’s law only in the last census. The
slope ranges from –1.181 in 1971 to –1.067 in 2011 and
R-square is over acceptable threshold in all cases. More-
over, it seems that the process of rapid urbanization tends
to limit significantly, as both slope (b) and the intercept
alpha (a) indicated. These results lead to the conclusion
that Greek urban cities tend to limit their population dif-
ferences. Especially during the last decades this conclu-
sion seems to be more valid taking into account that
R-square records higher values and the errors are lower.
On the other hand, the second dataset, where Athens and
Thessalonica are excluded from the analysis, is not com-
plied with the Zipf’s law in recent years. In 1971 the
Table 2. Results of ranks and population for all urban cit-
ies.
YearCase b a R2 SEE N
–1.067 13.793 0.965 0.198 146inc.A
&Th (0.017)(0.069)
–0.875 12.943 0.965 0.176 144
2011 exc.A
&Th (0.016)(0.064)
–1.074 13.756 0.962 0.201 146inc.A
&Th (0.017)(0.073)
–0.880 12.897 0.954 0.182 144
2001 exc.A
&Th (0.016)(0.066)
–1.106 13.755 0.963 0.203 146inc.A
&Th (0.017)(0.073)
–0.912 12.894 0.949 0.198 144
1991 exc.A
&Th (0.017)(0.072)
–1.157 13.828 0.954 0.239 146inc.A
&Th (0.021)(0.086)
–0.961 12.961 0.926 0.256 144
1981 exc.A
&Th (0.022)(0.093)
–1.181 13.760 0.926 0.316 146inc.A
&Th (0.027)(0.114)
–0.987 12.899 0.878 0.347 144
1971 exc.A
&Th (0.030)(0.126)
Errors are in parentheses

Applying Zipf’s Power Law over Population Density and Growth as Network Deployment Indicator 135
01 234 5
6
7
8
9
10
11
12
13
14
15
16
ln population (with A&Th)
ln ranks
ln1971
ln1981
ln1991
ln2001
ln2011
Linea r Regressio n
01 234 5
6
7
8
9
10
11
12
13
14
15
16
ln population (w/o A&Th)
ln ranks
ln1971
ln1981
ln1991
ln2001
ln2011
Linear Regression
Figure 1. Graphs of logarithms of ranks and population
with and without Athens & Thessalonica.
population was distributed in line with the law. However,
in 2011 the slope is not consistent with it. According to
these results, it seems that the distribution of population
in small urban cities tend not to follow the Zipf’s law.
Thus, further analysis is provided, in order to determine
the law validation over the Greek population.
After separating the sample in two subsets, above and
bellow 10 K inhabitants, Zipf’s law validation is tested
again with the same method of OLS (Table 3and Figure
22Figure 2). The threshold of 10 K inhabitants is in line
with the initiative “eEurope 2005, an information society
for all”, aiming to the subsidization of deployment of
fiber optical metropolitan networks in urban cities with
more than 10 K inhabitants (www.infosoc.gr).
According to the analysis of the results, the first
sub-sets comply with the law, while the second ones give
non acceptable results. More specifically, cities with
more than 10 K inhabitants–including Athens and Thes-
salonica seem to follow a stable population distribution.
Statistical results are above threshold of acceptance and
the slight increase in the intercept parameter, α, indicated
the general population increase.
Table 3. Results of ranks and population for urban cities
with more than 10 K inhabitants.
Year Caseb a R2 SEEN
–1.05613.777 0.920 0.28563
inc.A
&Th (0.039)(0.131)
–0.70912.516 0.924 0.17961
2011 excA
&Th (0.026)(0.086)
–1.06013.736 0.918 0.28763 inc.A
&Th (0.040)(0.134)
–0.70912.462 0.928 0.17961
2001 excA
&Th (0.025)(0.084)
–1.06913.666 0.920 0.28763 inc.A
&Th (0.040)(0.133)
–0.71712.387 0.930 0.17861
1991 excA
&Th (0.025)(0.084)
–1.06813.583 0.912 0.30163 inc.A
&Th (0.042)(0.140)
–0.71212.290 0.917 0.19361
1981 excA
&Th (0.027)(0.091)
–1.02513.312 0.902 0.30663 inc.A
&Th (0.043)(0.142)
–0.66812.018 0.918 0.18161
1971 excA
&Th (0.025)(0.085)
Errors are in parentheses
012 34
8
9
10
11
12
13
14
15
16
ln population (>1 0K with A&Th)
ln ranks
ln1971
ln1981
ln1991
ln2001
ln2011
Linear Regression
01234
8
9
10
11
12
13
14
15
16
ln population (>10K w/o A&Th)
ln ranks
ln1971
ln1981
ln1991
ln2001
ln2011
Linear Regression
Figure 2. Graphs of logarithms of ranks and population of
cities with more than 10 K inhabitants.
On the contrary, the estimated slopes in the second
In population (with A&Th)
In population (w/o A&Th)
In population (＞10k with A&Th)
In population (＞10k w/o A&Th)

Applying Zipf’s Power Law over Population Density and Growth as Network Deployment Indicator 136
sub-sets–excluding Athens and Thessalonica indicated an
upward process caused by the significant increase of
population in the considered cities. The slope, β, is con-
tinuously decreased from 1971 to 1991, although in 2001
there was a slight increase. Thus, population distribution
according to last census reveals smoothing tendency and
though the proportion signifies Zipf’s law is strongly
rejected in this case.
4.2. Zipf’s Law Validation Test using
Population’s Density
At this stage, a rank-size rule is applied to the whole
dataset based on their population density. In 2Table 4 and
in 2Figure 3 a comparison in results of both cases, with
and without the two main urban areas, according to OLS
method is presented. It is obvious that there is a similar-
ity with previous results for all censuses. Though, in the
first sub-sets where Athens and Thessalonica included in
analysis, population density complied with Zipf’s law. In
addition, calculated R-squares and errors boost the accu-
racy of the estimated results.
On the contrary, it seems that second sub-sets don’t
comply with Zipf’s law as the slope is not close enough
to –1. The distribution of population density in this case
seems to be stable in last decades and the estimated slope
indicated that there are slight differences regarding
population density among cities. Though, the majority of
the bigger urban cities with more than 10 K inhabitants
tend to grow in a similar way in terms of their density.
At a second stage, the analysis is applied in urban cit-
ies with population of more than 10 K inhabitants. In this
Table 4. Results of ranks and population density.
Year Case b a R2 SEE N
–1.031 10.732 0.939 0.229 146 inc.A
&Th (0.020) (0.088)
–0.827 9.572 0.921 144
2011 exc.A
&Th (0.018) (0.080)
–1.037 10.415 0.944 0.237 146
inc.A
&Th (0.020) (0.086)
–0.835 9.524 0.924 0.225 144
2001 exc.A
&Th (0.019) (0.081)
–1.051 10.330 0.952 0.223 146 inc.A
&Th (0.019) (0.080)
–0.846 9.430 0.941 0.199 144
1991 exc.A
&Th (0.017) (0.072)
–1.079 10.296 0.956 0.218 146
inc.A
&Th (0.019) (0.078)
–0.879 9.413 0.939 0.211 144
1981 exc.A
&Th (0.018) (0.077)
–1.073 10.120 0.963 0.198 146 inc.A
&Th (0.017) (0.071)
–0.876 9.254 0.951 0.188 144
1971 exc.A
&Th (0.016) (0.068)
Errors are in parentheses
case, as Table 5 and Figure 4 show, population density
complied with Zipf’s law only in the case where Athens
012345
4
5
6
7
8
9
10
11
12
13
ln population density (with A&Th)
ln ranks
ln1971
ln1981
ln1991
ln2001
ln2011
Linear Regression
0123 45
4
5
6
7
8
9
10
11
12
13
ln population density (w/o A&Th)
ln ranks
ln1971
ln1981
ln1991
ln2001
ln2011
Linear Regression
Figure 3. Graphs of logarithms of ranks and population
density with and without Athens and Thessalonica.
Table 5. Results of ranks and population density for urban
cities with more than 10 K inhabitants.
Year Case b a R2 SEE N
–0.983 10.283 0.893 0.33763
inc.A
&Th (0.043)(0.142)
–0.622 8.980 0.918 0.12161
2011
exc.A
&Th (0.023)(0.078)
–0.957 10.188 0.874 0.33163
inc.A
&Th (0.046)(0.154)
–0.580 8.826 0.951 0.11961
2001 exc.A
&Th (0.017)(0.056)
–0.999 10.177 0.887 0.32363 inc.A
&Th (0.045)(0.150)
–0.619 8.809 0.962 0.11161
1991 exc.A
&Th (0.016)(0.052)
–1.011 10.096 0.902 0.30263 inc.A
&Th (0.042)(0.140)
–0.643 8.765 0.962 0.11561
1981 exc.A
&Th (0.016)(0.054)
–1.018 9.964 0.911 0.28863
inc.A
&Th (0.040)(0.134)
–0.658 8.662 0.966 0.11261
1971 exc.A
&Th (0.016)(0.052)
Errors are in parentheses

Applying Zipf’s Power Law over Population Density and Growth as Network Deployment Indicator 137
01234
4
5
6
7
8
9
10
11
12
13
ln population density (>10K with A&Th)
ln ranks
ln1971
ln1981
ln1991
ln2001
ln2011
Linear Regression
01234
4
5
6
7
8
9
10
11
12
13
ln population density (>10K w/o A&Th)
ln ranks
ln1971
ln1981
ln1991
ln2001
ln2011
Linear Regression
Figure 4. Graphs of logarithms of ranks and population
density of cities with more than 10 K inhabitants.
and Thessalonica included in the analysis. Although
there is a slight increase in the slope from –1.018 to
–0.983, in 1971 and 2011 respectively, results are to
close to the expected slope of –1.
On the other hand, based on the results of the other
sub-sets–without Athens and Thessalonica the hypothesis
of Zipf’s law validation is strongly declined. In addition,
according to the estimated slope (b) and the intercept (a),
it seems that differentiations of population density in
urban cities are reduced significantly.
Thus, network infrastructure development e.g. tele-
communications network, should be carefully designed.
Decision makers should take into account that in these
cities the majority of potential users for telecommunica-
tions services is concentrated and though the appropriate
business models have to apply. The development of
high-cost infrastructures, such as fiber to the home net-
works, maybe should be rejected in areas where econo-
mies of scales are not favored by the population density.
4.3. Zipf’s Law Validation Test for Ranks and
Δ(Population)
Apart from the above tests, the analysis goes ahead with
Zipf’s law validation tests and exam the distribution of
difference in population–Δ(Population)–among censuses.
Firstly, the net difference between population is calcu-
lated, then the rank-size rule is applied to these differ-
ences and, finally, the Zipf’s law hypothesis is tested.
The analysis is conducted for population differentiation
regarding the time intervals of years 2011 to 2001, 2001
to 1991, 1991 to 1981 and 1981 to 1971.
The results of the applied OLS linear regression are as
presented in Table 6 and in Figure 5. Data seem not to
comply with Zipf’s law as the slope, β, R-square and
Standard Error of Estimate (SEE) have not acceptable
values.
Among the 146 examined cities 19, 27 and 22 had a
population decrease in 2001, 1991 and 1981 respectively.
It is estimated that in 2011 only 10 cities will decrease in
terms of population. The average decrease was about 5%
in all censuses (Table 7).
Athens and Thessalonica had the faster population
Table 6. Regression results of ranks and Δ(Population) for
all urban cities.
Year Case b a R2 SEEN
–1.127 11.917 0.878 0.414136 inc.A
&Th (0.032)(0.152)
–0.989 11.102 0.798 0.395134
2011
-
2001 exc.A
&Th (0.041)(0.147)
–1.180 11.866 0.879 0.411127inc.A
&Th (0.039)(0.155)
–0.994 11.060 0.808 0.455125
2001
-
1991 exc.A
&Th (0.043)(0.160)
–1.223 11.754 0.860 0.463119inc.A
&Th (0.045)(0.178)
–1.050 11.002 0.789 0.508117
1991
-
1981 exc.A
&Th (0.050)(0.197)
–1.453 12.795 0.871 0.526124inc.A
&Th (0.050)(0.200)
–1.238 11.850 0.805 0.572122
1981
-
1971 exc.A
&Th (0.055)(0.218)
Errors are in parentheses
012345
0,0
0,5
1,0
1,5
2,0
proportion in %
ln ranks
1981-1971
1991-1981
2001-1991
2011-2001
Linear Regression
Figure 5. Proportion of population growth expressed in
percentage.

Applying Zipf’s Power Law over Population Density and Growth as Network Deployment Indicator 138
Table 7. Basic statistical measures of cities with negative
population growth.
2011-2001 2001-1991 1991-1981 1981-1971
Max –0082 –0.169 –0.173 –0.168
Min –0.003 –0.001 –0.002 –0.004
Average –0.049 –0.057 –0.057 –0.052
Standard
Deviation 0.027 0.044 0.045 0.044
N 10 19 27 22
growth rate only from 1971 to 1981 and after that they
tend to grow more slowly than the other cities. This
means that the urbanization process and internal migra-
tion to these two big cities have been limited in recent
years. Moreover, according to the results, the population
growth of the considered urban cities was in general
higher in past decades and particularly in ‘80s.
In order to provide more reliable results, the propor-
tion of population growth is estimated and expressed in
percentage. The following 3Figure 6 shows this popula-
tion growth for both positive and negative differentiation.
According to 3Figure 5 and 3Figure 6, it is concluded
that population increase was more intense in last decades.
In addition, smaller cities grew in a faster way than the
bigger ones. Although the critical mass of population
inhabits the two main urban areas, smaller cities are con-
tinuously grown and in fact this increase is on the rise.
5. Discussion of Results
According to the results, population distribution in
Greece complies with the Zipf’s law when all urban cit-
ies with more than 10 K inhabitants are included in the
analysis. An exception is made by the total population
distribution, which complies with the law in the last cen-
sus. These results indicated that Greek urban cities tend
to grow unequally in terms of population. Thus, public
policies regarding the deployment of infrastructures such
as telecommunications networks should applied in line
with population concentration. Apart from public initia-
tives the private sector should also take into account
population distribution, as an indicator of potential users
of offered services.
Furthermore, the compliance of ranks and population
density is valid with Zipf’s law in both cases, for all ur-
ban cities and for those with more than 10 K inhabitants.
Although, according to the results when Athens and
Thessalonica were excluded from the analysis, data do
not comply with the law neither for all urban cities nor
with more than 10 K inhabitants. Though, the choice of
the appropriate sample is therefore very important for the
further research as it can affect the results, as it is also
-1
0
1
2
3
4
5
191725334149 57 6573818997105113121129137145
# of ci ti es
proport ion of populat ion gr owt h in %
1981-1971 1991-1981 2001-1991 2011-2001
Figure 6. Proportion of population growth expressed in
percentage for all urban cities.
stated in 3[31]. Thus, it can be concluded that the majority
of urban cities in Greece, excluding Athens and Thessa-
lonica, have the same population density, which is by far
sparser than in the two main urban areas.
Finally, population differentiations have been esti-
mated in order to test the validation of population growth
with the Zipf’s law and in same time determine the proc-
ess of this growth in all urban cities. From the analysis is
revealed that smaller cities developed in terms of popula-
tion growth rate faster than bigger ones. Moreover, the
development was more intense in 80s and in 90s. In the
last decade population growth was significantly limited
regarding previous decades. This may indicate that even
more urban cities gain the same comparative advantages
and people can be befit in the majority of these cities. As
Cuberes suggested in 3[32], the evolution of city growth is
sequential and though further analysis could reveal addi-
tional information.
As far as the regression is concerned, OLS seems to be
acceptable, but it can be observed by the results, that
there isn’t an absolute linear relationship between popu-
lation and rank-size for the upper tail of dataset. This
observation is inline with other related works 3[16],3[33].
The analysis of the urbanization process along with the
validation of the Zipf’s law is useful information for pol-
icy makers, urban scientists, infrastructure designers, etc.
Especially as the debate for power, transport and telecom
infrastructure development is increasing, in the light of
measures for information society development, this kind
of information is particularly useful for more effective
broadband population coverage, creation of broadband
development, transport design, firms installation (as dis-
cussed by Fujiwara et al. 3[34]), power networks etc.
6. Conclusions
Based on the assumption that population characteristics,
such as density and growth, contain useful information to
be used for decision making of networks’ deployment,

Applying Zipf’s Power Law over Population Density and Growth as Network Deployment Indicator 139
the present work evaluated the application of Zipf’s
power law over urban cities in Greece. The purpose was
the provision of qualitative and quantitative criteria, to
both the public and the private sector, in order to decide
the development of networks.
Results indicated that public policies regarding the de-
ployment of infrastructures such as telecommunications
networks should applied in line with population concen-
tration, not only in terms of public initiatives but from
the private sector as well. The private sector should take
into account the examined characteristics of the popula-
tion, in order to estimate the future demand for the of-
fered services and develop the appropriate infrastructures,
thus avoiding over or undersupply.
Apart from this, the study provides additional results,
according to the distribution of population density and
population differentiations during the last decades. It is
proved that the considered sample plays a crucial role to
the final conclusions, since the acceptance or the rejec-
tion of the law depends on it. Moreover, important in-
formation regarding the deployment of networks are re-
vealed and discussed.
The approach described in this work can be used as a
driver and an input for the construction of strategic plans
regarding the deployment of telecommunication or simi-
lar type networks.
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