297 Arheološki vestnik 70, 2019, 297–313
Assessing the intentionality of spatial organization. 
Cemetery of Župna Cerkev (Kranj, Slovenia) case study
Preučevanje namernosti prostorske ureditve. 
Primer grobišča Župna cerkev v Kranju
Katia Francesca ACHINO, Benjamin ŠTULAR, Jernej RIHTER, Janja RIHTER
Izvleček
Osnovni namen prispevka je poudariti pomen prostorske analize grobišč z orodji prostorske statistike. Naš pristop 
temelji na kombinaciji analize vzorca točkovne razmestitve ene spremenljivke (t. i. Ripleyjeva K-funkcija) z izborom 
tistih orodij prostorske statistike, ki upoštevajo vrednosti globalne in lokalne avtokorelacije. Uporabnost teh orodij v 
kontekstu arheoloških analiz grobišč smo preizkusili na primeru srednjeveškega grobišča Župna cerkev v Kranju. Na-
tančneje, preverili smo, ali je prostorska ureditev grobišča naključna, in če ne, ali je namerna. Prepoznali smo namerno, 
kronološko dinamično izbiro prostora pokopavanja.
Ključne besede: Slovenija, arheologija, prostorske analize, srednjeveška grobišča
Abstract
This article is focused on highlighting the importance of assessing spatial patterns in archaeological analyses of 
cemeteries through a statistically driven approach. It is based on the combination of Ripley’s K-Function and selected 
geostatistical tools that take into consideration the values of global and local autocorrelation. Their feasibility in funer-
ary contexts is demonstrated on the mediaeval cemetery of Župna Cerkev in Kranj (Slovenia). The case study was used 
to test whether the spatial distribution of graves is non-random and, if so, whether it is intentional. The methods used 
made it possible to recognize an intentional, chronologically driven choice in grave placement.
Keywords: Slovenia, archaeology, spatial analysis, mediaeval cemeteries
INTRODUCTION
The mediaeval cemetery of Župna Cerkev is 
situated at the heart of the ancient town of Kranj 
(Slovenia). Its suitable location on a promontory 
overlooking the confluence of the Sava and Kokra 
Rivers encouraged the occupation from the Iron 
Age onwards (Fig. 1). The town gained regional 
importance in the late Iron Age/early Roman period, 
and under the Langobards in the late antiquity pe-
riod and in the early mediaeval period. Due to the 
regional importance of the contemporary settlement 
and especially due to its size, the Župna Cerkev 
cemetery is deemed to be of regional importance 
for the archaeology of the early mediaeval period 
in the South-Eastern Alpine area.

298 Katia Francesca ACHINO, Benjamin ŠTULAR, Jernej RIHTER, Janja RIHTER
Early Medieval/Medieval grave / 
   Zgodnjesrednjeveški/srednjeveški grob
Section (see Fig. 2) / Izsek (glej sl. 2)
Contemporary city / Sodobno mesto
High/Late Medieval church / 
   Visoko/poznosrednjeveška cerkev
0         10                   20 m
Path / Pot
Fig. 1: Župna Cerkev in Kranj. Cemetery, the location of the site. Arrow represents the probable path as revealed by the 
gap in burials. Black square marks the extract presented in Fig. 2.
Sl. 1: Župna cerkev v Kranju, lega grobišča. Puščica prikazuje verjeten potek poti, ki jo dokazuje prazen prostor med 
grobovi. Črn pravokotnik označuje mesto izreza za sliko 2.
Fig. 2 / Sl. 2

299 Assessing the intentionality of spatial organization. Cemetery of Župna Cerkev (Kranj, Slovenia) case study
The cemetery was excavated between 1953 and 
2013, spanning several vastly different excavation 
methods. In total, 2,936 graves dating from the 8
th
 
to mid-18
th
 centuries have been excavated (Štular, 
Štuhec 2015, 34–42; Pleterski, Štular, Belak 2016, 7–25).
This article is part of an ongoing project that 
aims to catalogue, analyse, and document the site. 
The large number and especially the high density of 
burials – reaching up to 19 burials per square metre 
– requires a novel approach to the archaeological 
analysis of cemeteries. This article aims to present 
a toolkit of robust and versatile methods of spatial 
statistics that are executable in an off-the-shelf GIS 
environment and can be applied in the analysis of 
Župna Cerkev in Kranj and similar cemeteries.
THEORETICAL BACKGROUND
Spatial analysis in archaeology has a venerable 
tradition from the late 1970s onwards. It was pre-
dominantly oriented to reconstructing either the 
relationship between humans and the landscape 
(inter-site scale) or the use of space and the arrange-
ment of activities practised within archaeological 
and ethnoarchaeological contexts (intra-site scale) 
(for an overview, see e.g., Whallon 1973; 1974; Carr 
1984; Hietala 1984; Aldenderfer 1987; Voorrips, 
O’Shea 1987; Blakholm 1991; Kroll, Price 1991). 
Since then, archaeologists have adopted a wide 
range of theoretical concepts, models and theory-
dependent methods from various scientific fields, 
such as computer and social sciences, geography, 
geology, biology, and mathematics (Wheatley, Gill-
ings 2002; Conolly, Lake 2006; Salisbury, Keeler 
2007; Nakoinz, Knitter 2016). According to such 
inter-disciplinary theories, the archaeological data 
acquisition strategies are structured, the type of 
analysis chosen, and the interpretation of analysis 
results is influenced (Hodder, Hutson 2003).
Since the late 1980s, spatial analysis in archae-
ology has been characterized by an increasing 
application of GIS (Geographical Information 
System) for managing archaeological data and 
providing a fundamental tool for the interpreta-
tion of archaeological contexts (Zubrow 1990; 
Gillings, Sbonias 1999; Wheatley, Gillings 2002; 
Bevan, Conolly 2004). Ever more frequently, GIS 
is being applied on an intra-site basis, aimed at 
the interpretation of settlements and settlement 
activities (Peterman 1992; Pettitt 1997; Huggett 
2000; Lavachery, Conelissen 2000, 153; Moyes 2002; 
D’ Andrea, Gallotti 2004; Gallotti et al. 2011; 2012).
In a different vein, the archaeology of death and 
burials has not seen such a vigorous adoption of 
spatial analysis techniques.
Until the 1970s, the spatial component was all 
too often ignored (Goldstein 1981, 57). As an early 
example, the analysis of the Moundville (USA) 
cemetery – where monothetic-divisive cluster 
analysis using the information statistic was used 
for grouping the burials – can be cited (Goldstein 
1981, 62–63; see bibliography cited). The work 
on the El Cigarralejo (Spain) cemetery is an early 
implementation of GIS in archaeology, focusing on 
intra-site mapping (Quesada, Baena, Blasco 1995). 
Two edited volumes in the early 2000s demon-
strated a growing interest in the spatial analysis of 
funerary areas. However, most of the cemeteries 
analyzed were relatively small and low-density 
ones, and the prevailing method employed was 
a visual analysis of scatterplots or plan-drawings 
(Silverman, Small 2002; Šmejda, Turek 2004a). As 
a notable exception, the prehistoric cemetery at 
Holešov (Czech Republic) – where kernel density 
was used to map the distribution of artefacts and 
trend analysis of mean tin content – can be cited. 
Investigating the major concentration of specific 
archaeological markers, the author filtered the 
values of grid cells taking into account the input 
cell value (identified in the middle of the kernel) 
and the values of its immediate neighbours; in this 
way, it was also possible to identify and control the 
potential “false zero effect” that can arise close to 
site borders (Šmejda, Turek 2004b, 57–68).
Among the most advanced uses of spatial sta-
tistics in the study of cemeteries in archaeology is 
the application of Ripley’s K-function analysis to 
determine the proximity of statistically significant 
clusters within four early Anglo-Saxon cemetery 
sites (UK); the statistically significant distance 
suggested by this method was used to apply kernel 
density analysis to data sets, in order to visualize 
and define the areas of clustering for the data 
(Sayer, Wienhold 2013).
Despite the above-mentioned studies, scatter-
plots (intended for visual examinations) remain 
by far the most common method employed for 
the spatial analysis of cemeteries (Goldstein 1981, 
67; cf. Fotheringham 2002, 7; Bevan et al. 2013). 
The archaeology of large mediaeval cemeteries is 
no exception (e.g., Losert, Pleterski 2003; Filipec 
2012; Sokol 2016).
Moreover, it is at large mediaeval cemeteries 
with an extremely high density of burials, such 
as Župna Cerkev, where the shortcomings of this 

300 Katia Francesca ACHINO, Benjamin ŠTULAR, Jernej RIHTER, Janja RIHTER
method become painfully obvious: the high density 
of burials prevents visual assessment and inter-
pretation of data mapped as scatterplots (Fig. 2). 
Even the simplest of tasks, reliable delineation of 
the highest density areas, is all but impossible. 
Instead, some form of isopleth map is needed (cf. 
Banning 2000, 28–30). Most of this article deals 
with creating meaningful isopleth maps through 
the use of spatial statistics.
MATERIALS AND METHOD
Materials
The documentation of the Župna Cerkev cemetery 
in Kranj stems from six decades of archaeological 
excavations; therefore, it varies significantly in 
both quantity and quality. For method testing, the 
interference caused by this circumstance must be 
minimized. To this end, we are employing only 
the lowest-common-denominator data, i.e., data 
that are for all excavations from 1953 onwards in 
comparable qualities and quantities. The chosen 
datasets are location and a rough chronology.
Our primary analysis of spatial distribution is 
based on xy point data for each recorded burial. 
In order to ingest the data (stemming from six 
different ad hoc projected coordinate systems, 
e.g., xy measured from the corner of the church 
building, and four different recording systems) 
into the unified state plane coordinate system, we 
have adopted the following procedure:
– reconstruction of each ad hoc projected co-
ordinate system;
– mapping of each ad hoc projected coordinate 
system to the state plane coordinate system (GK 
D96);
– mapping of archaeological data – derived 
from either xyz measurements or archaeological 
drawings – to the state plane coordinate system.
This approach differs from the most commonly 
used one, in which archaeological drawings are 
directly georeferenced to the state plane coor-
dinate system using ground control points. The 
chosen approach was necessary (i) due to the 
lack of surviving ground control points, and (ii) 
in order to minimize the impact of errors made 
by surveyors at the time of data acquisition (e.g., 
mistakes made by laying down the grid using a 
simple tape measure) and the error introduced 
during the georeferencing process; while the two 
cannot be avoided, by using our approach the 
mistakes are added, whereas using GCPs mistakes 
are multiplied and distorted.
The result is a geodatabase of 2,881 individual 
burials with known location data, each represented 
with an xy point located at the occiput of the 
skeletal remains. This robust dataset is intended 
for quantitative analyses only.
Since the analysis of the site is on-going, a de-
tailed chronology is not yet available. However, a 
classification of burials in two chronological phases 
has been made in situ: the early mediaeval and 
post-early-mediaeval phase (high mediaeval, late 
mediaeval, and post-mediaeval graves could not be 
readily distinguished). This division, recognized by 
Fig. 2: Scatterplots of graves within the selected area: a – Early Mediaeval graves; b – Mediaeval graves; 
c – all graves. For the location see Fig. 1.
Sl. 2: Točkovni načrt grobišča, izsek: a – zgodnjesrednjeveški grobovi; b – po-zgodnjesrednjeveški grobovi; 
c – vsi grobovi. Za lokacijo glej sliko 1.

301 Assessing the intentionality of spatial organization. Cemetery of Župna Cerkev (Kranj, Slovenia) case study
different excavators independently of each other, 
was based on the following criteria: burial depth, 
the colour of the bones (a proxy for the state of 
decay of organic substances), the general state of 
burial preservation, and grave goods (if present).
Although such a crude method does not adhere 
to modern standards, a preliminary stratigraphic 
analysis on the subset of 158 burials already im-
plemented (Rihter 2016) confirmed the original 
estimation as 100% accurate: a Harris matrix has 
been produced based on the available stratigraphic 
data, and all of the burials marked as Early Medi-
aeval by the excavators proved to be the earliest. 
W e, therefore, assume that the in situ chronological 
division suffices for the method development and 
testing, which is the purpose of this article. Alas, 
the preliminary in situ dating was not recorded 
in the 2011–2013 excavation campaign that re-
excavated the entire cemetery in the search for 
burials that went undetected by older excavations, 
e.g., because archaeologists were not allowed to cut 
down the trees or remove portions of pavement. 
This means that preliminary dating is only avail-
able for 79.3% of burials, but the burials missing 
this information are, in the majority, dispersed 
throughout the cemetery.
Visual analysis of the scatterplot of all burials 
(Fig. 1 and Fig. 2) reveals that the cemetery is 
spread around the church buildings contemporary 
to each phase. Burials are most dense in the W , N 
and E sectors outside as well as in the NW corner 
inside the present-day church building built soon 
after 1430. A relatively high density can also be 
observed in the NW extension of the cemetery. 
In the S sector, the density is visibly less and is 
fading away from the church. Towards the W , the 
density is relatively uniform up to the linear gap 
that is presumably a path contemporary with the 
cemetery; across the linear gap, only sporadic 
burials have been excavated. Visual analysis of 
the early mediaeval phase scatterplot reveals the 
concentrations in the W and S sectors as well as 
in the NW and SW corners inside the present-day 
church. Burials of the later phase are concentrated 
in the N and E sectors, as well as immediately 
adjacent to the western church wall.
Method
In order to develop methods, a starting hypoth-
esis was set: the millennia of burials at the Župna 
Cerkev cemetery was characterized by a dynamic 
burial practice; this is reflected (among others) in 
burial density, i.e., the frequency of burial instances 
within a predefined grid.
As a null hypothesis, a random spatial distribu-
tion of burials was assumed. The rejection of the 
null hypothesis would be proof of an intentional 
dynamic spatial organization of the cemetery.
Therefore, first, the non-randomness of the 
spatial distribution of the burials was established. 
This was achieved by fitting a spatial distribution 
to different theoretical models of distribution using 
SPSS Statistics 22.0. The models used are Poisson, 
Geometric, Binomial, and Exponential. Except 
for the first model, associated with a random 
distribution, all the others mirror the existence of 
intentionality in their distribution (Achino 2016; 
Revelles et al. 2017).
The spatial pattern that characterizes the graves 
was explored by applying the following mathemati-
cal tools: Multi-Distance Spatial Cluster Analysis 
(Ripleys K-function), Spatial Autocorrelation 
(Global Moran’s I), Optimized Hot Spot Analysis 
(Getis-Ord G*) and Optimized Outlier Analysis 
(Local Moran’s I), implemented in ArcGis 10.3. 
They make it possible to identify whether graves 
are spatially distributed according to a) a regularly 
dispersed model, b) randomness, or c) clusters.
Ripley’s K-function
This statistical test, successfully utilized in numer-
ous other archaeological spatial analyses (Bevan, 
Conolly 2006; Crema et al. 2010; Vanzetti et al. 
2010; Winter-Livneh et al. 2010; Sayer, Wienhold 
2013; Duncan, Schwark 2014; Markofsky 2014;
Thacther, Milne, Park 2017, as examples), has 
proved to be an effective measure of the spatial 
relationship between point data. Specifically, it is 
a way to measure statistically significant cluster-
ing or aggregation and regularity or segregation 
of point data at multiple scales, regardless of the 
shape of the area being studied (Conolly, Lake 
2006, 166; Sayer, Wienhold 2013, 77). Within the 
ArcGis environment, it is a particularly effective 
analytical function because the tool combines a 
commonly used transformation (L(d)) (Winter-
Livneh et al. 2010, 288; Cable 2012, 148; Sayer, 
Wienhold 2013; Carrer 2015; Thacther, Milne, Park 
2017) of Ripley’s K-function with Monte Carlo 
simulation. Monte Carlo simulation randomly 
generates a distribution of points equal to the num-
ber of input points, which creates the confidence 

302 Katia Francesca ACHINO, Benjamin ŠTULAR, Jernej RIHTER, Janja RIHTER
intervals or envelopes according to the number 
of permutations (Winter-Livneh et al. 2010, 288; 
Sayer, Wienhold 2013, 78). This simulation makes 
it possible to verify whether the data fall above 
the high-confidence envelope created by it and 
consequently guarantees that the data are clustered 
in a statistically significant way; if the data fall 
below the confidence interval, they are dispersed 
in a statistically significant way. In contrast, when 
they fall between the lower and upper boundaries 
of the confidence interval created by simulation, 
the distribution does not statistically differ from 
randomness. In this case, 999 permutations were 
run in the Ripley’s K-function tool to create such 
a confidence level.
Spatial Autocorrelation: 
Global and Local Moran’s I
In order to better characterize the broader spatial 
distribution of graves, the Global Moran’s Index 
for Spatial Autocorrelation was first calculated. It 
quantifies the magnitude, extent and intensity of 
autocorrelation, as spatial dependence between the 
frequencies of the graves within the analysed area, 
when the null hypothesis of spatial randomness 
can be rejected; I values range from -1 (perfect 
dispersion) to +1 (perfect correlation) and a zero 
value indicates a random pattern (Cliff, Ord 1973; 
Moran 1950). If spatial dependence was certified, 
it was then determined from which distance the 
clustering occurs. The use of Moran’s I statistic is 
quite common in archaeological research (Kvamme 
1990; Premo 2004; Carrer 2015; Achino 2016). 
In addition to the Global Moran’s I index, the lo-
cal spatial autocorrelation was also calculated; it 
identifies the local regions of strong autocorrela-
tions, that is, concentrations in a particular zone 
of the global space, such as unusually high/low 
values of a variable, more than the expected mean 
value. Local indices of spatial association (LISA, 
Anselin 1995; Levine 2013) allow the local level 
of spatial autocorrelation to be examined, in order 
to identify areas where values of the variable are 
both extreme and spatially homogeneous; this leads 
to the identification of so-called hot spot areas, 
where the considered phenomenon is extremely 
pronounced across localities – as well as spatial 
outliers. In other words, this index highlights, in 
this case, the spatial distribution of similar and 
dissimilar values of autocorrelation between the 
frequencies of graves within the analysed area.
For this case study, Outlier Analysis as well as 
Hotspot Analysis, available within the ArcGIS 
environment, were applied. They identified statisti -
cally significant spatial clusters of high values (hot 
spots), low values (cold spots) and spatial outliers 
using the Anselin Local Moran’s I statistic and the 
Getis-Ord G* statistic, respectively. The program 
provides z-scores and p-values, i.e., measures of 
statistical significance that mirror whether or not 
to reject the null hypothesis of randomness. Such 
values indicate, for Cluster and Outlier Analysis, 
whether the apparent similarity (a spatial cluster-
ing of either high or low values) or dissimilarity 
(a spatial outlier) is more pronounced than one 
would expect in a random distribution. In the same 
way, the z-score and p-value indicate, for Hot Spot 
Analysis, whether the observed spatial clustering 
of high and low values is more pronounced than 
one would expect in a random distribution of those 
same values. Both tools are applied for this study in 
their optimized version since a sufficiently numer -
ous sample of graves is available.
RESULTS
As a first step in the analysis of the Župna 
Cerkev cemetery in Kranj, the non-randomness 
of the spatial distribution of the burials was es-
tablished by the rejection of the null hypothesis 
of a Poisson distribution. The data fitted mainly 
an exponential distribution, which mirrors an 
intentional spatial distribution of the variable 
under analysis. Furthermore, the Global Moran’s 
Index for Spatial Autocorrelation indicates that 
the spatial organization of graves is clustered, 
and there is a less than <1% likelihood that this 
pattern could be the result of random chance. 
According to the results of the Ripley K-function 
(Fig. 3), from a distance of 4 metres the observed 
K value is larger than the expected K value; then, 
from this particular distance, the distribution is 
more clustered than random.
Optimized Outlier Analysis (LISA) shows the 
presence of areas that are positively spatially auto-
correlated (Fig. 4); in the N sector of the cemetery, 
this means that high values surrounded by high 
values are concentrated. They are surrounded by 
some of the least dense squares (low values sur-
rounded by high values, outliers). The S sector and 
northern extension of the cemetery are character-
ized by positive autocorrelation, with low values 
surrounded by low values.

303 Assessing the intentionality of spatial organization. Cemetery of Župna Cerkev (Kranj, Slovenia) case study
Fig. 3: Ripley’s K-function analysis graph showing local distribution – L (d) –, i.e. significance from the distance of 4 
meters onwards.
Sl. 3: Rezultat analize vzorca točkovne razmestitve ene spremenljivke (t.i. Ripleyjeve K-funkcije) kaže statistično pomen-
ljivost za opazovane razdalje – L (d) – 4 metre in več.
Predictably, the Hot Spot Analysis (Getis-Ord 
G*) results adhere to an almost identical scenario: 
hot spots in the N, E and W sectors, in the NW 
corner inside the church and in part of the northern 
extension of the cemetery; the only noticeable cold 
spot, other than the fringes of the cemetery and 
the interior of the church, is a gap in the centre 
of the N sector where a mediaeval burial chapel 
stood (Fig. 5).
In continuation, the overall spatial distribution 
is compared to both chronological phases, the early 
mediaeval and post-early-mediaeval. The null hy-
pothesis of a Poisson distribution was rejected for 
each chronological phase individually. Similarly, the 
Global Moran’s Index for Spatial Autocorrelation 
indicates, in both cases, that there is a less than 
<1% likelihood that the spatial patterns could be 
the result of random chance.
Optimized Outlier Analysis (LISA) and Optimized 
Hot Spot Analysis (Getis-Ord G*) provided invalu-
able insight into the spatial pattern. Early mediaeval 
graves exhibit a very well-defined hot spot in the 
NW and a cold spot in the SE sector (Fig. 6).
The later phase exhibits an almost exactly op-
posite spatial distribution with a hot spot in the 
SE and a cold spot in the NW and S sectors. There 
is an additional smaller hot spot in the N sector 
(Fig. 7). The impression is, therefore, that while the 
two phases largely overlap, the focal areas of each 
are on the opposite sides of the church building.
DISCUSSION
The above analysis was designed to confirm 
or refute the hypothesis that the burial practice 
in Župna Cerkev cemetery in Kranj was dynamic 
and that this dynamic is reflected, among others, 
in spatial patterns. The hypothesis is confirmed 
since the chronological dynamics in the spatial 
pattern has been demonstrated.
There are further archaeological interpretations 
to be drawn.
(1) The non-randomness of the spatial distribution 
was clearly established, both for the entire cemetery 
and for each chronological phase individually. 
In the context of mediaeval and post-mediaeval 
burial practices (e.g., Steuer 1982; Parker Pearson 
1999, 11–17; Podpečan 2006, 19–20; Petts 2007; 
Eichert 2010; 2013), this can only be explained by 
intentional human choice governing the placement 
of individual graves. The spatial distribution of 
the Župna Cerkev cemetery in Kranj, therefore, 
exhibits statistically relevant intentional human 
choices in grave placement.
Although this inference may, at first, seem 
self-evident and, as such, pointless, an overview 
of the relevant literature reveals its importance. 
At least as far as archaeological explanations of 
spatial patterns in Central European early medi-
aeval cemeteries are concerned, for the most part, 
spatial patterns are not even discussed (Pleterski 
26
24
22
20
18
16
14
12
10
  8
  6
  4
  2
4          6          8         10        12        14       16        18        20        22       24
L (d)
Distance / Razdalja
Clustered / Gruče
Dispersed / Razpršeno
Expected K / Pričakovani K
Observed k / Opazovani K
Condence Envelope / Interval zaupanja

304 Katia Francesca ACHINO, Benjamin ŠTULAR, Jernej RIHTER, Janja RIHTER
Fig. 4: Result of Optimized Outlier Analysis representing outliers and clusters within the cemetery.
Sl. 4: Rezultat optimizirane analize izstopajočih vrednosti prikazuje osamelce in gruče na grobišču.
Low outlier / Nizke vrednosti
High outlier  / Visoke vrednosti
Cluster low / Gruča nizkih vrednosti
Cluster high / Gruča visokih vrednosti
Contemporary city / Sodobno mesto
High/Late Medieval church / 
   Visoko/poznosrednjeveška cerkev
Early Medieval church / 
   Zgodnejsrednjeveška cerkev
0         10                   20 m

305 Assessing the intentionality of spatial organization. Cemetery of Župna Cerkev (Kranj, Slovenia) case study
Fig. 5: Result of Optimized Hot Spot Analysis representing cold (blue), neutral (yellow) and hot (red) spots within the 
entire cemetery. Confidence level in percentage.
Sl. 5: Rezultat analize hladnih (modro), nevtralnih (rumeno) in vročih (rdeče) točk na celotnem grobišču. V odstotkih 
je izražen interval zaupanja.
99%
95%
90%
Not signicant / Nepomembno
90%
95%
99 % 
Contemporary city / Sodobno mesto
High/Late Medieval church / 
   Visoko/poznosrednjeveška cerkev
Early Medieval church / 
   Zgodnejsrednjeveška cerkev 
0         10                   20 m

306 Katia Francesca ACHINO, Benjamin ŠTULAR, Jernej RIHTER, Janja RIHTER
Fig. 6: Result of Optimized Hot Spot Analysis representing cold (blue), neutral (yellow) and hot (red) spots for Early 
Mediaeval graves. Confidence level in percentage.
Sl. 6: Rezultat analize hladnih (modro), nevtralnih (rumeno) in vročih (rdeče) točk za zgodnjesrednjeveške grobove. V 
odstotkih je izražen interval zaupanja.
2010, 127). Where the topic is raised, it is most 
often limited to being descriptive – e.g., burials 
in rows, reihengräberfeld (Steuer 1982, Abb. 95.1) 
– or focused on detecting the so-called horizontal 
stratigraphy (e.g., Knific 1974; Alajbeg 2015; Sokol 
2016). Notable exceptions addressing spatial pat-
terns have not received the attention they deserve 
(Stadler, V on Freeden, Wieczorek 1997; Macháček 
2001; Losert, Pleterski 2003).
(2) Hotspot analysis of all graves offered glimpses 
into this intentional human choice: the N, E, and W 
sectors were preferred. Observing the chronological 
dynamics is more insightful, however.
Firstly, the area inside the post-1430 church is, 
as expected, dominated by early mediaeval graves. 
These predate the post-1430 church and were 
buried adjacent to and outside the contemporary 
church. Burials made within the existing church, 
i.e., post-1430, are expectedly rare, since the area 
inside the church was reserved for clerics and the 
most affluent individuals (cf. Aries 1989, 32–33; 
Makarovič 1995, 162; Daniell 1997, 108–109).
Secondly, early mediaeval graves are concen-
trated in the NW sector, i.e., between the early 
mediaeval church building and the path leading 
towards the settlement (Fig. 1). It would seem 
that the choice of placement was governed by a 
duopoly, the church building on the one side and 
the path/settlement on the other.
Thirdly, later phase graves exhibit two focal 
areas. The focus SE from the late mediaeval church 
building can be readily explained by the desire to 
be buried as close to the church altar as possible 
(cf. Aries 1989, 32–33; Podpečan 2006, 20; Meier, 
99%
95%
90%
Not signicant / Nepomembno
90%
95%
99 %  
0         10                   20 m
Contemporary city / Sodobno mesto
High/Late Medieval church / 
   Visoko/poznosrednjeveška cerkev
Early Medieval church / 
   Zgodnejsrednjeveška cerkev

307 Assessing the intentionality of spatial organization. Cemetery of Župna Cerkev (Kranj, Slovenia) case study
Fig. 7: Result of Optimized Hot Spot Analysis representing cold (blue), neutral (yellow) and hot (red) spots for post-Early 
Mediaeval graves. Confidence level in percentage.
Sl. 7: Rezultat analize hladnih (modro), nevtralnih (rumeno) in vročih (rdeče) točk za po-zgodnjesrednjeveške grobove. 
V odstotkih je izražen interval zaupanja.
Graham-Campbell 2007, 434). The concentration 
N of the late mediaeval church is located exactly 
in front of the entrance to the burial chapel, an 
obvious second focal area. It can be expected that 
finer chronology will be revealed as meaningful for 
explaining the two. The avoidance of the S sector 
cannot be fully explained at this time. One can 
conjecture that the explanation could be found in 
the desire of late mediaeval citizens to maintain 
an open space S of the church, e.g., to be used 
as an open marketplace (Žontar 1982, 36–38; cf. 
Makarovič 1995, 145); in addition, the mystical 
symbolism in urban forms cannot be excluded (cf. 
Sattler 1983; Lilley 2004). However, at this point of 
the research, it is just as likely that the described 
anomaly is simply the consequence of the different 
methodology used in this area excavated in 1953.
CONCLUSION
The study of patterns within cemeteries is not 
a new topic of enquiry. However, for very large 
cemeteries with a high burial density, a predomi-
nant method of visual interpretation does not 
suffice. This article originates from the need to 
replace visual interpretation with statistically rel-
evant methods employed for understanding and 
interpreting the patterns within funerary space.
The increasing advances in computer analysis 
and statistical techniques applied to archaeologi-
cal contexts in an attempt to identify statistically 
significant clustering or regularity for different 
types of data drive the choice of the approach 
presented in this analysis. It consists of a combi-
nation of statistical and geostatistical techniques 
99%
95%
90%
Not signicant / Nepomembno
90%
95%
99 %  
0         10                   20 m
Contemporary city / Sodobno mesto
High/Late Medieval church / 
   Visoko/poznosrednjeveška cerkev
Early Medieval church / 
   Zgodnejsrednjeveška cerkev

308 Katia Francesca ACHINO, Benjamin ŠTULAR, Jernej RIHTER, Janja RIHTER
that have proved to work particularly well for 
cemetery analysis.
Ripley’ s K-function demonstrated its applicability 
to these contexts in the previous analysis (Sayer, 
Wienhold 2013) thanks to its flexibility in operating 
on multiple scales and at complex, heterogeneous 
sites. In the same way, statistical techniques that 
into account values of global and local autocor-
relation have proved their effectiveness in their 
application to the mediaeval cemetery at Župna 
Cerkev. Indeed, these methods made it possible to 
recognize an intentional, chronologically driven 
choice in grave placement.
Thus, in this analysis, a robust and versatile 
toolkit for spatial analysis using off-the-shelf GIS 
software, tested in its application to cemetery 
contexts, is proposed. Furthermore, this research 
confirms that the archaeological explanations re-
lated to spatial patterns of Central European early 
mediaeval cemeteries deserves more attention; this 
application will hopefully stimulate an increase of 
the research in this direction.
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Srednjeveško grobišče Župna cerkev leži v 
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zgodovinsko, rimskodobno in poznoantično nasel-
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sodi obravnavano grobišče med najpomembnejša 
zgodnjesrednjeveška grobišča jugovzhodnoalpskega 
prostora (sl. 1).
Izkopavanja, ki so potekala s presledki med 
letoma 1953 in 2013, so razkrila 2936 grobov, ki 
jih preliminarno datiramo v čas od 8. do 18. st. 
(Štular, Štuhec 2015, 34–42; Pleterski, Štular, Belak 
2016, 7–25).
Preučevanje namernosti prostorske ureditve. 
Primer grobišča Župna cerkev v Kranju
Povzetek
Teoretična izhodišča
Prostorske analize v arheologiji imajo bogato 
tradicijo (pregled npr. Whallon 1973, 1974; Carr 
1984; Hietala 1984; Aldenderfer 1987; Voorrips, 
O’Shea 1987; Blakholm 1991; Kroll, Price 1991), 
ki je v zadnjih desetletjih prevzemala metode 
iz različnih področij znanosti (Wheatley, Gill-
ings 2002; Conolly, Lake 2006; Salisbury, Keeler 
2007; Nakoinz, Knitter 2016). Tudi geografske 
informacijske sisteme (v nadaljevanju: GIS) v 
arheologiji uporabljamo že od poznih osemde-
setih let prejšnjega stoletja (Zubrow 1990; Peter-
man 1992; Pettitt 1997; Gillings, Sbonias 1999; 
Huggett 2000; Lavachery, Conelissen 2000, 153; 

311 Preučevanje namernosti prostorske ureditve. Primer grobišča Župna cerkev v Kranju
Moyes 2002; Wheatley, Gillings 2002; Bevan, 
Conolly 2004; D’Andrea, Gallotti 2004; Gallotti 
et al. 2011, 2012).
V endar te metode z nekaterimi izjemami (Gold-
stein 1981, 62–63; Quesada, Baena, Blasco 1995; 
Silverman, Small 2002; Šmejda, Turek 2004a, 
57–68; Sayer, Wienhold 2013) niso našle mesta v 
arheologiji smrti in arheologiji grobišč. Tako na 
tem področju vizualno preučevanje načrtov grobišč 
ostaja najpogosteje uporabljena metoda prostorske 
analize (Goldstein 1981, 67; prim. Fotheringham 
2002, 7; Bevan et al. 2013; za srednji vek npr. 
Losert, Pleterski 2003; Filipec 2012; Sokol 2016). 
Vendar ta metoda ni primerna za analizo najdišč 
z izjemno količino in gostoto pokopov, kakršno 
je grobišče Župna cerkev v Kranju (sl. 2).
Podatki in metode
Podatki
Analiza arheoloških podatkov grobišča Župna 
cerkev v Kranju je še v fazi primarnega vrednotenja 
gradiva. V prispevku uporabljamo enega od dose-
danjih rezultatov, prostorsko podatkovno zbirko. 
Ta že vsebuje natančno lego posameznih grobov 
(Pleterski, Štular, Belak 2016, 25–26).
V analizo smo vključili tudi primarno kronolo-
ško opredelitev, ki so jo izkopavalci določili že in 
situ, ko so ločevali zgodnjesrednjeveške grobove 
od mlajših, po-zgodnjesrednjeveških. Gre za zelo 
grobo kronologijo, ki pa se je pri stratigrafski 
analizi izkopavalne sezone 1984 že potrdila kot 
zanesljiva (Rihter 2016). Žal so ti podatki na voljo 
samo za 79,3 % grobov, a je njihova razporeditev 
v prostoru razmeroma enakomerna.
Vizualna analiza načrta grobišča (sl. 1; 2) kaže, 
da so grobovi razporejeni okoli vsakokratne soča-
sne cerkvene stavbe. Zgodnjesrednjeveški pokopi 
so najgostejši zahodno in južno od današnje cer-
kvene stavbe ter v severo- in jugozahodnem delu 
notranjosti te.
Metoda
Naše izhodišče pri razvoju metod prostorske 
statistične analize grobišča je bila naslednja hipo-
teza: za tisočletje pokopavanja na grobišču Župna 
cerkev v Kranju je značilna dinamika v pogrebnih 
praksah; ta dinamika se izraža, med drugim, v 
gostoti grobov, tj. v frekvenci posameznih poko-
pov, opazovanih znotraj vnaprej določene mreže.
Kot ničelno hipotezo smo predvideli naključno 
razporeditev grobov v prostoru; z ovrženjem te 
lahko postavimo alternativno hipotezo: prostorska 
ureditev grobišča je bila nenaključna.
Vzorec prostorske ureditve grobišča smo anali-
zirali z uporabo naslednjih matematičnih orodij:
– analiza vzorca točkovne razmestitve ene spre-
menljivke (t. i. Ripleyjeva K-funkcija: za metodo 
v arheologiji glej Conolly, Lake 2006, 166; Sayer, 
Wienhold 2013, 77; primeri uporabe v arheologiji 
npr. Bevan, Conolly 2006; Crema et al. 2010; Van-
zetti et al. 2010; Winter-Livneh et al. 2010; Sayer, 
Wienhold 2013; Duncan, Schwark 2014; Markofsky 
2014; Thacther, Milne, Park 2017);
– ocenjevanje prostorskega razporejanja (Mora-
nova I-globalna statistika: za metodo glej Moran 
1950; Cliff, Ord 1973; primeri uporabe v arheolo-
giji npr. Kvamme 1990; Premo 2004; Carrer 2015; 
Achino 2016);
– optimizirana analiza vročih in hladnih točk 
(Getis-Ord G*);
– optimizirana analiza izstopajočih vrednosti 
(Moranova I-lokalna statistika: Anselin 1995; 
Levine 2013).
Vse metode smo implementirali v programskih 
okoljih SPSS Statistics 22.0 in ESRI ArcGIS 10.3. S 
temi metodami lahko ugotovimo, ali je prostorska 
razporeditev grobov skladna z (a) modelom pravilne 
razpršenosti, (b) naključno ali pa se pojavlja (c) v 
skupkih oziroma gručah.
Rezultati
V prvem koraku smo ovrgli ničelno in dokazali 
alternativno hipotezo, da so grobovi nenaključno 
razporejeni v prostoru. Podatki večinoma kažejo 
eksponencialno distribucijo, ki odseva namerno 
urejanje grobiščnega prostora. Ocena prostorskega 
razporejanja kaže, da so grobovi urejeni v gruče, 
pri čemer je možnost naključne razporeditve manj-
ša od 1 %. Analiza vzorca točkovne razmestitve 
ene spremenljivke kaže, da je razporeditev bolj 
nagnjena h gručam kot k naključnosti, ko razdalja 
opazovanja preseže 4 metre (sl. 3). Optimizirana 
analiza izstopajočih vrednosti kaže pozitivno 
prostorsko avtokorelacijo v severnem in južnem 
sektorju grobišča (sl. 4). Skladno s pričakovanji te 
rezultate potrjuje tudi optimizirana analiza vročih 
in hladnih točk z vročimi točkami v severnem, 
vzhodnem in zahodnem sektorju ter v severoza-

312 Katia Francesca ACHINO, Benjamin ŠTULAR, Jernej RIHTER, Janja RIHTER
hodnem vogalu v notranjosti današnje cerkvene 
stavbe; edino hladno mesto je v osrednjem delu 
severnega sektorja, kjer je stala srednjeveška 
kapela (sl. 5).
V nadaljevanju smo prostorsko razporeditev 
preverjali še za vsako kronološko fazo posebej, 
tj. za zgodnjesrednjeveške in po-zgodnjesrednje-
veške grobove. Ničelna hipoteza je bila ovržena 
za vsako fazo posebej in tudi ocena prostorskega 
razporejanja kaže < da je možnosti naključne 
razporeditve manjša od 1%. Posebno dragoceni 
pa so rezultati optimizirane analize izstopajočih 
vrednosti in predvsem analize vročih in hladnih 
mest za zgodnjesrednjeveške grobove. Zgodnjesre-
dnjeveški grobovi izkazujejo izrazito vroče območje 
v severozahodnem in izrazito hladno območje v 
jugovzhodnem sektorju (sl. 6). Po-zgodnjesrednje-
veški grobovi izkazujejo skorajda zrcalno podo-
bo: vroče območje v jugovzhodnem in hladno v 
severozahodnem in južnem sektorju z dodatnim 
manjšim vročim območjem v severnem sektorju 
(sl. 7). Prostora pokopavanja obeh kronoloških faz 
se torej prekrivata, a imata žarišča na nasprotnih 
si straneh današnje cerkvene stavbe.
Diskusija
Namen analize je bil potrditi ali ovreči hipotezo, 
da so bile pogrebne prakse na grobišču Župna 
cerkev v Kranju dinamične in da ta dinamika, med 
drugim, odseva v prostorskih vzorcih. Hipotezo 
smo potrdili s tem, ko smo dokazali kronološko 
dinamiko nenaključnih prostorskih vzorcev.
Rezultati pa omogočajo dodatne interpretacije.
1 – Nenaključnost prostorskih vzorcev oziro-
ma urejanja prostora grobišča je bila potrjena za 
grobišče v celoti ter tudi za vsako kronološko fazo 
posebej. V kontekstu srednjeveških in po-srednje-
veških pogrebnih praks (npr. Steuer 1982; Parker 
Pearson 1999, 11–17; Podpečan 2006, 19–20; Petts 
2007; Eichert 2010; 2013) to lahko razložimo samo 
z namerno izbiro mesta posameznega pokopa. 
Slednje je torej za grobišče Župna cerkev v Kranju 
statistično relevantno dokazano.
Sklep se na prvi pogled zdi samoumeven in zato 
nesmiseln, vendar pregled relevantne literature 
pokaže drugače. Vsaj v srednjeevropski arheolo-
giji zgodnjesrednjeveških grobišč se raziskovalci s 
prostorskimi vzorci najpogosteje sploh ne ukvarjajo 
(Pleterski 2010, 127). V redkih primerih, če je 
tema že omenjena, so avtorji najpogosteje zgolj 
deskriptivni – npr. grobovi so v vrstah (Steuer 1982, 
sl. 95.1) – ali osredotočeni na t. i. horizontalno 
stratigrafijo (npr. Knific 1974; Alajbeg 2015; Sokol 
2016). Izjeme (Stadler, Von Freeden, Wieczorek 
1997; Macháček 2001; Losert, Pleterski 2003) so 
ostale izolirani primeri.
2 – Analiza vročih in hladnih točk nam je 
omogočila vpogled v zavestno umeščanje grobov: 
priljubljeni so bili severni, vzhodni in zahodni 
sektor. Bolj izpovedna je kronološka dinamika.
Prvič, v današnji cerkveni stavbi, ki stoji v tem 
obsegu od leta 1430, po pričakovanju prevladujejo 
zgodnjesrednjeveški grobovi. Ti so bili vkopani 
zunaj vsakokratne sočasne cerkvene stavbe. Pokopi 
znotraj sočasne cerkve so po pričakovanju redki 
in izjemni (prim. Aries 1989, 32–33; Makarovič 
1995, 162; Daniell 1997, 108–109).
Drugič, koncentracija zgodnjesrednjeveških gro-
bov v severozahodnem sektorju leži med sočasno 
cerkveno stavbo in potjo (sl. 1). Zdi se, da je bil 
prostor grobišča zamejen na eni strani s cerkvijo 
in na drugi s potjo.
Tretjič, po-zgodnjesrednjeveško grobišče kaže 
dve zgostitvi. Tisto jugovzhodno od današnje 
cerkve lahko pojasnimo z željo biti pokopan čim 
bliže oltarju (prim. Aries 1989, 32–33; Podpečan 
2006, 2; Meier, Graham-Campbell 2007, 434). 
Zgostitev severno od cerkve je tik pred vhodom 
v sočasno grobiščno kapelo, katere bližina je bila 
očitno zaželena. Podrobnejša kronologija grobov 
bo v prihodnosti zagotovo omogočila natančnejšo 
interpretacijo teh opažanj. Izogibanja južnemu 
sektorju za zdaj še ne moremo natančneje poja-
sniti. Ena od možnih razlag bi bila, da so meščani 
v nekem obdobju predel južno od cerkve – ena 
glavnih prečnih komunikacij med mestnimi pre-
deli (Žontar 1982, 36–38; prim. Makarovič 1995, 
145) – namenili komunikaciji. Trenutno ne more-
mo izključiti niti uporabe mističnega simbolizma 
v urejanju mestnega prostora (prim. Lilley 2004; 
Sattler 1983). Vendar se na tej stopnji raziskave 
zdi enako verjetna razlaga tudi da, da je manjša 
gostota zgolj posledica drugačne metode izkopa-
vanja leta 1953.
Zaključek
Analiza prostorskih vzorcev na grobiščih ni 
nova tema v arheologiji. Vendar za zelo velika 
grobišča z visoko koncentracijo grobov običajna 
metoda analize, opazovanje načrta grobišča, ne 
zadostuje. Pričujoči prispevek je nastal iz potrebe 
po nadomestitvi te vizualne analize s statistično 

313 Preučevanje namernosti prostorske ureditve. Primer grobišča Župna cerkev v Kranju
relevantnimi metodami, ki omogočajo analizo 
in interpretacijo vzorcev pogrebnega prostora. 
Pot, ki smo jo izbrali, je tlakovana z napredkom 
računalniških tehnologij in statističnih analiz v 
arheologiji. Želeni cilj je prepoznati statistično 
relevantne vzorce in vzorce. Končna metoda je 
kombinacija statističnih in geostatističnih orodij, 
ki se je izkazala za prav posebej primerno za 
analizo grobišč.
Analiza vzorca točkovne razmestitve ene spre-
menljivke, ki je že bila uporabljena za analizo 
srednjeveškega grobišča (Sayer, Wienhold 2013), je 
zelo primerna zaradi prilagodljivosti in zmožnosti 
analize v različnih merilih. Podobno so se kot zelo 
primerna pokazala statistična orodja, ki temeljijo 
na globalni in lokalni avtokorelaciji. Aplikacija teh 
metod na grobišču Župna cerkev v Kranju nam je 
omogočila, da smo prepoznali namerno, kronološko 
dinamično izbiro prostora pokopavanja.
V prispevku torej predstavljamo robusten in 
raznovrsten nabor orodij za prostorske analize 
grobišč, ki ga lahko uporabimo znotraj že ob-
stoječih programskih paketov GIS. Dodatno s 
prispevkom opozarjamo, da v prihodnosti ana-
lizam urejanja prostora srednjeveških grobišč, 
ki odseva v prostorskih vzorcih grobov, kaže 
nameniti več pozornosti.
Katia Francesca Achino
LAQU, Departament de Prehistòria
Universitat Autònoma de Barcelona
Facultat de Filosofia i Lletres, Edifici B, 
ES-08193 Bellaterra (Barcelona)
katia.francesca.achino@uniroma2.it
Benjamin Štular
Znanstvenoraziskovalni center SAZU
Inštitut za arheologijio
Novi trg 2
SI-1000 Ljubljana
benjamin.stular@zrc-sazu.si
Jernej Rihter
Znanstvenoraziskovalni center SAZU
Inštitut za arheologijio
Novi trg 2
SI-1000 Ljubljana
jernej.rihter@zrc-sazu.si
Janja Rihter
Pedagoška fakulteta
Univerza v Ljubljani
Kardeljeva ploščad 16
SI-1000 Ljubljana
janja.rihter@pef.uni-lj.si