CL-SNA: social network analysis with Lisp

Abstract

Social relations have been a research interest in many areas of social sciences. In sociology, for example, individuals up in the power hierarchy in a group can be determined quantitatively by looking at the number of direct relations to others in the group[1]. Similarly, in management and economics, alliance relationships between firms are examined carefully to explain phenomenon such as innovation and market leadership[6]. Similar problems were encountered in Anthropology, Zoology, and many other fields. In most studies regarding social relations, one must look into the content of social relations in addition to their structure, an endeavor which demands ethnographic methods. Nevertheless, analysis of the structure alone has been a powerful tool which not only enables quantitative assessment of social structures, but also prompts elaboration of interpretive process.

Full text

CL-SNA: Social Network Analysis with Lisp
[Draft Paper]
Mehmet Gencer
Computer Science
Department
Istanbul Bilgi University
Kurtulus Deresi Cad. No:47
34440, Dolapdere, Istanbul,
Turkey
mgencer@cs.bilgi.edu.tr
Coskun Gunduz
Computer Science
Department
Istanbul Bilgi University
Kurtulus Deresi Cad. No:47
34440, Dolapdere, Istanbul,
Turkey
cgunduz@cs.bilgi.edu.tr
Vehbi Sinan Tunalioglu
Computer Science
Department
Istanbul Bilgi University
Kurtulus Deresi Cad. No:47
34440, Dolapdere, Istanbul,
Turkey
vst@cs.bilgi.edu.tr
Keywords
Common Lisp, Social Network Analysis, Graph The-
ory, Graph Visualization
1. INTRODUCTION
Social relations have been a research interest in
many areas of social sciences. In sociology, for ex-
ample, individuals up in the power hierarchy in a
group can be determined quantitatively by looking
at the number of direct relations to others in the
group[1]. Similarly, in management and economics,
alliance relationships between firms are examined
carefully to explain phenomenon such as innova-
tion and market leadership[6]. Similar problems
were encountered in Anthropology, Zoology, and
many other fields. In most studies regarding so-
cial relations, one must look into the content of
social relations in addition to their structure, an
endeavor which demands ethnographic methods.
Nevertheless, analysis of the structure alone has
been a powerful tool which not only enables quan-
titative assessment of social structures, but also
prompts elaboration of interpretive process.
Methods used in analysis of social relations was
originally coined as sociometrics by Psychothera-
pist Jacob Moreno in 1930s, while he developed
systematic ways to represent and assess like-dislike
relations between school children[8]. Today, social
network analysis (SNA) is the generally preferred
term for this growing corpus of methods. How-
ever, use of these methods, majority of which orig-
inated in social sciences, are very common in other
fields. A well known example is popularity rank-
ing of websites by looking at how many times they
were linked from other sites[7], as in Google search
engine. Although various metrics defined in SNA
are substantially void of any meaning which is so-
cial per se but simply definitions over graphs, the
term social network analysis is widely regarded for
the very fact that it gives such meanings to them
(For a good review see Scott[10]).
As SNA methods became widespread, many soft-
ware tools and libraries were developed to compute
metrics and visualize social networks. UCINET[11]
was among the first to offer a comprehensive set of
features, and is a commercial software. A more re-
cent package, Pajek[9], is freeware. There also ex-
ist a few libraries for R-Project[4]. However, most
of the open source packages which are available
seem to be incomplete when one needs a toolkit
which can provide a wide range of SNA metrics
for different types of graphs (e.g. including di-
rected graphs), means for partitioning and cluster-
ing, tools for visualization, and at the same time
one that is easily re-programmable for specific needs
suitable to exchange data with other software tools.
CL-SNA package aims to bridge this gap by being

feature rich and easily extensible by the virtue of
being written in Lisp. Following framework sets
the design principles of CL-SNA:
•A social graph, or a set of graphs, can be
constructed by means of reading in a concise
format, or in a programmatic way.
•Graph nodes and edges can be attributed with
meta-information, in form of a mapping, to
facilitate selective processing of sub-graphs
later.
•A variety of SNA metrics including, but not
limited to, degree centrality, betweenness, close-
ness, eigenvalue centrality, are provided. New
ones can be easily added using graph search
or matrix based methods.
•SNA measures of graph nodes can be exported
for statistical processing in other software such
as R.
•Graphs can be visualized in graphics inter-
face, exported in suitable image formats, or
exported in formats suitable for visualization
in other packages such as Pajek.
Although all of the aspects above are important
for user convenience, an important part of CL-
SNA’s competence lies in variety and accessibil-
ity of SNA metrics implemented. For the large
part we have drawn from comprehensive work of
Wasserman et.al. [12] in the implementation, and
referenced others whenever necessary.
CL-SNA package is distributed with General Pub-
lic License[5] and it comes with a variety of ex-
amples and comprehensive documentation for both
novice users and more experienced users who wish
to extend it for their particular problem.
2. KEY FEATURES
CL-SNA’s operation consists of three phases:
1. data input,
2. processing, and
3. visualization and data export.
While trying to satisfy the requirements of a social
network analysis methodology, we attempt to pro-
pose open standards in each phase. Data import
and export is of great importance among these.
Another important issue is a well defined API which
enables further development and porting of the ap-
plication suite to other programming languages and
environments, such as R, SciLab, Python or Mat-
lab.
International Network for Social Network Analy-
sis[3] provides a compilation of available software
for social network analysis[2]. Most of them are
special purpose software. Besides covering most
methodologies, CL-SNA attempts to fill the gap to
provide a well defined input format.
Wasserman et.al.[12] refers to three different nota-
tions which are consistent with each other: Graph
theoretic, sociometric and algebraic notations. Graph
theoretic, among these, can be generalized easily
to multirelational networks and this notation is
adopted in CL-SNA. On the other hand, this is
a well known and easily interpretable language for
software developers. A well defined data input for-
mat has been defined to represent social network
data with an important addition: metadata. Meta-
data is necessity for describing the data set, re-
quired for classification, processing and outputting.
We pay much attention to a particular issue: Soft-
ware development methodology. While agile method-
ology has been employed during development, we
simultaneously aimed for a robust API specifica-
tion which enables us to extend both the API and
the implementation incrementally, i.e. brand new
functionality can be added easily to the software.
Thus, the documentation of the API is a serious
task among others, so that, at the end, it intro-
duces the possibility of similar SNA implementa-
tions in different programming languages and en-
vironments.
Finally, CL-SNA offers a rich set of visualization
and data oriented output facilities. Generic inter-
faces allow us, users and future developers to visu-
alize the output both in CL-SNA framework and
external viewers including Graphviz, ImageMag-
ick, gnuplot etc., while providing the advantage of
exporting results and data with and without ma-
nipulating them.

3. IMPLEMENTATION APPROACH
There are various types of networks which may
be the subject of SNA methods. In graph theo-
retic terms, these networks can be: (1) directed or
undirected, (2) one or two mode, (3) weighted or
not weighted, and (4) signed or not signed. Fur-
thermore, the corresponding graphs can be trees,
bipartite graphs etc. Although CL-SNA package
does not claim to handle all combinations, it does
attempt to generalize analysis implementation and
provide convenience methods for converting and
dissecting network data for further processing.
Social networks may come in various sizes and dif-
ferent organizational features. Naturally, one should
not expect a single recipe leading to enlightenment
about all networks one may encounter. In this re-
spect, we attempt to provide a package which has
sensible defaults for most analysis procedures, but
remain open to recombination of procedures ac-
cording to social researcher’s interpretation of the
specific problem in hand. In addition the family of
research problems in consideration necessitates de-
scriptive methods through better visualization and
capability to combine power of CL-SNA package
with other specialized analysis tools.
In order to convene our approach to accommodate
these various constraints, the following three sec-
tions summarize the implementation approaches
for analysis, visualization and data exchange.
3.1 Organization of Network Analysis
Procedures
Different levels of analysis leads to a variety of net-
work metrics. There are several types of measures
for assessment of properties for a particular node,
a group of nodes, or the whole network:
Network Level Measures: A common measure
is graph density, which is defined as a ratio
of the number of existing links to the number
of all possible links. However, most measures
are more challenging to compute for large
number of nodes and/or links. For example,
one would need the reachability matrix, so
that we can check partitions in the graph,
etc.
Actor(Node) level measures: An actor’s loca-
tion in a social network is defined through its
relations with others. Several measures have
been employed for quantification of structural
and locational properties of actors in differ-
ent contexts. In addition to simpler measures
such as degree centrality, which is basically
the number of links to the actor, other mea-
sures such as betweenness centrality, close-
ness centrality, or information centrality have
been defined. In betweenness centrality, for
example, one must check how often an actor
stands on the way linking two actors, which
requires substantial time to compute for larger
networks.
Group level measures: Discovery and compari-
son of structural subgroups in a social group
has been very interesting for social scientists.
Different methods for discovery of subgroups
have been proposed, for example, based on
reach diameters or nodal degrees. In addi-
tion relations of different subgroups can be
assessed similar to the case of actors.
SNA literature reveals various approaches for es-
tablishing such measures. The key split in this
corpus of approaches is the use of graph search
methods and matrix methods. For large networks,
matrix methods impose an overwhelming computa-
tional demand in obtaining some measures. Imag-
ine, for example, using matrix methods for a social
network having number of nodes, n, equal to 20,000
and represented as a matrix, S, which is an n×n
matrix . Even a simple check such as connectivity
will require computing Sn, which imposes a com-
putational complexity at the level of O(n3log(n)).
For these reasons, our approach in CL-SNA is to
represent social networks as S-Expressions and only
when matrix methods are more convenient switch
to using them.
In order to speak of group level measures, one needs
means to determine subgroups. Identification of
subgroups is perhaps one of the most interesting
tasks in social network analysis. For this purpose,
the package also provides several methods based
on established group cohesion tests in SNA litera-
ture such as LS sets or Lambda sets, and efficient
generation of candidate subgroups.
One example to define subgroups is LS sets. Let
Nbe the set of all nodes in the graph, which has
nnodes, and let us consider a subset, Ns. We will
define a subset of nodes taken from Nsas Lso that
L⊂Ns. The set of nodes, Nsis an LS set if any

proper subset L⊂Ns, has more lines to nodes in
Ns−L(other nodes in the subset) than to N−Ns
(nodes outside the subset). A search without using
any heuristics this search will mean testing rela-
tive connectivity of Pi=2 nn!
i!(n−i)! candidate sub-
sets. Thus especially for large networks, tractabil-
ity of such probing requires a sensible selection of
subgroup candidates. There are various matrix or
search based approaches in SNA literature regard-
ing such subgroup investigations (see Scott[10] for
an excellent review of such methods), having names
as k-cores, n-cliques, LS sets, Lambda sets, etc.
Providing a rich library of these methods is a key
long-term target for CL-SNA package.
3.2 Visualization
One of the research branches in graph theory is the
efficient visualization of graphs. There are algo-
rithms developed to achieve this aim. We’ve leaved
to implement and developed such algorithms out of
the scope of the application. This job is delegated
to the Graphviz suit, which is the main visualiza-
tion output of the application.
However, even Graphviz cannot always automati-
cally generate well-balanced, compact visualization
of social network data. For this, we approached to
define subgraphs (in our terminology subnets), and
use them as a proxy to compact and balanced vi-
sualizations.
Also, we add further information to visualization
which are derived from social network metrics. For
example, actors with higher degree of centrality are
marked with darker colours. Further information
is put on the graph visualization as text labels on
demand, such as graph density or graph centrality.
3.3 Data Input and Export
Currently there are two methods for data input.
One is reading matrix files, and the other is reading
a custom graph data file. The custom graph for-
mat uses a markup based on S-Expressions which
can be read (parsed) and written easily by Lisp
programs. These S-Expressions is also the way the
social network is stored and passed around in CL-
SNA package. The markup follows XML tagging
conventions. It is also possible to add necessary
meta attributes for the whole network, or node and
edges. Such an example input data file is shown in
Figure 1. The < key, value > pairs in various el-
ements are free-form attributes. These attributes
(SOCIAL-NETWORK
(METADATA
(VERSION 1.0)
(NAME "Florentine Families")
(DESCRIPTION "Marriage ties of Florentine
families.")
(AUTHOR "Isthisa Record")
(DATE "2002-03-07")
(DIRECTED No)
(@ (KEY-1 VAL-1)
(KEY-2 VAL-2)
(KEY-3 VAL-3)))
(DATA
(NODE Medici (@ (KEY-1 VAL-1)
(KEY-2 VAL-2)
(KEY-3 VAL-3)
(KEY-4 VAL-4)))
(NODE Pucci)
(EDGE Medici Pucci (@ (WEIGHT 10)
(KEY-1 VAL-1)))))
Figure 1: Custom social graph data format
can be employed in further merging or dissection of
graphs for analysis and CL-SNA package provides
essential methods for this purpose.
Unlike matrix notation, it is required in this format
for nodes to have distinct names, which in turn is
used in describing edges.
In addition to S-Expression format the package
can read sociomatrix files, an example of which is
shown in the next section. Furthermore, it is possi-
ble to export social networks in ‘comma separated
values’ format which is a standard for statistical
analysis programs such as SPSS and R or other
network analysis packages such as UCINET.
4. EXAMPLE DIRECT USAGE
For demonstration purposes, let us take one of the
examples used by Wasserman and Faust[12]: mar-
riage ties between Florentine families of 16th cen-
tury. There are only 16 entities in this data set, but
it is sufficient to demonstrate typical types of anal-
ysis. For example, we may look into which families
are more central in the set or what groups emerge
through marriage relations.
To start the analysis, we first need a way to load
the data of the graph corresponding to our social

"Acciaiuoli" "Albizzi" ... "Tornabuoni"
0000000010000000
0000011010000000
0000100010000000
0000001000100010
0010000000100010
0100000000000000
0101000100000001
0000001000000000
1110000000001101
0000000000000100
0001100000000010
0000000000000000
0000000010000011
0000000011000000
0001100000101000
0000001010001000
Figure 2: The matrix representing data for
marriage ties between Florentine families
network. In this example, we have a matrix rep-
resentation, so called ‘adjacency matrix’, as shown
in Figure 2. Note that there is no specification in
matrix notation whether the corresponding graph
is directed or weighed. The relation in considera-
tion, namely the marriage relation, is not directed.
Thus, the matrix is symmetrical. And all weights
are 1s.
We will use the low level access to CL-SNA in
the following example. Let us read the social net-
work data with CL-SNA and put into a variable
for future processing. This data comes from a ma-
trix file so it needs some conversion first by using
matrix2sexp:
* (setf graph
(matrix2sexp
(read-matrix-from-file
"florantine-families.txt"
:labels t )))
:labels t statement refers to that there exist la-
bels in the matrix file to identify the nodes in the
graph. Now, let us look at the graph-wide property
of density:
* (graph-density graph)
1/6
Now we can compute degree prestige of individual
nodes:
* (setf nodenames (get-node-names graph))
* (setf edges (get-edges graph))
* (print-degrees
(degree-centrality-of-all-nodes
nodenames edges))
in-degree of Acciaiuoli : 1
in-degree of Albizzi : 3
in-degree of Barbadori : 2
in-degree of Bischeri : 3
in-degree of Castellani : 3
in-degree of Ginori : 1
in-degree of Guadagni : 4
in-degree of Lamberteschi : 1
in-degree of Medici : 6
in-degree of Pazzi : 1
in-degree of Peruzzi : 3
in-degree of Pucci : 0
in-degree of Ridolfi : 3
in-degree of Salviati : 2
in-degree of Strozzi : 4
in-degree of Tornabuoni : 3
Before we proceed to node and subgroup level prop-
erties of this data set, let us have a look at it. To do
this we will first need to export it into Graphviz’s
dot format:
* (graph2dotfile "florantine.dot" graph)
NIL
The above command will save the graph in a for-
mat suitable for display in Graphviz program, into
file “./florantine.dot”. Which in turn can be visual-
ized with various Graphviz command-line utilities.
The result is shown in Figure 3.
This version of visualization is quite rudimentary.
As no guidance in grouping the nodes for display
is provided to the external tool (Graphviz) it is
hard to visually spot distinctive nodes, such as the
Medici family which has more relations than any
other family.
A suggested visualization of groups in our example
using the LS set approach is shown in Figure 4.
The groups are better visible in this version, how-
ever, further work is necessary to achieve better
integration with Graphviz.

Figure 3: Visualization of marriage ties be-
tween Florentine families
Figure 4: Better visualization emphasizing
subgraphs
5. COMPUTATIONAL ASPECTS
The package includes the implementations of social
network metrics on the basis of graph theoretic no-
tation. This notation brings some important key-
points of graph theory to this approach. For many
functions, runtime analysis should be covered dur-
ing implementation and efficiency was a concern as
much as functionality.
Adjacency matrices are used for feeding the input
to the software, too. If there are nvertices in the
graph i.e. nodes or elements in the social network,
then there are n2numbers in the adjacency matrix
by its definition. Thus, even for simpler functions,
the runtime of the code goes up to O(n2), which is
bigger than many functional and useful procedures
like sorting.
As an example, to calculate the maximum degree
of centrality in the graph, the whole matrix should
be traversed and degree of centrality for each ver-
tex should be calculated. Then, the maximum of
these values is found as the output of the related
function. That makes n2+narithmetic operations
that corresponds to O(n2). For increasing the ef-
ficiency of, the traversing step can be faster if the
graph is undirected. This property makes the adja-
cency matrix symmetric so that only checking the
lower half (or the upper half without loss of gener-
ality) may reduce the runtime of traversing process
by half. That results in (n2/2) + narithmetic op-
erations which is still O(n2).
Degree of centrality is an easy function to imple-
ment. So that it is easy to reduce the number
of arithmetic operations by trivial methods. On
the other hand, there are some functions which are
much more complex in terms of algorithm and run-
time analysis.
Subgroup identification is an important problem in
social network analysis. In this paper, subgroups
are defined as LS sets as explained in part 3.1.
When this definition is taken into consideration,
a function is needed to produce all subsets of a set
of nodes. Also for other social network analysis
tasks, such a function will be useful. In this spe-
cific subgrouping problem, generating all subsets
of a set of nodes, then for each set, counting the
edges to that set and to the complement of that
set outcomes an O(n3) runtime. So, some pruning
needed by defining some heuristics such that the

star node and the adjacent nodes are taken in the
same set to start with. Another heuristic is putting
the nodes with only one edge to the same set with
its adjacent node. Since these heuristics speed up
the subgrouping procedure, it is hard to calculate
a new runtime result. Because, one can not make
a decision named as an average case such that if
there are nnodes, kof them are adjacent to star
node etc. That’s why, O(n3) runtime declaration
is not updated.
6. LARGER EXAMPLE SIMPLER IN-
TERFACE
The examples above can be cumbersome for sim-
ple analysis. For this reason, CL-SNA package
provides several convenience functions to facilitate
easier and faster experimentation with social net-
work graphs. In order to avoid repetition of com-
mands and computation of some essential mea-
sures, two convenience functions, namely savews
and loadws, are provided to store and retrieve user’s
workspace between separate runs.
As another example, we will look at the relations
between software packages in Debian GNU/Linux
Distribution1. There are 20,610 graph nodes repre-
senting software packages in this project and 92,534
graph edges representing dependency links. Al-
though the nodes in this graph are not people,
since each package is maintained by a developer
the graph also represents dependency between de-
velopers. The example sessions below shows usage
of this toolkit functions for Debian packages data.
* (new-project "dpkgs.sexp")
Graph loaded successfully.
Graph Name : Debian packages
Number of nodes: 20610, Number of edges:92534
* (summary)
GRAPH SUMMARY:
Graph Name : Debian packages
Number of nodes: 20610, Number of edges:92534
Graph Density: 0.000218
Finding node degrees. This will take
about 5.721377 minutes.
Most central nodes with degree>1057:
LIBSTDC++6 : 1864
PYTHON : 1127
LIBGCC1 : 2392
1see http://www.debian.org
LIBICE6 : 1065
LIBSM6 : 1057
ZLIB1G : 2080
PERL : 1721
LIBC6 : 9387
XLIBS : 2665
LIBXEXT6 : 1821
* (savews)
When a work session is saved as above, certain
properties of graph nodes will be saved along. So
the following commands in the next session will dis-
play top ten nodes most faster than the first run
and one will not see ‘Finding degrees ...’ warning:
* (loadws)
* (summary)
-------------------------
GRAPH SUMMARY:
Graph Name : DEBIAN
Number of nodes: 20610, Number of edges:92534
Graph Density: 0.000218
Most central nodes with degree>1057:
LIBSTDC++6 : 1864
.
.
.
One can manage multiple workspaces by using load-
wsfrom and savewsto functions which accept file
path parameter for location to save or load the
workspace.
With such large graphs, visualization of the whole
population is useless as structural outline would
not be visually detectable. One possible mediation
is to display a limited subset of nodes, for example
those that have higher degree centrality than a cer-
tain limit. In the following example, we will switch
into a context where we examine a subgraph, ex-
port the graph to Graphviz format, then switch
back to our older context which is the whole graph:
* (intograph (makesubgraph-degreelimit 500))
* (dotto "dpkg500.dot")
* (numcontexts)
Number of contexts stacked:1
* (exitgraph)
* (numcontexts)
Number of contexts stacked:0
Graph visualization using nodes with centrality higher
than 500 is shown in Figure 5. In this version two

Figure 5: Subset of Debian packages net-
work with nodes having centrality larger
than 500
nodes are visually detectable as highly central.
6.1 Benchmarks
Since determining a node’s centrality is a search
which takes up time proportional to the number of
edges, even this simple measure takes some time to
compute.
In our tests it took 7 minutes2to finish the sum-
mary for Debian packages network in the section
above, core of which involves computing degree
centrality of all nodes in the graph.
7. DISCUSSION: FUTURE PROSPECTS
FOR CL-SNA
Current CL-SNA implementation has no features
supporting analysis of network dynamics, i.e. changes
in social network. This type of analysis would re-
quire comparing two or more snapshots of a social
network taken at different moments. In order to
do this, one should be able to identify same sub-
groups in two snapshots, determine which nodes
have undergone significant changes in their prop-
erties such as centrality, etc. Furthermore, cluster-
ing of social network with respect to user defined
attributes should be incorporated into the longitu-
dinal analysis. This is a challenging task. However,
dynamic network analysis in an important emerg-
ing field and would be a valuable addition to any
network analysis software.
Other promising prospects for future development
of CL-SNA package would be better visualization
and statistical analysis capabilities. Graph visual-
ization should be seen as a separate field of work,
thus it is best to stick to the approach to simply
support exporting graphs for visualization by ex-
ternal tools. However, for complex and crowded
2on a Pentium 4 desktop computer with 512MB of
Ram
social networks two dimensional visualization may
deem insufficient. Support for three dimensional
and more flexible graph visualization software is
worth considering.
Statistical analysis can prove valuable in identi-
fying structural properties of social networks and
subsequent driving of network analysis. There are
various statistical software packages available. Some
such as R-Project are very powerful, have suitable
licenses and is command driven which eases inte-
gration. Not only extension of CL-SNA with in-
tegration of such package to provide statistical ca-
pabilities is useful, but also CL-SNA can be inte-
grated to R-Project to enable statistical processing
of social graphs with full power of R.
Many of the methods used in SNA are computa-
tionally demanding for crowded networks. Paral-
lelization of analysis procedures can greatly im-
prove performance of the package. Sharing and
management of multiple workspaces is another en-
gineering issue which is not yet addressed in the
implementation of CL-SNA.
8. SUMMARY
CL-SNA is a package for social network analysis
written in Lisp. It provides
•a well defined data format for input and out-
put of social network data supporting use of
metadata,
•implementations of many metrics developed
in the literature,
•a powerful and rich set of data export facili-
ties for visualization and suspending the anal-
ysis session, and
•a robust and extensible API for future devel-
opment.
Being organized towards a social researcher’s per-
spective, CL-SNA provides an easily workable and
comprehensive environment for those engaged in
quantitative analysis of social network structures.
But even more importantly, it aims to accommo-
date the very needs of researchers in its future
evolution through its design principles, and to be
amenable to problem specific modification.

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