Complex Systems: Risk Model Based on Social
Mauro Faccioni Filho
Universidade do Sul de Santa Catarina – UNISUL
Pedra Branca - Palhoça - Santa Catarina - Brazil
Abstract—Risk is difficult to analyze and predict in complex
systems, especially if it is necessary to evaluate mission-critical
systems risks in real-time. This work proposes a theoretical
model, based on social network analysis and risk classification.
The work objective is to understand risks from data and evidence
obtained in real time, not coming from statistics of similar
systems nor risk probabilities taken a priori. The analysis model
seeks to design the structure or environment at risk as a complex
system in which all components and relations are essential. These
components and their relations form a social network, which can
be analysed through the mathematics of Graphs. This is the main
point and the novelty of the work, which will allow users of the
method to assess risks in real time. As an example to illustrate
the model application a typical datacenter diagram is showed in
the paper, and used as a complex system to perform a case study.
Keywords— Risk, Complex System, Risk Model, Social Network
Analysis, Datacenter, Power Distribution Systems.
The aim of this paper is to present a new analysis model of
risks for complex systems.
Complex systems are systems in which components are
interrelated and cannot be reduced at the risk of extinction of
the system. To do risk analysis in real time, the model uses
concepts of Social Network Analysis – SNA  associated to
measurements obtained in the field by means of IoT (Internet
of Things) sensors coupled to the various components of a
complex system. As an example of application in a real
complex system, the paper presents a typical datacenter
diagram, with its components and redundancies. A datacenter
monitoring and management platform, such as Datacenter
Infrastructure Management Systems (DCIM), uses Internet of
Things as a fundamental part of measurement tools.
To classify and determine the risk levels, the model uses a
classification derived from the social network analysis theory,
and assigns levels for risks (Risk Index) in accordance with the
characteristics of the node network connections and their
implications. The proposal is theoretical and will, in future
research projects, develop applications to calculate the Risk
This paper is organized as follows. Section 2 will introduce
the concepts adopted for complex systems and some related
examples, which will be considered for the risk model
proposed. Section 3 will explain basic principles of social
network analysis and the complex system example, from the
Section 2, modeled as a social network. Section 4 will present
the risk model as an interrelation between system layers, and
how these various network layers and sub-layers determine risk
levels for the entire complex system. Finally, Section 5 will
present the conclusions of the study, ongoing projects and
The concept of a complex system, adopted in this article
and in the risk model proposed, is defined as that system
wherein all components are interdependent, such that the
removal of one of these components will affect the system as a
whole . Complex systems are systems that depend on the
integration of its components, and will be deeply changed or
even destroyed if a component or a relationship between
components, for any reason, is affected.
Complex systems may not be confused with "complicated"
systems. Complicated systems sometimes have the appearance
of complex ones, but do not have an internal degree of
interdependence between components, as occurs with complex
Complicated systems are those wherein removal of a
component does not affect the behavior of the system. While
the "complicated" systems can be reduced, complex systems
may not, without losing its characteristics. This comprehension
is necessary and important so that we can create the
appropriate model for risk analysis and assessment .
Considering industrial applications, examples of complex
systems are power distribution systems, datacenters, building
automation networks, factory automation networks and several
other industrial systems and installations. In all of them, their
internal components behave like actors in a social network, and
their relationships are essential to the operation of the system.
To illustrate this, Figure 1 shows a datacenter diagram as an
example of a complex system, which will be modelled next in
this paper. Datacenters are mission-critical environments where
maximum reliable operation and minimum downtime are
essential. The various components are interrelated and
redundancy of components and connections is fundamental
(see in the figure the left and right sides symmetry)  .
Figure 2 illustrates a schematic Power Panel (PP), which is
one of the datacenter equipment, responsible for power
distribution and protection of circuits (note at figure 1 the MPP
and PP). The power panel, due to its characteristics and despite
its small magnitude when compared to the whole datacenter, is
in itself a complex system. Though the Power Panel is a
subsystem of the datacenter, and this is important to understand
when building the Risk Model.
Examples of Figures 1 and 2 will be resumed in the next
section, where will be presented the models of these systems
according to the concepts of social networks analysis,
necessary for the risk modeling proposed.
Complex systems, because of their characteristics, can be
modeled as social networks, and from that we can apply the
mathematics of social network analysis to get information on
The social network analysis has been applied in various
fields and organizations, political and economic systems,
educational systems and many others .
By the 1950s the term "social network" was first used,
having roots in Sociometry. Analytical evolution came with the
incorporation of mathematical tools (graph theory) and
computing   .
Basically social networks are formed by actors (nodes) and
their connections (links). The actor can represent an individual,
a corporation or a social collective (if we refer to a human
society), or a device, a power distribution or power line (if we
refer to an installation, for example).
A connection between two actors in a social network is a
“link”. When there are more than three actors in a network, the
network is called a “group”. To be analyzed, the social network
must have a defined set of players, that is, the social network is
a "finite set of actors and their connections."
Figure 3 shows an example of a very simple social network
using the notation of graph theory (left) and his matrix notation
(right), where the presence of connections between nodes is
represented by “1”, and the absence of connections is
represented by “0” or "empty" cell.
The use of matrices, called here sociomatrices, is useful for
the computation of large networks with thousands or even
millions of nodes.
Social networks can be called “connected” or
“disconnected”. The network is called connected when there is
a possible path between any two network nodes. If this is not
possible, the network is considered disconnected.
Figure 4 shows a disconnected network by the withdrawal
of a node (the “cutnode”), or by the removal of a link (the
CB1 CB2 CB3 CB4 CB5 CBn
Figure 2. Schematic presentation of a power pane
l, with circuit breakers,
electrical switches and busway
UPS2 UPS3 UPS4
Figure 1. Schematic diagram of a datacenter. Datacenter is an example of a
complex system. (GEN – Generator, T – Power Transformer, PP – Power
Panel, MPP – Main Power Panel, AC – Air Conditioning, UPS –
Uninterruptible Power System, PDU – Power Distribution Unit.)
If the network under study is a complex system, the
occurrence of failures on nodes or on links may directly impact
the system, because these failures will transform the network
on a disconnected one.
These failures in complex systems observe the following
• If a node is a cutnode, then it has not a parallel
redundancy, but if a node has not a parallel
redundancy, not necessarily it is a cutnode.
• If a link is a bridge, then it has not a parallel
redundancy, but if a link has not a parallel redundancy,
not necessarily it is a bridge.
• If a cutnode is removed, the disconnected network will
have two or more components.
• If a bridge is removed, the disconnected network will
have only two components.
• In a complex system all cutnodes are equivalent in
• In a complex system all bridges are equivalent in
Considering now an example, the Figure 5 represents the
complex system of the datacenter from Figure 1 as a social
network, using the graph notation. The Figure 6 represents the
power panel from Figure 2 as a social network model. These
examples will be useful to illustrate the following risk model.
The social network in Figure 5 shows each of the schematic
datacenter equipment of Figure 1. The nodes MPP1, MPP2,
Busway and PP1 are cutnodes because the withdrawal of any
one of them will isolate other network nodes, making the
network disconnected. From the point of view of risk, these are
In the case of a complex system like the datacenter, a set of
equipment operates redundantly, as it happens for GEN2
regarding to GEN1, MPP2 regarding to MPP1, and so on. As
redundancy is associated with the risk of the datacenter
deadlock, even the removal of a seemingly lateral node or a
less important one can affect the entire system.
The social network of Figure 6 shows the graph
representation of the schematic power panel of Figure 2, which
in itself is a complex system (despite the apparent simplicity),
Figure 6. The social network re
presentation of the power panel from Figure 2;
each circuit breaker and busway is identified as a node
Figure 5. The social network representation of the schematic datacenter of
Figure 1, where each equipment is identified as a node.
Figure 4. Disconnected network due to a removal of a node (cut node) or due
to a removal of a link (bridge).
1 1 1
1 1 1
Figure 3. Graph representation of a social network with n nodes (left) and its
symmetrical sociomatrix (right) showing “1” for any connections between
which in turn is a subsystem of the datacenter (e.g., MPP1).
Here “Busway” is a cutnode, whose withdrawal implies total
collapse of the power panel network. Its failure also implies the
failure of one node of the larger network, datacenter,
aggravating problems in a failure chain.
This understanding of failures in systems and their
subsystems, characterizing them as social networks of complex
systems, form the theoretical basis for the proposed risk
analysis model in the following section.
Risks are usually defined from statistical and probability
analysis. Ongoing analysis in project and engineering
management, for example, checks risk possibilities and what
kind of actions can mitigate them .
However, in complex and dynamic systems such as the
example cited of the datacenter and several other networks, the
risk can be seen as an index obtained from analysis of real time
monitoring measurements. That is, the risk of problems can be
obtained as a trend calculated in real time by monitoring
parameters, read by means of various sensors coupled to the
system components, and constantly calculated and presented to
the manager of the complex system. IoT will play a key role on
this real time monitoring.
Thus, the risk of complex system failures will be a
consequence of the operation of the network, either by failures
in the nodes (the actors of the social network) or in its links
(connections between the actors).
In this sense, the theoretical model presented here is based
on social networks, and the complex system risk index is given
based on the social networks analysis, modeled according to
the complex system of reference.
Network connections form a complex system of
The risk index of this complex system of interrelationships
can be set between two extremes. The minimum index, or 0%,
means that the system is idle or not yet in operation. The
maximum rate, or 100%, occurs when the operating system
collapses and there is a breakdown. For this reason, once the
system starts running, a level of risk should be considered,
even if it is very small.
The risk index of the complex system must then be
obtained from the social network calculation, considering that
the nodes of this network have values, i.e., each node can
represent a subsystem and have its own risk. Thus, each node
has its own risk index (called “actor attribute” at social network
analysis theory), and from there one can see the entire network
as a block and calculate the risk of the complete system.
TABLE I. L
Risk Index RX Description of System Status (or node status)
01 Working appropriately
02 Node in alert mode
03 Link in alert mode
04 Node lost
05 Link lost
06 Critical node (cutnode) lost
07 Critical link (bridge) lost
08 System partially stopped
09 System stopped completely but may restart
Then each node will have a value, an attribute, classifying
it from “00” to “10”. These will be the node risk indices. Table
I presents a proposal of risk indices classified according to the
description of the system status, made up of nodes and their
links, considering the complex system as a social network.
Let's use the illustration of Figure 7 to exemplify the
theoretical model. The complex system S1 consists of a set of
nodes, from S1N1 to S1Nn, with their respective links. The
online analysis of the S1 network can bring each moment a risk
index ranging from RX00 to RX10. However we can see that
the S1N2 node is equivalent to the entire subsystem S2, which
will have its own risk index ranging from RX00 to RX10. In its
turn, the S2N3 node from the subsystem S2 is equal to the sub-
subsystem S3, and so on. In other words, the model considers
the main layer as S1 and its sublayers the subsystems S2, S3
and so forth..
This deepening of risk analysis will be possible if each part,
or node, of a system, can be monitored and evaluated as a
complete subsystem, then providing risk information to the
In the given datacenter example of Figure 1, represented as
a social network in Figure 5, the S1 system is a macro view of
the datacenter, with equipment (nodes) and all its connections
(links). But we can deepen the analysis doing the monitoring of
each one of the equipment or the various component parts of
If we take as an example the electrical panel of Figure 2 as
a subsystem, shown in Figure 6 as a social network, it will
have a specific analysis and a specific risk calculus result. The
result of this analysis will feed the risk calculus of the upper
level system. So it is possible to calculate an index for the
entire network. If this network represents a node on an upper
network level, the value of the upper network node will take
over this value.
As the results are obtained, the manager of the complex
network can evaluate every moment the risk indices of the
system and their subsystems, acting on each one preventively
or as required.
For the risk characterization of a system, based on the risk
indices of a complex subsystem, Table II illustrates a typical
case of influence between systems and their impacts.
In the example showed at Table II, the risk index for S1N2,
i.e., the node that is the result of S2 subsystem behavior, may
impact in several different final risks to S1. In other words, the
risk index of the whole subsystem S2 will be the risk index of
the single node S1N2 on the higher system S1. Any problems
with the subsystem S2 will affect, therefore, the risk index of
the node S1N2, which will contribute in determining the final
risk index of S1.
TABLE II. I
What does it imply?
At Table II if S1N2 represents an index RX04, that is, there
was the loss of a node in S2, this may imply a RX02 index for
S1, which defines alert mode for S1N2 node. If S1N2
represents an index RX06 or index RX07, i.e., S2 became a
disconnected network, this may imply a RX02 index, or an
alert mode. The stop or breakdown of S2 will bring a RX09 or
RX10 index for the S1N2 node, which defines the loss of a
node in S1 (risk RX04) or even the loss of a cut node (risk
RX06), depending on S1N2 status at S1.
Many other assumptions could be established and
calculated each time from the sensing done in the various
network components. The risk index will show, online, the
trouble spots of the complex system under analysis.
This paper presents a theoretical model for risk analysis of
complex systems, based on social network analysis theory.
The novelty of the described model is to evaluate risks of
complex systems in real-time, characterizing risks as failure
rates of network nodes and links and their level of importance
to the network operation. Another novelty of the model is to
recognize, and calculate, the network nodes as consolidated
representations of smaller networks or subnets.
To model the any system under analysis it is necessary to
follow a sequence of five steps:
• Step 1 – reduce the structure under analysis only to its
essential, keeping only the parts that cannot be
removed without damaging it or transforming it;
• Step 2 – define and draw the nodes and connections of
the structure, and then build the sociomatrix which
• Step 3 – for each node do the same procedure,
considering that the node contains a subsystem that
must be modelled;
• Step 4 – automate the whole structure under analysis to
collect data in real time;
• Step 5 – analyze the complex system and subsystems
to obtain the Risk Index RX continuously.
Finally, to obtain practical results with the method, one can
perform the computation analysis using social network tools
such as Ucinet  and other software packs. These results are
ongoing projects and will be presented in future work.
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Figure 7. The complex system S1 as a social network where node S1N2
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