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Complex Systems: Risk Model Based on Social

Network Analysis

Mauro Faccioni Filho

Universidade do Sul de Santa Catarina – UNISUL

Pedra Branca - Palhoça - Santa Catarina - Brazil

mauro.faccioni@unisul.br

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.

I. I

NTRODUCTION

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 [1] 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

Index.

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

future work.

II. C

OMPLEX

S

YSTEMS

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 [2]. 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

systems.

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 [3].

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) [4] [5].

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.

III. S

OCIAL

N

ETWORK

A

NALYSIS

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

such systems.

The social network analysis has been applied in various

fields and organizations, political and economic systems,

educational systems and many others [1].

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 [6] [7] [8].

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

“bridge”).

BUSWAY

MCB

CB1 CB2 CB3 CB4 CB5 CBn

Figure 2. Schematic presentation of a power pane

l, with circuit breakers,

electrical switches and busway

.

BUSWAY

RACK1

RACKn

UPS1

PDU1

UPS2 UPS3 UPS4

PDU2

PP2

PP3

GEN1

AC1

PP1

MPP2 MPP1

GEN2

AC2

T3

T1 T2

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

statements:

• 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

importance.

• In a complex system all bridges are equivalent in

importance.

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

critical nodes.

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),

BUSWAY

MCB

CB1

CB2

CB3 CB4

CB5

CBn

Figure 6. The social network re

presentation of the power panel from Figure 2;

each circuit breaker and busway is identified as a node

.

BUSWAY

RACK1

RACKn

UPS1

PDU1

UPS2 UPS3

UPS4

PDU2

PP2 PP3

GEN1

AC1

PP1

MPP2 MPP1

GEN2

AC2

T3

T1

T2

Figure 5. The social network representation of the schematic datacenter of

Figure 1, where each equipment is identified as a node.

N

1

N

2

N

3

N

4

N

n

N

5

N

1

N

2

N

3

N

4

N

n

N

5

Cut node

Bridge

Figure 4. Disconnected network due to a removal of a node (cut node) or due

to a removal of a link (bridge).

N

1

N

2

N

3

N

4

N

5

N

n

N

1

1 1

N

2

1

N

3

1 1 1

N

4

1 1 1

N

5

1 1

N

n

1

N

1

N

2

N

3

N

4

N

n

N

5

Figure 3. Graph representation of a social network with n nodes (left) and its

symmetrical sociomatrix (right) showing “1” for any connections between

nodes

.

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.

IV. R

ISK

M

ODEL

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 [9].

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.

Risk Model

Network connections form a complex system of

interrelationships.

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

EVELS OF

R

ISK

I

NDEX

Risk Index RX Description of System Status (or node status)

00 Idle

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

10 Breakdown

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

superior system.

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

the equipment.

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

MPACTS OF

R

ISK

S2 Impact

What does it imply?

Risk Index

S1N2 S1

RX04

RX02

RX06

RX02

RX07

RX02

RX09

RX04

RX06

RX10

RX04

RX06

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.

V. C

ONCLUSIONS

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

represents it;

• 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 [10] and other software packs. These results are

ongoing projects and will be presented in future work.

R

EFERENCES

[1] S. Wasserman and K. Faust, Social Network Analysis: Methods and

Applications. Cambridge Univ. Press, Cambridge, UK, 1994.

S1

S2

S3

Sn

S1N1

S1N2 S1N3

S1N4

S1N5

S1N6

S1Nn

S3N1

S3N2 S3N3

S3N4

S3N5

S3N6 S3Nn

SnN1

SnN2 SnNn

S2N1

S2N2

S2N3

S2N4

S2N5

S2Nn

S3N7

Figure 7. The complex system S1 as a social network where node S1N2

represents the subsystem S2, where node S2N3 represents the subsystem S3,

and so on.

[2] J. Miller and S. Page. Complex adaptive systems, an introduction to

computational models of social life. Princeton University Press,

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Institute, LLC, 2010.

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[7] A. Degenne and M. Forsé, Introducing Social Networks, Sage

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