=Paper=
{{Paper
|id=Vol-2502/paper1
|storemode=property
|title=Redefining Betweenness Centrality in a Multiple IoT Scenario
|pdfUrl=https://ceur-ws.org/Vol-2502/paper1.pdf
|volume=Vol-2502
|authors=Francesco Cauteruccio,Giorgio Terracina,Domenico Ursino,Luca Virgili
|dblpUrl=https://dblp.org/rec/conf/aiia/CauteruccioTUV19
}}
==Redefining Betweenness Centrality in a Multiple IoT Scenario==
https://ceur-ws.org/Vol-2502/paper1.pdf
Redefining Betweenness Centrality in a Multiple
IoT Scenario?
Francesco Cauteruccio1 , Giorgio Terracina1 , Domenico Ursino2 , and Luca
Virgili2
1
DEMACS, University of Calabria, Cosenza, Italy
2
DII, Polytechnic University of Marche, Ancona, Italy
Abstract. Betweenness centrality is one of the most known centrality
measures in network analysis. It has been largely investigated in the
past, and several extensions tailored to specific contexts, also involving
IoT, have been proposed. However, the classical betweenness centrality
is not able to correctly evaluate the centrality of nodes in a multiple IoT
scenario, i.e., a scenario where several networks of smart objects cooper-
ate with each other. In fact, in such a context, the classical betweenness
centrality disregards that each network of a MIoT maintains its auton-
omy (so that a MIoT does not coincide with a single big network) but,
at the same time, cooperates with the other networks through suitable
cross nodes. In this paper, we propose three new measures of between-
ness centrality specifically conceived for a multiple IoT scenario. First
we define them and, then, we show how they can achieve the objectives
missed by the classical betweenness centrality.
Keywords: IoT; Multiple IoT Scenario; MIoT; Betweenness Centrality; In-
ner Betweenness Centrality; Cross Betweenness Centrality
1 Introduction
The betweenness centrality of a node in a network is defined as the fraction
of the shortest paths between all the pairs of nodes that pass through it. Be-
tweenness centrality is well suited for measuring the influence of a node over the
information spread through the network [3, 20], to identify boundary spanners
(i.e., nodes acting as bridges between two or more subnetworks), and to measure
the “stress” (in the sense of a higher usage) that a node must undergo during
network activities [5, 6, 9, 13]. Due to its relevance in network analysis, between-
ness centrality has been largely investigated in the past, and several extensions,
tailored to specific contexts, have been proposed (see, for instance, [26, 10, 11,
4]). Also in the context of the Internet of Things (IoT), several approaches for
the computation of betwenness centrality have been presented [15, 23, 17].
?
Copyright 2019 for this paper by its authors. Use permitted under Creative Commons
License Attribution 4.0 International (CC BY 4.0)
However, the classical betweenness centrality is not able to correctly evaluate
the centrality of nodes in a multiple IoT scenario, i.e., a scenario where several
networks of smart objects (SO) cooperate with each other. In such a scenario
(known as Multi-IoT or MIoT in the literature [2, 12, 18, 25]), IoT (i.e., networks
of SO) are interconnected thanks to those nodes simultaneously belonging to
two or more of them. We call cross nodes (c-nodes) these nodes and inner nodes
(i-nodes) all the other ones. Then, a c-node connects at least two IoT of the
MIoT and plays a key role in favoring the cooperation among i-nodes belonging
to different IoT. As a consequence, the nodes of a MIoT are not all equal: c-
nodes will presumably play a more important role than i-nodes for supporting
the activities in a MIoT. Here, the classical betwenness centrality is not able to
distinguish c-nodes from i-nodes and to evidence the key role played by c-nodes
in favoring communication and cooperation between SO belonging to different
IoT of the MIoT.
In this paper, we aim at providing a contribution to address this problem.
Indeed, we propose three new measures of betweenness centrality, well suited for
a MIoT and, more in general, for a scenario consisting of a set of related IoT.
These measures are called Inner Betweenness Centrality (IBC), Soft Cross Be-
tweenness Centrality (SCBC) and Hard Cross Betweenness Centrality (HCBC).
They have been designed to clearly distinguish the contributions of c-nodes and
i-nodes and we show that they are able to reach this objective. In particular, IBC
has been conceived for measuring the betweenness centrality with a focus on a
single IoT of the MIoT and it privileges i-nodes over c-nodes. As will be clarified
in the following, it does not coincide with the classical betweenness centrality
because, differently from this last one, it also considers paths which connect two
nodes of the same IoT but, at the same time, involve nodes belonging to other
IoT of the MIoT. By contrast, SCBC and HCBC are specialized to measure the
betweenness centrality of nodes by privileging paths involving more IoT of the
MIoT and, therefore, c-nodes over i-nodes. As it is indicated by their names, this
privilege is more marked in HCBC than in SCBC.
This paper is organized as follows. In Section 2, we provide an overview of
related literature. In Section 3, we illustrate the MIoT paradigm in detail. In
Section 4, we introduce our new betweenness centrality measures. In Section
5, we describe our experimental analysis. Finally, in Section 6, we draw our
conclusions and have a look at some possible future developments of our research
efforts.
2 Related Literature
As one of the most important centrality measure, betweenness centrality [13]
has been the subject of in-depth studies in the literature [9, 8]. Recognizing
high spreading power nodes is fundamental in social networks but, based on its
definition, the cost for computing the betweenness centrality of a node is high.
For this reason, several heuristic approaches, aiming at providing the closest
possible value of the betweenness centrality of a node in a reasonable time, have
been proposed in the past (see [7, 1, 14, 24], to cite a few).
As for the IoT, which is an example of a very dynamic and constantly evolving
network, the approaches for the incremental computation of betweenness cen-
trality are extremely interesting. Among these, we mention the ones described in
[15, 23, 17]. Specifically, in [15], the authors propose iCENTRAL, which is well
suited for large and evolving biconnected graphs. In [23], the authors illustrate an
approach for a quick incremental computation of betweenness centrality. After
a pre-processing phase, the computational cost of this approach is independent
of the network size. In [17], the authors describe an approach that reduces the
search space by finding a set of candidate nodes that are the only ones to be
updated during the incremental computation of the betweenness centrality.
Surprisingly, despite the strong tie existing among betweenness centrality
and information diffusion, there are very few studies concerning the role of be-
tweenness centrality in IoT. To the best of our knowledge, the only approaches
dealing with centrality in IoT have been proposed as part of methods for deter-
mining trustworthiness [22] or network navigability [19, 21] in IoT. Anyway, in
all these cases, centrality is simply a part of the proposed approaches and not
the central topic to investigate. By contrast, betweenness centrality (or better,
the redefinition of betweenness centrality in a MIoT scenario) is one of the main
goals of this paper, and all the results we present here can be applied in many
contexts comprising the two mentioned above, along with several other ones.
3 The MIoT paradigm
In this section, we provide a brief overview of the MIoT paradigm. In particular,
we introduce those concepts necessary to understand the rest of the paper. The
interested reader can find all details about this paradigm in [2, 18, 25].
A MIoT M can be defined as a set of m IoT: M = {I1 , I2 , · · · , Im }, where
Ik is an IoT. Consider an object oj of M. We assume that, if oj belongs to Ik ,
it has an instance ιjk , representing it in Ik .
In M, a set M Dj of metadata are associated with oj . The MIoT paradigm
considers a rich set of metadata for an object, because metadata play a key
role in favoring the interoperability of IoT and of their objects, which is the
ultimate objective of a MIoT. M Dj consists of three different subsets: M Dj =
hM DjD , M DjT , M DjO i. Here, M DjD represents the set of descriptive metadata,
which denote the type of oj . In order to represent and handle descriptive meta-
data, our paradigm uses a proper taxonomy, such as the one defined by the IPSO
Alliance3 . M DjT represents the set of technical metadata. These are compliant
with the object type. The IPSO Alliance provides a well defined set of technical
metadata for each object type. Finally, M DjO represents the set of operational
metadata. These regard the behavior of oj and is defined as the union of the sets
of the operational metadata of the instances of oj .
3
IPSO Alliance - https://www.omaspecworks.org/
It is possible to represent Ik by means of a graph: Gk = hNk , Ek i where Nk
indicates the set of the nodes of Ik . There is a node njk for each instance ιjk of
an object oj in Ik . Instead, Ek denotes the set of the edges of Ik . There is an
edge ejqk = (njk , nqk ) if there exists a certain form of relationship (for instance,
proximity) between the instances ιjk and ιqk of the objects oj and oq in the IoT
Ik .
Finally, a MIoT M can be modeled as a graph G = hN, Ei were:
Sm
– N = k=1 Nk ; in other words, N is the union of the sets of the nodes of the
corresponding IoT. Sm
– E = EI ∪ EC . Here, EI = k=1 Ek . EC = {(njk , njq )|njk ∈ Nk , njq ∈
Nq , k 6= q}; in this definition, njk and njq are the nodes corresponding to
the instances ιjk and ιjq of oj in Ik and Iq .
In other words, the set E of the edges of M consists of two subsets, EI and
EC . EI is the set of the inner edges of M and is the union of the sets of the
edges of the corresponding IoT. EC is the set of the cross edges of M; there
is a cross edge for each pair of instances of the same object in different IoT.
We call: (i) i-edge an edge of M belonging to EI ; (ii) c-edge an edge of M
belonging to EC ; (iii) c-node a node of M involved in at least one c-edge; (iv)
i-node a node of M not involved in any c-edge; (v) c-object an object having at
least one pair of instances whose corresponding nodes are linked by a c-edge.
4 Redefining Betweenness Centrality for a MIoT
Given a node nj of a graph G, the classic definition of betweenness centrality is
the following:
X σns nt (nj )
BC(nj ) =
σns nt
ns ∈N,nt ∈N,ns 6=nj ,nt 6=nj
where σns nt is the total number of the shortest paths from ns to nt , whereas
σns nt (nj ) is the number of those shortest paths passing through nj .
If we apply BC to the graph Gk associated with an IoT Ik and consider Ik
isolated from the MIoT, this formula involves shortest paths which only pass
from nodes of Ik . In order to consider also the potential shortest paths that
connect nodes of Gk but pass through nodes of the other IoT of the MIoT, it
should be applied to the graph G corresponding to the whole MIoT. However,
in this way, it does not capture that a MIoT consists of different autonomous
IoT cooperating with each other thanks to c-nodes, which play a key role that
should be evidenced by any measure of centrality conceived for a MIoT. We
argue that, owing to these weaknesses, BC could present several problems in a
MIoT context, especially when it is necessary to compute a centrality measure,
which privileges those nodes that allow the crossing from an IoT to another.
To address the challenges mentioned above, we define three new centrality
metrics. The first of them is called Inner Betweenness Centrality (IBC) and is
defined as follows.
Let njk ∈ Nk be the node corresponding to the instance ιjk of the object oj
in the IoT Ik of the MIoT M. The Inner Betweenness Centrality IBC(njk ) is
defined as:
X σ nsk ntk (njk )
IBC(njk ) =
σ n sk n t k
nsk ∈Nk ,ntk ∈Nk ,nsk 6=njk ,ntk 6=njk
where σ nsk ntk is the total number of the shortest paths from ns to nt that
involve also nodes of the MIoT not belonging to Nk , and σ nsk ntk (njk ) is the
total number of these shortest paths that pass through njk .
IBC can be considered as an evolution of BC, capable of evaluating inner
central nodes taking into account the fact that the network Ik is not alone
but it is part of a MIoT. As a consequence, if all the paths connecting nsk
to ntk include at least one node belonging to networks different from Ik but
inside the MIoT, then BC does not capture them and considers nsk and ntk
unconnected. By contrast, in a more precise way, IBC considers that there may
exist one or more connections between them in the MIoT, even if they require
the intervention of nodes belonging to other networks.
The second betweenness centrality measure that we propose in this paper is
called Soft Cross Betweenness Centrality (SCBC) and is defined as follows. Let
njk ∈ Nk be the node corresponding to the instance ιjk of the object oj in the
IoT Ik . The Soft Cross Betweenness Centrality SCBC(njk ) is defined as:
X σ nsu ntv (njk )
SCBC(njk ) =
σ n su n t v
nsu ∈Nu ,ntv ∈Nv ,u6=v
In few words, SCBC(njk ) computes the centrality of a node by selecting only
the shortest paths between nodes belonging to different networks. There is no
constraint on the node njk for which we are computing the SCBC. As a matter
of fact, njk could belong either to Nu or to Nv or, finally, to another IoT of the
MIoT different from Nu and Nv .
SCBC can be considered as an evolution of BC capable of detecting central
(in the betweenness centrality sense) c-nodes and i-nodes by taking into account
that these nodes do not belong to a single-IoT scenario but that they are part
of a MIoT, and this fact can influence the shortest paths considered in the
computation of betweenness centrality.
The last betweenness centrality measure we are proposing here is called Hard
Cross Betweenness Centrality (HCBC) and is defined as follows. Let njk ∈ Nk
be the node corresponding to the instance ιjk of the object oj in the IoT Ik . The
Hard Cross Betweenness Centrality HCBC(njk ) is defined as:
X σ nsu ntv (njk )
HCBC(njk ) =
σ n s u n tv
nsu ∈Nu ,ntv ∈Nv ,k6=u,k6=v,u6=v
In few words, analogously to SCBC(njk ), HCBC(njk ) computes the cen-
trality of a node by selecting only the shortest paths between nodes belonging
to different networks. Furthermore, differently from the definition of SCBC, the
node njk is constrained to belong to a network different from the ones of the
source and the destination nodes of the path.
HCBC can be considered as an evolution of BC along the same direction
as SCBC. The only difference between SCBC and HCBC is that the latter is
capable of detecting central c-nodes and i-nodes linking at least three IoT.
IBC, SCBC and HCBC are capable of overcoming the limits characterizing
the classic BC in a MIoT. We remark again that IBC is different from the
classical BC because it considers that the corresponding IoT is not isolated but
inside the MIoT. Given the complexity of a MIoT, such a specific study can be
really useful for several applications.
By contrast, if we want to know the most central nodes in a MIoT, the most
suitable choices are SCBC and HCBC. SCBC is capable of highlighting the
most suitable nodes which allow the cooperation of nodes belonging to different
IoT. The term “Soft” characterizing SCBC is due to the soft restrictions of its
constraints.
HCBC, instead, is much more restrictive than SCBC. As a consequence, it
detects few nodes presenting very high values of betweenness centrality. In fact,
they ensure a high cooperation level in the MIoT because they are linked to a
higher number of IoT than the other nodes.
The choice between SCBC and HCBC depends on the application context.
For instance, if we consider information diffusion, SCBC is well suited for fast
information diffusion. HCBC, instead, is a better choice for spreading informa-
tion among many IoT, even though the diffusion process will be slower than the
one guaranteed by SCBC, because of the reduced number of nodes with a high
HCBC.
5 Experiments
5.1 Testbed
We derived our testbed from Thingful4 , a search engine for the Internet of Things
supporting the search of data regarding a huge number of existing things, dis-
tributed all over the world. Thingful also provides some suitable APIs, which
can be used for querying it through a software program and which we exploited
for the construction of our testbed. In order to obtain our testbed, we needed
to perform several tasks. They are described in detail in [2]. Here, we limit our-
selves to illustrate the characteristics of our testbed thus allowing the reader to
understand the presented experiments.
Our MIoT consists of 11 IoT, reported in the first column of Table 1. We
associated an object with each thing. Since we had 250 things, we obtained 250
objects. 200 of these objects had associated only one instance; 35 of them had
associated two instances; finally, 15 of them had associated three instances. As
a consequence, we had 315 instances in our testbed, distributed among the 11
IoT of our MIoT, as shown in Table 1.
4
Thingful: a Search Engine for the Internet of Things - https://thingful.net
IoT Number of instances
a.home 22
a.health 22
a.energy 22
a.transport 22
a.environment 22
b.near 14
b.mid 38
b.far 53
c.plain 44
c.hill 50
c.mountain 6
Table 1. Number of instances present in each IoT of our MIoT
Fig. 1. A graphical representation of our MIoT
A (necessarily complex) visualization of our testbed is presented in Figure
1. The interested reader can find the corresponding dataset (in .csv format) at
the address www.barbiana20.unirc.it/miot/datasets/miot2. The password
to type is “za.12&;lq74:#”.
5.2 Tests
In this section, we describe the tests that we carried out to evaluate the signif-
icance of our new betweenness centrality measures in a MIoT and to compare
Nodes BC rank IBC rank SCBC rank HCBC rank
76b 1 208 1 1
76c 2 207 2 2
99b 3 202 3 48
99c 4 201 4 47
54b 5 2 158 98
12b 6 293 5 3
76a 7 209 6 4
41a 8 232 7 116
244c 9 245 8 143
244b 10 246 9 144
149c 11 288 10 258
12a 12 294 11 5
Table 2. IBC, SCBC and HCBC ranking of the top-12 central nodes returned by BC
them with the classical betweenness centrality. In our test activity, we adopted
the testbed illustrated in the previous section.
We started our experiments considering the top-12 central nodes returned by
BC and verifying the rank of the same nodes when the other centrality measures
are applied5 . Obtained results are reported in Table 2.
From the analysis of this table we can clearly observe that BC and IBC return
completely different results. In fact, 11 of the top-12 central nodes returned by
BC have a rank higher than 200 in IBC. Instead, a good correspondence can be
observed between the ranks of BC and SCBC, denoting that BC shows a good
capability of finding the most “soft” central nodes in a MIoT. By contrast, there
is a very loose correspondence between BC and HCBC. This denotes that BC is
incapable of finding the most central hard c-nodes. In conclusion, it seems that
the BC’s incapability of distinguishing between c-nodes and i-nodes and between
c-edges and i-edges leads it to show a behavior (someway similar to the one of
SCBC) intermediate between IBC and HCBC.
Then, we repeated the same evaluation for the top-12 central nodes returned
by IBC. Obtained results are reported in Table 3. From the analysis of this table
we can observe that the ranks returned by IBC and those returned by SCBC
and HCBC are totally different. Actually, this was an expected result. However,
it is interesting to observe that there is a weak correspondence between IBC and
BC, because the top-12 central nodes returned by IBC have a rank between 5
and 95 in BC.
After this, we analyzed the top-12 central nodes returned by SCBC. Obtained
results are reported in Table 4. Again, we observe a certain correspondence
between SCBC and BC, a totally different behavior characterizing SCBC and
IBC and a weak correspondence between SCBC and HCBC.
5
Recall that our MIoT consists of 315 nodes.
Nodes IBC rank BC rank SCBC rank HCBC rank
177c 1 37 248 224
54b 2 5 158 98
57b 3 55 156 94
33c 4 72 173 127
21c 5 74 208 172
211a 6 29 216 182
133c 7 76 289 277
91a 8 63 124 56
212c 9 65 215 181
156b 10 82 267 249
144c 11 94 277 265
142c 12 95 279 267
Table 3. BC, SCBC and HCBC ranking of the top-12 central nodes returned by IBC
Nodes SCBC rank BC rank IBC rank HCBC rank
76b 1 1 208 1
76c 2 2 207 2
99b 3 3 202 48
99c 4 4 201 47
12b 5 6 293 3
76a 6 7 209 4
41a 7 8 232 116
244c 8 9 245 143
244b 9 10 246 144
149c 10 11 288 258
12a 11 12 294 5
40c 12 13 233 117
Table 4. BC, IBC and HCBC ranking of the top-12 central nodes returned by SCBC
All the previous conclusions are confirmed by the analysis of the top-12 cen-
tral nodes returned by HCBC, reported in Table 5. Observe, also, in this table
the substantial difference between HCBC and SCBC, due to the restriction char-
acterizing the definition of the former.
To further verify our previous conclusions and to quantify them, we decided
to apply the Kendall Tau rank distance metric [16]. This is a metric aiming
at measuring the differences between two different rankings by counting the
number of pairwise disagreements between them. More formally, it determines
the number of swaps necessary to make the two ranks equal. The higher its value,
the higher the distance between the two ranks.
We computed the Kendall Tau rank distance metric for all the possible pairs
of ranks determined by considering the four metrics mentioned above. Obtained
results are reported in Table 6. From the analysis of this table we can see that
Nodes HCBC rank BC rank IBC rank SCBC rank
76b 1 1 208 1
76c 2 2 207 2
12b 3 6 293 5
76a 4 7 209 6
12a 5 12 294 11
191c 6 14 269 13
2c 7 20 237 19
191a 8 22 271 21
2a 9 26 239 25
12c 10 35 292 33
2b 11 38 238 35
184a 12 42 276 39
Table 5. BC, IBC and SCBC ranking of the top-12 central nodes returned by HCBC
τ1 τ2 K(τ1 , τ2 )
BC IBC 18204
BC SCBC 8489
BC HCBC 24997
IBC SCBC 27907
IBC HCBC 30195
SCBC HCBC 14816
Table 6. Values of Kendall Tau rank distance for all the possible pairs of Betweenness
Centralities considered in this paper
all of our previous conjectures about the metric characteristics and similarities
are confirmed. In fact, we can see that IBC and HCBC are completely different.
The same happens for IBC and SCBC. Quite a high difference can be observed
for BC and HCBC. A certain (not very high) difference can be observed for BC
and IBC and for SCBC and HCBC. Finally, BC and SCBC present the highest
similarity.
6 Conclusion
In this paper, we have presented an attempt to redefine betweenness centrality in
a multiple IoT scenario, i.e., a scenario where several networks of smart objects
cooperate with each other. We have seen that the classical notion of betweenness
centrality, which is well suited for a single IoT, present several weaknesses in this
new scenario. Indeed, both if it is applied to one IoT at a time and if it is applied
to the MIoT as a whole, classical betweenness is not capable of capturing the
specificity of the MIoT scenario. In particular, it does not consider the fact that
in MIoT there exist several autonomous networks of objects which cooperate
with each other through c-nodes that, therefore, play a key role and should be
privileged over i-nodes by a centrality measure operating in such a scenario.
Then, we have introduced new betweenness centrality measures and we have
discussed their features w.r.t. the classic betweenness centrality. Finally, we have
presented some experiments devoted to confirm the inadequacy of the classical
betweenness centrality for a MIoT and, then, to show the adequacy of the new
measures.
In our opinion, this preliminary paper is a starting point for addressing many
challenges in the context of MIoT. For instance, analogously to what we have
done for betweenness centrality, it is possible to investigate new forms of central-
ities specifically suited for a MIoT. Furthermore, we argue that smart objects
are becoming more and more intelligent and autonomous, showing a behavior
increasingly similar to the one of humans. In this case, it is not out of place to
investigate issues like object profiling and object reliability, as well as to define
techniques to detect anomalous and possibly malicious behaviors of one or more
objects in a MIoT.
Acknowledgments
This work was partially supported by: (i) the Italian Ministry for Economic
Development (MISE) under the project “Smarter Solutions in the Big Data
World”, funded within the call “HORIZON2020” PON I&C 2014-2020 (CUP
B28I17000250008), and (ii) the Department of Information Engineering at the
Polytechnic University of Marche under the project “A network-based approach
to uniformly extract knowledge and support decision making in heterogeneous
application contexts” (RSAB 2018).
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