Visualizing Temporal Graphs using Visual Rhythms

A Case Study in Soccer Match Analysis

Daniele C. Uchoa Maia Rodrigues

1

, Felipe A. Moura

2

,

Sergio Augusto Cunha

3

and Ricardo da S. Torres

1

1

Institute of Computing, University of Campinas, Campinas, Brazil

2

Laboratory of Applied Biomechanics, State University of Londrina, Londrina, Brazil

3

College of Physical Education, University of Campinas, Campinas, Brazil

Keywords:

Visual Rhythm, Temporal Graph, Complex Network, Soccer Analysis.

Abstract:

In several applications, a huge amount of graph data have been generated, demanding the creation of appropri-

ate tools for graph visualization. One class of graph data which is attracting a lot of attention recently are the

temporal graphs, which encode how objects and their relationships evolve over time. This paper introduces

the Graph Visual Rhythm, a novel image-based representation to visualize changing patterns typically found

in temporal graphs. The use of visual rhythms is motivated by its capacity of providing a lot of contextual

information about graph dynamics in a compact way. We validate the use of graph visual rhythms through the

creation of a visual analytics tool to support the decision-making process based on complex-network-oriented

soccer match analysis.

1 INTRODUCTION

Huge volumes of graph data have been generated in

several applications, demanding the development of

appropriate tools for storing, processing, and anal-

ysis. Examples of applications include social net-

work (Zhao and Tung, 2012; Brandes et al., 2012),

sport analysis (Duch et al., 2010; Cotta et al., 2013;

Pe

˜

na and Touchette, 2012; Passos et al., 2011), and

urban planing (Nahman and Peri, 2017). One partic-

ular class of graphs that is attracting a lot of attention

recently are the temporal graphs, which basically rep-

resent the insertion and deletion of vertices and edges

over time (Leskovec et al., 2005).

In this paper, we are interested in visually repre-

senting temporal graphs, with the objective of sup-

porting the identiﬁcation and analysis of temporal

pattern changes. In this context, several approaches

have been proposed to the visualization of tempo-

ral graphs (Brandes and Corman, 2003; Hurter et al.,

2014; Brandes et al., 2012; Beck et al., 2016). Most

of the approaches rely on the use of node-link dia-

grams, where different visual marks (typically circle

glyphs) are used for representing vertices and lines to

visually represent relations among vertices. Differ-

ent additional visual properties associated with visual

marks (e.g., position, size, length, angle, slope, color,

gray scale, texture, shape, animation, blink, motion)

are employed to highlight properties associated with

both vertices and edges (Beck et al., 2016). A typical

challenge faced by those initiatives refers to the visu-

alization of huge volumes of data. In these scenarios,

complex interaction controls have been proposed to

handle occlusion and to support browsing activities

over graph data.

In this paper, we address this problem from a

different perspective. We propose a graph-to-image

transformation, so that large volumes of sequence

graphs can be visually represented in a compact way,

enabling fast and easy visual identiﬁcation of pattern

changes. Our solution relies on the use of the visual

rhythm representation (Ngo et al., 1999). This ap-

proach has been typically used for efﬁcient video data

processing and analysis (Bezerra and Lima, 2006;

da Silva Pinto et al., 2015), as it allows the repre-

sentation of the whole video content by means of an

image, whose columns are deﬁned by the extraction

of features from pixels of frames. In this paper, we

extend this idea by encoding properties of graph se-

quences, leading to a representation we name graph

visual rhythm. For each instant of time, graph proper-

ties are represented as a column of an image, allowing

the compact representation of important graph fea-

tures associated with changes of vertices and edges

96

C. Uchoa Maia Rodrigues D., A. Moura F., Cunha S. and da S. Torres R.

Visualizing Temporal Graphs using Visual Rhythms - A Case Study in Soccer Match Analysis.

DOI: 10.5220/0006153000960107

In Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2017), pages 96-107

ISBN: 978-989-758-228-8

Copyright

c

2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

over time. Our solution is somehow similar to pre-

vious initiatives focusing on encoding graph dynam-

ics using matrix representations (Burch et al., 2011;

Vehlow et al., 2013; Bach et al., 2014). Different

from those initiatives, however, our approach does not

rely on radial layouts, nor on complex representations

such as small multiples and stacked matrices. To the

best of our knowledge, this is the ﬁrst attempt to en-

code complex temporal graph changes in a easy-to-

interpret single image representation.

The proposed method is validated in the context

of soccer match analysis. Recently, sport science re-

searchers have been dedicated to the representation of

soccer match events by means of graphs (Duch et al.,

2010; Cotta et al., 2013; Pe

˜

na and Touchette, 2012;

Passos et al., 2011). Usually, players are represented

as vertices and their relations (e.g., passes, proxim-

ity) are encoded as edges. In some of those applica-

tions, graph properties, deﬁned in terms of complex

network topological measures are used in the match

analysis. In this paper, we describe the use of graph

visual rhythms deﬁned in terms of complex network

measures for understanding complex temporal pat-

terns associated with the match dynamics.

In summary, the contributions of this paper are

twofold: (i) the introduction of a novel compact vi-

sual representation for temporal graphs, named graph

visual rhythm; and (ii) the presentation of different

scenarios of its use in the context of the analysis of

real soccer matches using complex network measures.

2 BACKGROUND

2.1 Visual Rhythms

Visual Rhythm is a sampling method widely used

to video processing and analysis (Ngo et al., 1999;

Guimar

˜

aes et al., 2003; Chun et al., 2002). Its ob-

jective is to transform tridimensional information into

bidimensional images by sampling one dimensional

information from video frames. Let V be a digital

video (in domain 2D + t) composed of T frames f

t

,

i.e., V = ( f

t

), t ∈ [1, T ], where T is the number of

frames. Let H and W be, respectively, the height and

width from each frame f

t

.

The visual rhythm computation consists in using a

function to map each f

t

into a column of an image in

domain 1D+t. The ﬁnal image generated is known as

visual rhythm image (VR). More formally, the com-

putation of the VR image is deﬁned as follows (Ngo

et al., 1999; Guimar

˜

aes et al., 2003):

V R(t, z) = f

t

(r

x

× z + a, r

y

× z + b), (1)

!!

!!

Height!(H)!

Height!(H)!

Width!(T)!

Width!(W)!

Time!(T)!

Figure 1: Example of visual rhythm computed by extracting

the pixel values deﬁned by the central vertical line. In this

example, r

x

= 1, r

y

= 0, a = 0, and b =

W

2

. This leads

to a visual rhythm V R = f

t

(z,

W

2

), where z ∈ [1, H

V R

] and

t ∈ [1, T ], H

V R

= H is the height of the visual rhythm image,

and T is its width.

where z ∈ [1, H

V R

] and t ∈ [1, T ], H

V R

and T are the

height (i.e., H

V R

= H) and the width of the visual

rhythm image; r

x

and r

y

are ratios of pixel sampling; a

and b are shifts on each frame. Figure 1 illustrates the

computation of visual rhythm based on the pixel val-

ues deﬁned by the vertical line passing in the center

of the frame.

A more general deﬁnition of visual rhythms as-

sumes that it is possible to use a function F to

represent each frame of a video as point in an n-

dimensional space. Let f

t

be a frame deﬁned in

terms of D, a set of pixels. Function F is deﬁned as

F : D → R

n

. For example, a widely used implemen-

tation of function F relies on the computation of the

histogram associated with each frame f

t

(Guimar

˜

aes

et al., 2003). In this case, the visual rhythm image is

a 2D representation encoding all frame histograms as

vertical lines, i.e.,

V R(t, z) = H ( f

t

), (2)

where H ( f

t

) is a function that computes the his-

togram of frame f

t

, t ∈ [1, T ] and z ∈ [1, L], T is

the number of frames and L the number of histogram

bins.

2.2 Complex Network Measurements

Soccer is one of the most difﬁcult sports to analyze

quantitatively due to the complexity of the play and

to the nearly uninterrupted ﬂow of the ball during

the match. Indeed, unlike other sports, in which in-

dividual game-related statistics may properly repre-

sent player performance, in soccer it is not trivial to

deﬁne quantitative measures of an individual contri-

bution (Duch et al., 2010). Moreover, simple statis-

tics such as number of assists or number of shots may

not provide a reliable measure of a player’s true im-

pact on team performance and, consequently, the out-

comes of a match (Duch et al., 2010; Moura et al.,

Visualizing Temporal Graphs using Visual Rhythms - A Case Study in Soccer Match Analysis

97

2014). Instead, the real contribution of a given player

sometimes is hidden in the plays of the team, such

as participating from a passing sequence to a shot on

goal (Duch et al., 2010). This type of information is

important to detail the role of a team member on team

performance. Thus, this study uses complex network

measurements for extracting features from graphs to

represent individual behavior and thus to represent

team performance using a visual analytical tool. Two

measurements were considered in this work: Diver-

sity Entropy and Betweenness Centrality.

2.2.1 Diversity Entropy

The dynamic aspects associated with passes among

players in a match (such as the ‘ball ﬂow’ among the

players of a team) are important cues for game tacti-

cal analysis (Duch et al., 2010). In this paper, we use

the diversity entropy (Travenc¸olo and Costa, 2008;

Travenc¸olo et al., 2009) as a variable to characterize

the dynamic nature of the match, characterizing the

possibility of passes among players.

Diversity Entropy considers the transition proba-

bility (P

h

( j, i)) that a node i reaches a node j after h

steps in a self avoiding random walk. Let Ω be the set

of all nodes but i. The normalized diversity entropy

of a node i is deﬁned as (Travenc¸olo et al., 2009):

E

h

(Ω, i) = −

1

log(N − 1)

N

∑

j=1

P

h

( j, i)log(P

h

( j, i)), if P

h

( j, i) 6= 0,

0, if P

h

( j, i) = 0.

(3)

2.2.2 Betweenness Centrality

In this paper, the centrality of players in a match is re-

lated to his role in the passing ﬂow along the time. We

used betweenness centrality to characterize the role

of players in terms of the graph shortest paths with

which the players are involved.

Betweenness centrality (Costa et al., 2007) of a

node u is quantiﬁed as the sum over all distinct pairs

of vertex i, j of the number of shortest paths from i to

j that pass through u (θ(i, u, j)) divided by the total

number of shortest paths between i and j (θ(i, j)):

B

u

=

∑

i j

θ(i, u, j)

θ(i, j )

(4)

3 GRAPH VISUAL RHYTHMS

We deﬁne a temporal graph G as a sequence G =

hG

1

, G

2

, . . . , G

T

i, where G

t

= (V

t

, E

t

) is a weighted

graph at timestamp t ∈ [1, T ] composed of a set of

vertices, V

t

, and a set of edges, E

t

. We refer to the

graph deﬁned at a particular timestamp t (say G

t

) as

1

3

5

8

1

3

5

8

V4

V1 V1 V1

V2 V2

V2

V3 V3

V3

V4

V4

V5

time

V1 V2 V3 V4

0.0 0.5 1.0 1.5 2.0 2.5 3.0

V1 V2 V3 V4

0.0 0.5 1.0 1.5 2.0 2.5 3.0

V1 V2 V3 V4 V5

0 1 2 3 4

. . .

2

2

3

1

0

2

3

3

2

0

2

3

4

2

1

. . .

. . .

V5

V1

V4

V3

V2

V5

V4

V3

V2

V1

Vertex Degree Vertex Degree Vertex Degree

A

A

A

B B B

C

V1

V2

V3

V4

1

2

3

0

0

1

2

3

0

V1

V2

V3

V4

1

2

3

0

4

V1

V2

V3

V4 V5

Width (T)

Height (H)

t

n

t

n

t

2

t

1

t

1

t

2

Figure 2: Flowchart illustrating how a graph visual rhythm

is extracted.

an instant graph. By building one graph for each in-

stant of time considering the vertices’ interaction, it is

possible to capture the temporal nature of the graph

dynamics. Our goal is to represent the interaction

among vertices at each instant using a visual rhythm

representation GV R. We follow a similar formulation

employed in Eq. 2 to deﬁne GV R:

GV R(t, z) = F (G

t

), (5)

where F

G

t

: G → R

n

is a function that represents a

graph G

t

∈ G as a point in an n-dimensional space,

t ∈ [1, T ] and z ∈ [1, n].

Figure 2 illustrates the computation of a graph vi-

sual rhythm for a temporal graph. Changes in the

graph sequence are highlighted in red. For example,

at timestamp t

2

, an edge linking vertices v

2

and v

4

is

created. At timestamp t

n

, vertex v

5

is created along

with an edge from v

5

to v

3

. In this example, function

F

G

t

computes the degree of vertices for each instant

of time (arrows labeled with A). The degree informa-

tion is later used to create the graph visual rhythm

Visual Graph Rhythm

Image Computation

(d)

Complex Network

Measure Computation

(c)

0.55

0.35

0.35

0.35

0.40

0.80

Players’ Location

Extraction

(a)

GraphExtraction

(b)

99.598 33.6378

73.646 46.1074

75.5410 19.6833

79.6112 33.3785

67.6252 27.5689

56.8979 9.6359

67.4589 35.2626

Figure 3: Analysis framework.

IVAPP 2017 - International Conference on Information Visualization Theory and Applications

98

image (arrows B). Again different visual properties

(e.g., color, opacity) may be used to highlight graph

changes. In the case of the example, a heatmap-based

color layout is employed (arrow C).

4 CASE STUDY: SOCCER MATCH

ANALYSIS

This study is based on the use of graph visual rhythms

for identifying events on temporal graphs associated

with soccer matches.

4.1 Soccer Match Analysis Framework

The graph-based soccer match analysis framework

employed in this study comprises four steps, as illus-

trated in Figure 3:

(a) Extraction of players’ location in ﬁeld over time:

This step is accomplished using the DVideo soft-

ware (Figueroa et al., 2006a; Figueroa et al.,

2006b) applied to ofﬁcial soccer matches. This

process starts with soccer match videos and re-

sults in ﬁles containing players xy location on

the pitch and annotation related to match events,

such as passes accomplished, fouls, shots on goal,

among others. The extraction frame rate is 30

frames per second, so for a typical 45-minute half

time of a match, we have 81,000 frames. We used

a dataset related to two ofﬁcial soccer matches (re-

ferred to as Match 1 and Match 2 along the paper)

of the Brazilian Professional First League Cham-

pionship.

(b) Graph Extraction: This step builds graphs from

soccer match frames. In our experiments, two

different kinds of graphs were built: Delaunay

Triangulation Instant Graphs and Flow Networks,

which are detailed in Section 4.2.

(c) Complex Network Measure Computation: This

step comprises the approach described in Sec-

tion 2.2. Basically, complex network measures

are computed from graphs obtained in Step b. In

this experiment, two measures were considered:

Diversity Entropy and Betweeness Centrality. In

this context, these measures are extracted by F

G

t

,

the function that encodes one graph into a column

of a graph visual rhythm.

(d) Visual Graph Rhythm Image Computation: This

step is concerned with the creation of graph vi-

sual rhythm images. From those images, it is

possible to analyze patterns that represent match

events such as attacking and defensive strategies

from each team.

0 20 40 60 80 100

0 10 20 30 40 50 60 70

x

y

Graph Plot − Frame: 10

1

2

3

4

5

6

7

8

9

10

11

15

16

17

18

19

20

21

22

23

24

25

1

2

3

4

5

6

7

8

9

10

11

15

16

17

18

19

20

21

22

23

24

25

Figure 4: Examples of Delaunay Triangulation instant

graphs of two teams (represented in blue and red).

4.2 Soccer Temporal Graphs

Our analyses are based on the characterization of in-

teraction among players along the match. Let G

0

be

a sequence G

0

= hG

1

, G

2

, . . . , G

T

i. A vertex v ∈ V

t

is associated with a player, whereas an edge e

jk

∈ E

t

connecting two vertices v

j

∈ E

t

and v

k

∈ E

t

is deﬁned

based on the location (or any other relation) of play-

ers (v

j

and v

k

) of the same team at timestamp t. The

weight w(e

jk

) may encode different properties of the

interaction of players, such as their distance – possi-

bly measured by the Euclidean distance of players j

and k in the ﬁeld – or the number of passes between

them.

Considering the importance of interaction be-

tween players on soccer matches, we consider

two different approaches for constructing temporal

graphs: Instant Graphs based on Delaunay Triangu-

lation and Flow Networks. Both of them take into

consideration passes between players from the same

team. Instant graphs represent possibilities of passes

according to the players’ position on the pitch at each

timestamp, while Flow Networks represent all accom-

plished passes between players in a time interval.

4.2.1 Instant Graphs based on Delaunay

Triangulation

In this representation, for each time stamp, it is

computed the Delaunay Triangulation (Preparata and

Shamos, 2012) considering as input the players’ po-

sition in the pitch. Two triangulations are computed,

one for each team. Figure 4 shows examples of instant

graphs. Blue vertices (players labeled from 1 to 11)

and edges represent Team A, while red ones (players

labeled from 15 to 25) represent Team B.

4.2.2 Flow Networks

One important research venue refers to the identiﬁca-

Visualizing Temporal Graphs using Visual Rhythms - A Case Study in Soccer Match Analysis

99

tion of interaction patterns among players for a given

time interval. One common approach relies on the

use of Flow Network (Duch et al., 2010). Flow net-

work graphs can be deﬁned as G

t

i

,t

j

(V, E), in which

vertices are players from a team, and weighted edges

represent passes accomplished between them during

a time interval [t

i

, t

j

].

We extend this approach by proposing ball posses-

sion ﬂow networks. Those networks show paths that

only happen in time (Santoro et al., 2011; Casteigts

et al., 2011), which means that no instant graph has

all the edges shown in a ﬂow network. Basically, we

extract different ﬂow networks, which represent ball

passing among teammate players within the time in-

terval in which they have ball possession. Figure 5

shows two possession ﬂow networks. In Graph (a),

the team has the ball, and accomplishes eight passes

among teammates. Graph (b) illustrates the match sit-

uation in which a team has the ball possession, but no

passes are accomplished until losing the ball posses-

sion again.

6

5

3

1

2

7

8

4

9

10

11

(a)

6

5

3

1

2

7

8

4

9

10

11

(b)

Figure 5: Examples of Ball Possession Flow Networks.

(a) Graph from a team that performed eight passes among

teammates during a ball possession interval. (b)In another

ball possession interval, no passes were performed.

5 ANALYSIS AND DISCUSSION

This section discusses several usage scenarios in

which graph visual rhythms are used to identify visual

temporal patterns related to teams’ strategies when

defending or attacking.

5.1 Defensive Patterns

The ﬁrst usage scenario considers the use of graph

visual rhythms in the identiﬁcation of defensive pat-

terns.

Considering the ﬁrst half time of a match, we gen-

erated the Delaunay Triangulation Instant Graphs and

computed the Diversity Entropy from each node in

the instant graph (F

G

t

). For each instant graph, di-

versity entropy values were ordered and linked to-

gether vertically resulting in an image GV R

xy

, where

x is equal to the amount of frames from the match

and y is amount of players from graph (11 players in

(a) Match 1 – Team A

(b) Match 1 – Team B

Figure 6: Graph visual rhythm images for teams of

Match 1.

each team). Diversity Entropy values between 0 and

1 in GV R

xy

were normalized to 0 to 255, generating

a grey-scale image. In this case, lower entropy val-

ues are darker, and higher values are lighter. For the

player who has ball possession, entropy values may

be associated with the ‘complexity’ of the decision-

making scenario. If entropy is high, it means that the

player has many options (i.e., teammates) to interact

with and this is a less complex situation in case that

the player has to perform a pass as fast as possible.

On the other hand, lower entropy values may repre-

sent few teammates to interact with. This complex

situation requires the player to evaluate this scenario

more carefully, identify who are these few options of

interaction, and thus make the decision to perform a

pass.

Figures 6 and 7 present the resulting graph visual

rhythms images obtained for teams of two matches

(Match 1 and Match 2). In both matches, Team A

is the same. It is possible to notice a clear pattern,

deﬁned in terms of vertical darker blocks, that distin-

guishes all images. Considering the performance of

Team A in both matches, we can observe that there are

darker regions for Match 2, which means that players

of Team A in this match were usually not free, i.e.,

there were opponents close to them more frequently.

By zooming in the graph visual rhythms of Fig-

ure 6 for the frames in the range deﬁned between

IVAPP 2017 - International Conference on Information Visualization Theory and Applications

100

(a) Match 2 – Team A

(b) Match 2 – Team C

Figure 7: Graph visual rhythm images for teams of

Match 2.

55000 and 58000, we obtain the images shown in Fig-

ure 8. We plotted the corresponding graph from the

instant highlighted in red, to analyze the game strat-

egy employed in the time period related to a darker

block. It is possible to observe that for a darker block,

Team A (in blue) is compressed in a defensive strat-

egy while Team B (in red) is attacking. Team B is

well positioned in the ﬁeld with many possibilities of

passes among players, which is represented in its own

graph visual rhythm image. Thus, entropy values may

represent team strategy both in attacking and defend-

ing perspectives. The distances among teammates de-

ﬁne the team compactness on the pitch during attack-

ing and defending actions (Moura et al., 2012; Moura

et al., 2013). In this case, Team-A players occupy the

ﬁeld in a very compact way, with a no clear purpose of

performing a man-to-man marking. This strategy may

favor the attacking team in order to allow a greater

number of options for passes between players. If this

condition is maintained over time (which is easily de-

tected in the graph visual rhythm image), it may in-

dicate a technical and tactical superiority for the team

with lower entropy values.

One goal was scored by Team A of Match 1 at

frame 24825. Figure 9 shows the graph visual rhythm

images associated with this moment. It is interesting

to notice that Team A was attacking, but, differently

from the situation depicted in Figure 8, both teams

(a) (b)

0 20 40 60 80 100

0 10 20 30 40 50 60 70

x

y

1

2

3

4

5

6

7

8

9

10

11

15

16

17

18

19

20

21

22

23

24

25

(c)

Figure 8: Graph Visual Rhythm in details: Highlighted dark

block and the corresponding match situation. Team A (in

blue) is compressed in a defensive strategy while Team B

(in red) is attacking.

(a) (b)

0 20 40 60 80 100

0 10 20 30 40 50 60 70

x

y

Graph Plot − Frame: 24825

1

2

3

4

5

6

7

8

9

10

11

15

16

17

18

19

20

21

22

23

24

25

1

2

3

4

5

6

7

8

9

10

11

15

16

17

18

19

20

21

22

23

24

25

(c)

Figure 9: Graph visual rhythms of teams at a goal event

timestamp.

have higher diversity entropy scores. In this case, this

phenomenon is observed due to the fact that the goal

was originated from a corner kick.

Visualizing Temporal Graphs using Visual Rhythms - A Case Study in Soccer Match Analysis

101

5.2 Most Valued Player: A

Centrality-oriented Perspective

We conducted a preliminary study considering the

computation of the betweeness centrality applied to

instant graphs. The intention here is to support the

identiﬁcation of players whose centrality scores are

higher during the match, and so they could be con-

sidered more valued than others in the game strat-

egy. Figure 10 shows the centrality-based graph vi-

sual rhythm image for Match 2, using darker colors to

highlight players with higher centrality scores. It can

be noticed that during almost all the match, centrality

scores are low for most of the players. The low and

homogeneous centrality scores show that there was no

‘star topology.’ Each had nearly the same connectiv-

ity, indicating that the teams did not depend on one

single player (Clemente et al., 2015).

We can also notice that for Player 7 of Team A,

there were darker pixels along the match. By analyz-

ing his performance during the game, we could realize

that this player was involved in more passes than all

the others (47 passes in the ﬁrst half time, while the

team’s passes average was 33.1), which could mean

that he was well positioned in the pitch during ball

possession.

This same pattern is observed for Team B. It is

possible to observe a darker pixel line for Player 6,

who was also the one involved in more passes (42

passes in the ﬁrst half time against the team’s passes

average of 26.4). We observed similar patterns for

other matches: players with higher centrality scores,

when compared to teammates, are involved more fre-

quently with successful passes. Thus, graph visual

rhythm images allow to identify players who had in-

ﬂuential contributions in a speciﬁc match, and, ap-

plied during the entire tournament, they may help

coaches to identify the most important players. In

other words, it helps to answer in an objective man-

ner whether, for example, the most famous players

fulﬁlled the expectations placed on them (Duch et al.,

2010). However, in a collective evaluation, both en-

tropy and centrality may be interpreted with caution.

The work of (Grund, 2012) shown in 760 matches in

the English Premier League that high levels of inter-

action (i.e., passing rate) lead to increased team per-

formance. However, centralized interaction patterns

lead to decreased team performance. In fact, even in

a social context, teams with denser networks had a

tendency to perform better and remain more viable.

Furthermore, these variables, analyzed over the

match, may help also to identify who are the play-

ers more affected by fatigue. By decreasing the num-

ber of players involved, it is possible to allow some

(a) Match 2 – Team A

(b) Match 2 – Team C

Figure 10: Graph visual rhythm images based on the play-

ers’ centrality for Match 2. We highlighted in red the play-

ers with higher centrality scores.

players to rest actively. Moreover, it can characterise

teams’ attacking strategies. The direct play may in-

crease centrality among some players and involves a

lot of participation from forwards and strikers, for ex-

ample (Clemente et al., 2015).

5.3 Patterns of Passes

We also investigated the possibility of using graph

visual rhythms for analyzing patterns of passes. In

this case, we have employed graphs deﬁned by Flow

Networks. From soccer matches, we computed the

Ball Possession Flow Networks, in which vertices are

players and edges are passes accomplished among

teammates while the team has the ball possession.

Considering the ﬁrst half time from each analyzed

match, it is possible to construct N different ﬂow net-

work graphs, considering all N time intervals in which

each team has the ball possession. We computed the

graph visual rhythm image for each team in a match.

This image contains all passes accomplished among

teammates in each ball possession ﬂow network, i.e.,

in this case, F

G

t

computes the occurrences of passes

among players. Pixels representing an speciﬁc pass

performed in a network were colored according to the

location in the pitch where the ball passing occurred.

Figure 11 shows color patterns used. We divided

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102

Figure 11: Pitch color patterns: defensive area in cold col-

ors, while attacking area in hot colors.

(a) Match 1 – Team A

(b) Match1 – Team B

Figure 12: Graph visual rhythms encoding the patterns of

passes of teams in Match 1.

the pitch in 4 sections, where defensive area of a team

was colored in cold colors (light blue and dark blue),

while attacking area of a team (the opponent’s pitch)

was colored in hot colors (light red and dark red).

Also, when a network does not have any edges (no

passes performed), all its pixels are grey. Using this

color pattern, it is possible to visually understand pat-

terns of passes for a team.

We analyzed the ﬁrst half time of the same two

matches. The resulting graph visual rhythm images

are shown in Figures 12 and 14. The Y axis has labels

of players involved in successful passes (e.g., passes

from player 3 to player 10), and the X axis refers to

the ﬂow networks considering ball possession. It is

(a) Match 1 – Team A

(b) Match1 – Team B

Figure 13: Graph visual rhythms (ordered by players) en-

coding the patterns of passes of teams in Match 1.

possible to notice some patterns in each match. Dur-

ing Match 1 (Figure 12), Team A performed more

passes among teammates than Team B (more colored

pixels in image of Team A). Also, Team A has longer

vertical lines of pixels colored, which means that for

each ball possession, many passes were activated in-

volving many players. Figure 13 presents a graph vi-

sual rhythm for this same match, but now with y-axis

representing passes ordered by players (from player 1

to 11). It is also possible to notice that many passes

(vertical pixel lines) involve both defensive, middle,

and forward players, in different ﬁeld regions. Fur-

thermore, some passes occurred many times along

networks, and some of them only in its defensive area

(cold-colored pixels). Team B has performed less ball

passes, and passes in a single ball possession period

involve only two players. Most of those passes occur

in the attacking area (predominance of hot-colored

pixels).

During Match 2 (Figure 14), Team B has per-

formed more passes than Team A. It is interesting to

notice that many of them occurred in its defensive

area (predominance of cold-colored pixels), while

Visualizing Temporal Graphs using Visual Rhythms - A Case Study in Soccer Match Analysis

103

(a) Match 2 – Team A

(b) Match 2 – Team C

Figure 14: Graph visual rhythms encoding the patterns of

passes of teams in Match 2.

team A performs more passes in the attacking area.

Figure 15 presents a graph visual rhythm for this same

match, but now with y-axis representing passes or-

dered by players (from player 1 to 11). It can be

noticed that ball possession involves few players. In

this match, Team C performed passes involving more

players, from defensive to forward players. Note also

that for two different matches, Team A has very dif-

ferent performance in terms of patterns of passes (see

Figures 12(a) and 14(a)).

5.4 Pass Patterns in Attack Actions

It is also possible to create graph visual rhythm im-

ages considering a subset of players. For example,

it might be interesting to show pass patterns involv-

ing only forward players. With this purpose, we cre-

ated graph visual rhythms from passes involving only

players with role, which is depicted in Figure 16. In

this case, we refer to Match 1. We can observe that

not only did forward players of Team A accomplish

more passes than players of Team B, but also they

accomplished those passes in the opponent area (pre-

(a) Match 2 – Team A

(b) Match 2 – Team C

Figure 15: Graph visual rhythms (ordered by players) en-

coding the patterns of passes of teams in Match 2.

dominance of hot-colored pixels). We can conclude

that Team A exploited more frequently the strategy of

using multiple passes in attacking actions.

5.5 Soccer Visual Analytics Tool

We have created a soccer visual analytics tool that

integrates the different graph extraction approaches,

and visual rhythm image computation algorithms de-

scribed in this paper. This tool allows loading data

about soccer matches (usually, information about

players’ location over time), and encode them into

graphs, depending on the type of analysis deﬁned by

the user. All complex network measures described in

this paper were implemented, so it is possible to visu-

ally analyze them by means of graph visual rhythms.

Figure 17 presents a typical usage example. In

this case, we have graph visual rhythm images of two

teams computed from instant graphs represented by

the diversity entropy of their vertices. By clicking

on the side-bar check boxes (area labeled with A), a

user can highlight match events, as goals and attack-

ing moments, and also, can deﬁne a speciﬁc period of

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104

(a) (b)

Figure 16: Graph visual rhythms encoding the patterns of passes of forward players in Match 1.

A

B

C

Figure 17: Screen shot of the soccer visual analytics tool developed.

time for zooming in targeting speciﬁc regions of the

images (shown in region B). User can also view corre-

sponding graphs or temporal graphs videos, by click-

ing anywhere on the graph visual rhythm image, or

selecting an area of interest in the image (ﬁeld graph

view in region C).

6 CONCLUSIONS

This paper has introduced the graph visual rhythm

representation, a compact visual structure to encode

changes in temporal graphs, making it a suitable so-

lution to handle large volumes of data. We demon-

strate its applicability in several usage scenarios con-

cerning the analysis of soccer matches, whose several

Visualizing Temporal Graphs using Visual Rhythms - A Case Study in Soccer Match Analysis

105

dynamic aspects are encoded into temporal graphs.

This research opens novel opportunities for inves-

tigation related to the use of several image process-

ing algorithms to highlight important patterns in tem-

poral graphs. We plan to follow this research venue

in our future work. We also plan to incorporate ma-

trix reordering methods (Behrisch et al., 2016) aim-

ing to improve the identiﬁcation of changing patterns

in graph visual rhythm representations. Another is-

sue refers to the implementation of suitable visualiza-

tion approaches to handle players’ substitutions in a

match.

ACKNOWLEDGEMENTS

The authors would like to thank CAPES, CNPq (grant

#306580/2012-8), FAPESP (grants #2013/50169-1

and #2013/50155-0 ) for the ﬁnancial support. Au-

thors are also grateful for the support of PUC-

Campinas.

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