3 Metabolic Graphs

gc()

          used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells 2767419 147.8    5141138 274.6  4916595 262.6
Vcells 4561965  34.9   10146329  77.5  8388589  64.0

load(file='metadag_work_space.RData')
gc()

           used  (Mb) gc trigger  (Mb) max used  (Mb)
Ncells  2867110 153.2    5141138 274.6  4916595 262.6
Vcells 38144536 291.1   49087077 374.6 38165243 291.2

We present here some analysis examples of the metabolic graphs generated in GraphML format.

3.1 Metabolic graphs for each organism

Read the individual metabolic graphs generated for Homo sapiens (KEGG id: hsa) in the directory(Individuals/hsa)

experiment=
  "0a845f74-826e-3b46-aed9-e7ecf74db262/"
path_exp=paste0("data/",experiment)
files_hsa=dir(paste0(path_exp,"Individuals/hsa"))
files_hsa

 [1] "hsa_mDAG.graphml"       "hsa_mDAG.pdf"           "hsa_mDAG.svg"          
 [4] "hsa_mDAG_adj.csv"       "hsa_mDAG_biggerDAG.pdf" "hsa_mDAG_biggerDAG.svg"
 [7] "hsa_mDAG_nl.csv"        "hsa_mDAG_structure.csv" "hsa_R_adj.csv"         
[10] "hsa_R_nl.csv"           "hsa_RC.graphml"         "hsa_RC.pdf"            
[13] "hsa_RC.svg"             "hsa_summary.txt"

files_Individual_hsa	Description
hsa_mDAG.graphml	m-DAG GraphML format
hsa_mDAG.pdf	m-DAG pdf graphic
hsa_mDAG.svg	m-DAG svg graphic
hsa_mDAG_adj.csv	csv file with the adjacency matrix of the m-DAG
hsa_mDAG_biggerDAG.pdf	pdf graphic with the biggest conected component of the m-DAG
hsa_mDAG_biggerDAG.svg	svg graphic with the biggest conected component of the m-DAG
hsa_mDAG_nl.csv	csv file with the node (MBBs) labels of the m-DAG
hsa_mDAG_structure.csv	csv file with all connected components of the m-DAG
hsa_R_adj.csv	csv file with the adjacency matrix of the reaction graph
hsa_R_nl.csv	csv file with the node (reactions) labels of the reaction graph
hsa_RC.graphml	reaction graph GraphML format
hsa_RC.pdf	reaction graph pdf graphic
hsa_RC.svg	reaction graph svg graphic
hsa_summary.txt	text summary file with the number of MBBs, reactions, etc. in the previous graphs

3.2 Pan & core metabolic graphs

Pan and core metabolic graphs for every group were generated. For instance, one can read the pan and core metabolic graphs generated for the group Algae in the directory (Groups/Algae).

files_Algae=dir(paste0(path_exp,"Groups/Algae"))
files_Algae

[1] "core" "pan"

The global core reaction graph, which is the core of all the organisms’ reaction graphs in this Eukaryotes test, is empty.

graph_core_RC=read.graph(
  paste0(path_exp,
         "Global/core/core_RC.graphml"),
  format = "graphml")
summary(graph_core_RC)

IGRAPH 089f3be D--- 0 0 -- 
+ attr: color (v/c), label (v/c), id (v/c)

The global core reaction graph has 0 vertex and 0 edges. It is an empty graph.

The core reaction graph for the Algae group is:

knitr::include_graphics(
  paste0(path_exp,"Groups/MSA_Cluster_3/core/MSA_Cluster_3_core_RC.pdf"))

Algae core reaction graph

The global core m-DAG, i.e., the core of all organisms in this example is empty.

graph_core_mDAG=read.graph(
  paste0(path_exp,"Global/core/core_mDAG.graphml"),
  format = "graphml")
summary(graph_core_mDAG)

IGRAPH 08b0d3a D--- 0 0 -- 
+ attr: color (v/c), label (v/c), id (v/c)

The global core m-DAG has 0 vertex and 0 edges. It is an empty graph.

The core metabolic DAG for the Algae group is:

knitr::include_graphics(paste0(path_exp,                              "Groups/Algae/core/Algae_core_mDAG.pdf"))

Core m-DAG for Algae

The global pan reaction graph for the Animals Kingdom is:

graph_pan_RC=read.graph(
  paste0(path_exp,
         "TaxonomyLevels/Kingdom/Animals/pan/Animals_pan_RC.graphml"),
  format = "graphml")
summary(graph_pan_RC)

IGRAPH 08d0e67 D--- 4556 5798 -- 
+ attr: color (v/c), label (v/c), id (v/c), id (e/c)

This pan reaction graph has 4556 nodes and 5798 edges.

3.3 Graph’s topology

From the GraphML files, one can extract topological information. Some examples are as follows.

The diagram below illustrates the distribution of node degrees for an m-DAG.

graph_mDAG=read.graph(
  paste0(path_exp,
         "Individuals/hsa/hsa_mDAG.graphml"),
  format= "graphml")
summary(graph_mDAG)

IGRAPH 08e076b D--- 1026 1086 -- 
+ attr: color (v/c), label (v/c), id (v/c), id (e/c)

barplot(table(igraph::degree(graph_mDAG,mode="all")),
        ylim=c(0,350),col="blue",
        main="Frequency of Node Degrees",
        ylab="Frequency",xlab="Degree")

The connected components of every graph as well as the size of every connected component can be obtained as:

compo=components(graph_mDAG,mode = "weak")
str(compo)

List of 3
 $ membership: num [1:1026] 1 1 1 1 1 1 1 1 1 1 ...
 $ csize     : num [1:167] 589 1 1 1 1 1 4 3 4 3 ...
 $ no        : num 167

compo$csize

  [1] 589   1   1   1   1   1   4   3   4   3   2   3   3   1   1   1   2   6
 [19]   3   1   3   6   1   1   1   1   1   3   1   6   2   1   1   1   2   1
 [37]   1  14   1  16   1   6   2   2   4   1   1   1   1   1   1   1   1   1
 [55]  13   1   1   1   1   2   6   5   5   2   2  10   1   1   1   2   2   1
 [73]   1   1  62   6   2   1   2   1   1   1   2   1   2  14   3   1   1   1
 [91]   1   1   1   1   1   1   3   6   1   3   1   3   2   1   1   1   2   2
[109]   3   1   1   2   5   1   1   2   3   2   1   1   2   3   4   1   1   2
[127]   1   1   2   1   1   1   1   1   3   1   2   2   1   6   1   1   1   2
[145]   1   1   1   1   1   2   7   1  15   3   1   1   1   1   2   1   3   1
[163]   1   1   1   1   2

k=which.max(compo$csize==max(compo$csize))
k

[1] 1

table(compo$membership)


  1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20 
589   1   1   1   1   1   4   3   4   3   2   3   3   1   1   1   2   6   3   1 
 21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40 
  3   6   1   1   1   1   1   3   1   6   2   1   1   1   2   1   1  14   1  16 
 41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60 
  1   6   2   2   4   1   1   1   1   1   1   1   1   1  13   1   1   1   1   2 
 61  62  63  64  65  66  67  68  69  70  71  72  73  74  75  76  77  78  79  80 
  6   5   5   2   2  10   1   1   1   2   2   1   1   1  62   6   2   1   2   1 
 81  82  83  84  85  86  87  88  89  90  91  92  93  94  95  96  97  98  99 100 
  1   1   2   1   2  14   3   1   1   1   1   1   1   1   1   1   3   6   1   3 
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 
  1   3   2   1   1   1   2   2   3   1   1   2   5   1   1   2   3   2   1   1 
121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 
  2   3   4   1   1   2   1   1   2   1   1   1   1   1   3   1   2   2   1   6 
141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 
  1   1   1   2   1   1   1   1   1   2   7   1  15   3   1   1   1   1   2   1 
161 162 163 164 165 166 167 
  3   1   1   1   1   1   2

vertex=which(compo$membership==k)
length(vertex)

[1] 589

Big_Component=induced_subgraph(graph_mDAG, vids=vertex)
igraph::vcount(Big_Component)

[1] 589

igraph::ecount(Big_Component)

[1] 774

And the plot of the bigger component of the m-DAG in Homo sapiens is:

knitr::include_graphics(paste0(path_exp,
                               "Individuals/hsa/hsa_mDAG_biggerDAG.pdf"))

#path_exp="data/result_bb261b6e-95c6-3e39-b82b-b68eea80e30b/data/" 
list_names=dir(paste0(path_exp,"Individuals/"))
list_names= list_names[-1] # filter 0000_RefPw
length(list_names)

[1] 884

graphs_list=paste0(path_exp,"Individuals/", list_names,"/",list_names, "_MDAG.graphml")

knitr::include_graphics(
  paste0(path_exp,"Individuals/cang/cang_RC.pdf"))

3.4 Graph statistics

The number of connected component in each generated m-DAG with their frequency in the entire set of m-DAGs, can be obtained as follows:

read_mDAG=function(x) {DAG=read.graph(file=x,
                                      format="graphml")
return(DAG)}
mDAG_components=function(x) {
  sort(components(x,mode = "weak")$csize,
       decreasing=TRUE)
}

compo_list=lapply(graphs_list,
                  FUN=function(x) {
                    gg=read_mDAG(x)
                    aux=list(
                      mDAG_components=mDAG_components(gg),
                      degree_count=igraph::degree(gg,mode="total"))
                    return(aux)}
)

names(compo_list)=list_names
n=max(sapply(compo_list,FUN=function(x) {length(x[[1]])}))
n

[1] 234

size_compo_list=lapply(compo_list,FUN=function(x) {
  return(c(x[[1]],rep(NA,n-length(x[[1]]))))})

aux=do.call(bind_cols,size_compo_list)
weak_components_size=pivot_longer(aux,aaf:zvi,names_to="Organism",
                                 values_to="csize") %>% 
  arrange(Organism,-csize)
weak_components_size$index=rep(1:n,times=dim(aux)[2])
weak_components_size=weak_components_size %>%
  left_join(meta_taxo,by="Organism") %>% filter(!is.na(Kingdom),!is.na(csize))
weak_components_size_raw=weak_components_size

Organism=names(compo_list)

size_MBB=function(org){
  #org="hsa"
  x=Results %>% filter(Organism==org) %>% select(!contains("_rev"))
  x=as.character(x[1,6:dim(x)[2]])
  x=x[(!is.na(x))]
  x=x[x!="NA"]
  tt=data.frame(sort(table(x),decreasing=TRUE),org)
  names(tt)=c("MBB","size","Organism")
  return(tt)
}


size_list_raw= lapply(Organism,FUN=function(x) size_MBB(x))
names(size_list_raw)=Organism

size_MBB_df=do.call(rbind,size_list_raw)
max(size_MBB_df$size)

[1] 757

size_MBB_df=size_MBB_df %>% left_join(meta_taxo%>% select(Organism,Kingdom),by="Organism") %>% filter(!is.na(Kingdom))

We can visualize the sizes of the weak components for each m-DAG, using colors to represent the different Kingdoms, also we scale the results by a log-log plot:

COLOR_KINGDOM=c("red","yellow","green","black")
colors_kingdom=weak_components_size%>% select(Organism,Kingdom) %>% distinct()
names(COLOR_KINGDOM)=sort(unique(colors_kingdom$Kingdom))

p1<- ggplot(data=weak_components_size) + 
  geom_line(mapping=aes(x=index,
                        y=csize,group = Organism,
                        color=Kingdom),
            na.rm=TRUE) + 
  scale_x_continuous(trans="identity") + 
  scale_y_continuous(trans="identity") +
  ylim(0,640)+
  ggtitle("Plot of weak components size decreasing order.")+
  ylab("Weak components size") + xlab("Order")+
  scale_color_manual(values =COLOR_KINGDOM[colors_kingdom$Kingdom])

p2<- ggplot(data=weak_components_size) + 
  geom_line(mapping=aes(x=index,
                        y=csize,group = Organism,
                        color=Kingdom),
            na.rm=TRUE) + 
  scale_y_continuous(trans='log10') + 
  scale_x_continuous(trans='log10') +
  scale_color_manual(values =COLOR_KINGDOM[colors_kingdom$Kingdom])+
  ggtitle("Plot log10-log10 of size  weak components decreasing order.") +
  ylab("Log10 weak component size") + xlab("Log10 order")
p1

p2

A table with the frequencies of the weak connected components sizes, displayed by Kingdom, can be obtained as follows:

aux=table(weak_components_size$csize,weak_components_size$Kingdom)
table_wcc_size=tibble(Order=1:dim(aux)[1],
                      Wcc_size=as.integer(unlist(dimnames(aux)[1])),
                      Animals=aux[,1],
                      Fungi=aux[,2],
                      Plants=aux[,3],
                      Protists=aux[,4])
knitr::kable(table_wcc_size, 
             caption = "Weak Connected Componet Size")%>% kable_styling(bootstrap_options = "striped", full_width = FALSE) %>%
  scroll_box(height = "300px", width = "100%")

Weak Connected Componet Size
Order	Wcc_size	Animals	Fungi	Plants	Protists
1	1	57634	15311	15024	4462
2	2	13528	2118	2908	932
3	3	7018	1070	911	317
4	4	2459	313	292	96
5	5	1962	215	389	81
6	6	1778	154	323	49
7	7	633	46	111	15
8	8	278	57	110	7
9	9	174	76	151	22
10	10	671	6	124	7
11	11	411	14	6	20
12	12	109	12	4	5
13	13	369	92	132	7
14	14	774	9	2	2
15	15	234	1	5	6
16	16	79	6	1	1
17	17	55	8	1	1
18	18	4	5	9	5
19	19	5	3	87	4
20	20	9	3	0	1
21	21	13	2	12	1
22	22	7	2	2	0
23	23	21	1	3	0
24	24	19	1	3	1
25	25	20	0	2	1
26	26	12	0	39	0
27	27	1	1	11	0
28	28	5	2	77	0
29	29	40	1	0	1
30	30	0	1	1	0
31	31	72	8	1	0
32	32	11	7	1	0
33	33	1	0	0	2
34	34	6	0	0	0
35	35	2	0	0	0
36	36	3	0	0	0
37	37	5	1	2	0
38	38	0	0	0	1
39	39	5	0	0	0
40	40	5	1	0	0
41	41	4	0	0	0
42	42	1	0	0	0
43	43	2	0	0	1
44	44	6	0	0	0
45	45	1	0	0	0
46	46	5	0	0	0
47	47	9	0	0	0
48	48	1	0	0	0
49	49	1	1	0	0
50	50	1	0	0	0
51	51	4	0	0	0
52	53	50	1	0	1
53	54	6	0	0	0
54	55	1	0	0	0
55	56	8	0	0	0
56	57	2	0	0	0
57	58	12	1	0	0
58	59	6	0	0	0
59	60	30	1	0	0
60	61	5	0	0	0
61	62	15	0	0	0
62	63	4	0	0	0
63	64	2	0	0	0
64	65	34	0	0	0
65	66	6	0	0	0
66	67	1	0	0	0
67	69	1	0	0	0
68	70	2	0	0	1
69	71	1	0	0	0
70	72	1	0	0	0
71	73	6	0	0	0
72	77	2	0	0	1
73	78	1	0	0	1
74	83	0	0	0	2
75	84	1	0	0	0
76	87	1	0	0	0
77	88	1	0	0	1
78	90	2	0	0	1
79	91	1	0	0	0
80	94	4	0	0	1
81	95	1	0	0	0
82	96	1	0	0	1
83	97	0	0	0	1
84	99	1	0	0	1
85	100	2	0	0	0
86	101	1	0	0	0
87	102	0	0	0	1
88	103	3	0	0	1
89	104	0	0	0	2
90	105	0	0	0	1
91	107	0	0	0	1
92	108	1	0	0	2
93	110	2	0	0	0
94	111	1	0	0	0
95	112	0	1	0	0
96	113	2	0	0	0
97	114	1	0	0	1
98	116	1	0	0	0
99	117	3	0	0	0
100	120	1	0	0	0
101	121	2	0	0	0
102	125	1	0	0	0
103	127	1	0	0	1
104	128	0	0	0	2
105	153	0	1	0	0
106	166	0	0	0	1
107	175	0	0	0	2
108	181	0	0	0	1
109	183	0	0	0	2
110	184	1	0	0	0
111	187	0	0	0	1
112	193	1	0	0	1
113	195	0	0	0	1
114	196	0	0	0	1
115	198	1	0	0	0
116	203	0	0	0	1
117	205	0	0	0	1
118	210	2	0	0	0
119	219	1	0	0	1
120	220	1	0	0	0
121	229	1	0	0	0
122	231	0	0	0	1
123	232	1	0	0	0
124	233	0	1	0	0
125	235	1	0	0	0
126	238	3	0	0	0
127	243	1	0	0	0
128	245	0	1	0	0
129	246	1	1	0	0
130	248	0	1	0	0
131	249	0	2	0	0
132	250	0	2	0	0
133	251	0	1	0	0
134	252	1	2	0	0
135	253	1	0	0	0
136	254	0	1	0	0
137	255	2	0	0	0
138	256	2	1	0	0
139	257	4	0	0	0
140	258	1	1	0	0
141	259	1	0	0	0
142	260	2	1	0	1
143	261	2	1	0	0
144	262	2	0	0	0
145	263	4	1	0	1
146	264	4	0	0	0
147	265	3	4	0	2
148	266	2	1	0	0
149	267	2	1	0	0
150	268	2	3	0	1
151	269	3	1	0	0
152	270	3	0	1	0
153	271	1	1	0	0
154	272	2	2	0	0
155	273	4	3	0	1
156	274	2	1	0	0
157	275	4	2	0	0
158	276	0	2	0	0
159	277	4	4	0	0
160	278	3	3	0	1
161	279	5	0	0	1
162	280	1	0	0	0
163	281	3	4	0	0
164	282	4	1	0	0
165	283	5	1	0	0
166	284	4	1	0	0
167	285	5	1	0	0
168	286	4	2	0	1
169	287	1	0	0	0
170	288	2	3	0	0
171	289	1	0	0	0
172	290	3	0	0	0
173	291	1	1	0	0
174	292	1	3	0	1
175	293	5	1	0	0
176	294	6	0	0	0
177	295	1	2	0	0
178	296	5	1	0	0
179	297	4	1	0	0
180	298	2	1	0	0
181	299	2	0	1	1
182	300	2	0	0	0
183	301	4	2	0	0
184	302	1	0	0	1
185	303	3	0	0	0
186	304	3	0	0	0
187	305	3	0	0	0
188	306	2	1	0	0
189	307	4	1	0	0
190	308	1	0	0	0
191	310	1	0	0	0
192	311	1	0	1	0
193	313	2	2	0	0
194	315	1	0	0	0
195	316	1	0	0	0
196	317	1	0	1	0
197	318	0	2	0	0
198	319	1	0	0	0
199	320	3	1	1	0
200	321	1	0	0	0
201	322	3	0	0	0
202	323	2	0	0	0
203	325	1	0	0	0
204	327	2	1	0	0
205	328	5	1	1	0
206	330	0	1	0	0
207	332	1	0	0	0
208	333	1	1	1	1
209	335	1	0	0	0
210	338	1	0	0	0
211	339	0	0	1	1
212	340	1	1	0	0
213	341	1	0	0	0
214	342	1	0	0	1
215	343	2	1	0	0
216	344	0	0	1	0
217	345	2	0	0	0
218	346	1	0	0	0
219	347	2	0	0	0
220	349	2	0	0	0
221	350	1	0	0	0
222	351	1	0	0	0
223	352	3	0	0	0
224	353	1	0	0	0
225	354	1	0	0	0
226	355	2	0	0	0
227	356	1	1	0	0
228	357	1	2	0	0
229	358	2	1	0	0
230	359	0	0	1	0
231	360	1	0	1	0
232	361	1	3	0	0
233	362	1	2	0	0
234	363	2	3	0	0
235	365	2	1	0	0
236	366	1	0	0	0
237	367	1	0	0	0
238	368	2	1	0	0
239	369	3	1	0	0
240	370	0	2	0	0
241	371	0	2	0	0
242	372	1	0	0	0
243	373	2	2	0	0
244	374	3	1	0	0
245	375	2	1	0	0
246	376	0	1	0	0
247	377	0	1	0	0
248	378	2	0	0	0
249	380	0	3	0	0
250	381	2	1	0	0
251	382	2	1	0	0
252	383	3	1	1	0
253	384	0	1	0	0
254	385	0	1	0	0
255	387	2	2	0	0
256	388	1	2	0	0
257	389	1	0	0	0
258	391	2	0	0	0
259	392	0	1	0	0
260	393	1	1	0	0
261	394	3	0	0	0
262	396	1	0	0	0
263	397	0	2	0	0
264	398	2	0	0	0
265	399	1	1	0	0
266	400	0	0	1	0
267	401	1	1	0	0
268	402	0	1	0	0
269	404	1	1	0	0
270	405	3	1	0	0
271	406	0	1	0	0
272	407	0	2	0	0
273	408	1	1	1	0
274	409	2	0	0	0
275	411	3	0	0	0
276	412	1	0	0	0
277	413	2	1	0	0
278	415	1	0	0	0
279	416	2	0	0	0
280	417	0	1	0	0
281	418	0	1	0	0
282	419	0	1	0	0
283	420	0	1	0	0
284	421	1	2	0	0
285	423	0	2	0	0
286	424	0	1	0	0
287	426	2	0	0	0
288	428	1	0	0	0
289	431	0	1	0	0
290	432	1	0	0	0
291	433	3	0	0	0
292	435	1	0	0	0
293	438	0	1	0	0
294	439	0	1	0	0
295	443	1	0	0	0
296	444	1	0	0	0
297	445	2	1	0	0
298	446	2	0	0	0
299	447	1	0	0	0
300	452	1	0	0	0
301	453	1	0	0	0
302	455	1	0	0	0
303	459	1	0	0	0
304	462	1	0	0	0
305	463	2	0	0	0
306	465	1	0	0	0
307	468	1	0	0	0
308	470	1	0	0	0
309	471	0	0	1	0
310	473	0	0	1	0
311	475	2	0	0	0
312	480	1	0	0	0
313	481	1	0	0	0
314	482	1	0	0	0
315	483	1	0	0	0
316	485	0	0	1	0
317	487	1	0	0	0
318	491	3	0	0	0
319	492	1	0	0	0
320	493	3	0	0	0
321	496	2	0	0	0
322	497	3	0	0	0
323	500	0	0	1	0
324	501	1	0	0	0
325	502	5	0	0	0
326	503	1	0	0	0
327	504	1	0	1	0
328	507	2	0	0	0
329	508	2	0	0	0
330	509	1	0	0	0
331	510	1	0	0	0
332	511	2	0	0	0
333	512	5	0	0	0
334	513	2	0	0	0
335	514	0	0	2	0
336	515	4	0	5	0
337	516	4	0	0	0
338	517	5	0	1	0
339	518	1	0	0	0
340	519	3	0	1	0
341	520	2	0	0	0
342	521	2	0	1	0
343	523	5	0	1	0
344	524	3	0	1	0
345	525	2	0	1	0
346	526	0	0	1	0
347	527	2	0	0	0
348	528	2	0	4	0
349	529	7	0	0	0
350	530	1	0	2	0
351	531	2	0	1	0
352	532	2	0	2	0
353	533	2	0	2	0
354	534	2	0	0	0
355	535	2	0	2	0
356	536	2	0	0	0
357	537	1	0	0	0
358	538	3	0	0	0
359	539	1	0	1	0
360	540	0	0	4	0
361	541	2	0	0	0
362	542	0	0	2	0
363	544	0	0	3	0
364	545	0	0	1	0
365	546	1	0	1	0
366	547	0	0	1	0
367	548	1	0	1	0
368	549	1	0	2	0
369	550	0	0	6	0
370	551	4	0	2	0
371	553	1	0	1	0
372	554	0	0	3	0
373	555	2	0	9	0
374	556	0	0	1	0
375	557	2	0	4	0
376	558	0	0	2	0
377	559	1	0	3	0
378	560	1	0	4	0
379	561	0	0	4	0
380	562	3	0	2	0
381	563	3	0	0	0
382	564	1	0	2	0
383	565	1	0	0	0
384	566	0	0	1	0
385	567	3	0	3	0
386	568	3	0	0	0
387	569	5	0	1	0
388	570	4	0	2	0
389	571	2	0	2	0
390	572	1	0	2	0
391	573	2	0	2	0
392	574	2	0	4	0
393	575	5	0	4	0
394	576	6	0	1	0
395	577	7	0	4	0
396	578	7	0	0	0
397	579	2	0	0	0
398	580	3	0	0	0
399	581	3	0	3	0
400	582	7	0	2	0
401	583	2	0	0	0
402	584	3	0	1	0
403	585	4	0	0	0
404	586	3	0	0	0
405	587	1	0	1	0
406	588	1	0	0	0
407	589	1	0	0	0
408	590	1	0	0	0
409	591	5	0	0	0
410	592	2	0	0	0
411	594	3	0	0	0
412	595	2	0	0	0
413	597	0	0	1	0
414	598	2	0	0	0
415	601	2	0	0	0
416	602	1	0	0	0
417	603	1	0	0	0
418	604	2	0	0	0
419	605	1	0	0	0
420	611	1	0	0	0
421	618	1	0	0	0
422	640	1	0	0	0

A table with the frequencies of the MBBs sizes displayed by Kingdom can be obtained as follows:

size_MBB_df_table= size_MBB_df %>% group_by(Kingdom,size) %>% summarise(n=n())

table_MBB_size = size_MBB_df_table %>% pivot_wider(names_from = Kingdom, values_from = n, values_fill = list(n = 0)) %>% arrange(size)
knitr::kable(table_MBB_size, caption = "MBB Size: Frequency by Kingdom")%>% kable_styling(bootstrap_options = "striped", full_width = FALSE) %>% scroll_box(height = "300px", width = "100%")

MBB Size: Frequency by Kingdom
size	Animals	Fungi	Plants	Protists
1	408027	74872	109638	17773
2	7426	2464	2306	678
3	5087	464	758	303
4	2613	324	632	115
5	948	340	49	56
6	390	131	274	46
7	190	167	27	16
8	544	70	127	27
9	137	7	124	10
10	492	20	2	10
11	91	29	132	8
12	44	3	6	4
13	21	4	0	2
14	15	10	0	1
15	195	2	0	5
16	23	6	0	3
17	7	5	1	0
18	410	122	118	3
19	3	7	0	0
20	4	0	0	7
21	1	0	0	0
22	0	0	0	2
23	3	0	0	0
24	5	1	0	0
25	2	1	0	2
27	1	0	1	0
29	1	2	0	0
30	0	1	0	1
31	2	4	0	2
32	0	4	0	1
33	1	2	0	0
34	3	0	0	0
35	5	0	0	0
36	1	0	0	1
37	1	2	0	1
39	1	0	0	0
44	1	0	0	4
45	0	1	0	0
46	1	0	0	0
47	0	0	0	3
48	0	0	0	2
49	1	0	0	1
50	1	0	0	0
51	1	0	0	0
53	2	0	0	0
54	1	0	0	0
56	1	0	0	0
57	3	0	0	0
92	0	0	0	1
103	0	0	0	1
107	0	0	0	1
117	0	0	0	1
118	0	0	0	1
119	0	0	0	1
120	0	0	0	3
121	0	0	0	5
136	1	0	0	0
139	0	0	0	1
162	0	0	0	1
181	1	0	0	0
186	0	0	0	1
189	0	0	0	1
203	0	0	0	1
222	0	0	1	0
224	0	0	0	1
226	0	0	0	1
232	0	0	0	1
233	1	0	0	0
234	0	0	0	1
240	0	0	0	3
241	0	0	0	1
250	1	0	0	0
259	0	0	1	0
276	1	0	0	1
284	0	1	0	1
285	0	0	1	0
286	1	0	0	0
291	0	0	0	1
296	0	1	0	1
300	0	0	1	0
306	0	0	0	1
307	0	1	0	0
314	0	0	1	0
326	1	0	0	0
329	0	0	1	0
331	0	0	0	1
332	0	1	0	0
336	0	0	1	0
340	0	0	0	1
343	0	0	1	0
344	0	1	0	0
348	0	0	0	1
350	0	1	0	0
360	1	0	0	0
361	0	0	1	0
363	0	0	0	1
364	0	1	0	0
371	0	0	0	1
373	1	0	0	0
375	1	0	0	0
381	0	1	1	0
387	0	1	0	0
390	0	1	0	0
392	0	0	0	1
393	1	0	0	0
401	0	2	0	0
402	0	1	0	0
403	1	0	0	0
409	0	1	0	0
410	0	1	1	0
417	1	1	0	0
419	0	1	0	0
420	0	0	1	1
421	0	0	1	0
422	0	2	0	0
423	1	1	0	0
427	0	1	0	0
428	1	1	0	0
429	1	0	0	0
430	0	1	0	0
433	0	1	0	0
437	1	1	0	0
438	0	1	0	0
441	0	1	0	0
443	1	1	0	0
444	0	1	0	0
446	0	1	0	0
447	1	2	0	0
449	1	1	0	0
450	1	0	0	0
451	0	3	0	0
452	1	0	0	0
454	0	1	0	0
455	0	1	0	0
456	1	0	0	0
457	1	1	0	0
458	1	1	0	0
459	2	0	0	0
461	1	1	0	0
462	1	2	0	0
463	0	3	0	0
465	1	0	0	0
466	1	0	0	0
467	1	0	0	0
468	0	2	0	0
469	2	0	0	0
470	1	0	0	0
471	1	1	0	0
473	2	1	0	0
474	3	0	0	0
476	0	2	0	0
477	1	0	0	0
478	1	1	0	0
479	1	0	0	0
480	0	1	0	0
481	2	0	0	0
482	2	0	0	0
483	2	0	0	0
484	2	1	0	1
485	0	2	0	0
486	1	1	0	0
487	6	0	0	0
488	1	2	0	0
489	1	0	0	0
490	1	0	0	0
491	2	1	0	0
492	2	0	0	0
493	1	1	0	0
494	0	1	0	0
495	2	1	0	0
496	4	1	0	0
498	5	3	0	0
499	2	0	0	0
500	2	0	0	0
501	1	1	0	0
502	3	3	0	0
503	1	0	0	0
504	6	0	0	1
505	5	2	0	0
506	5	2	0	0
507	1	2	0	0
508	4	0	0	0
509	0	1	0	0
510	4	2	0	0
511	3	1	0	0
512	1	0	0	0
513	6	1	0	0
514	5	0	0	0
515	1	1	0	0
516	1	0	0	0
517	6	0	0	0
518	6	0	0	0
519	0	1	0	0
521	0	1	0	0
522	5	1	0	0
523	1	2	0	0
524	2	2	0	0
525	2	2	0	0
526	0	1	0	0
527	5	2	0	0
528	6	3	0	0
529	2	1	0	0
530	1	0	0	0
531	3	1	0	0
532	0	1	0	0
533	4	0	0	0
534	3	0	0	0
535	1	0	0	0
536	1	0	0	0
537	1	0	0	0
538	1	0	0	0
539	0	1	0	0
540	1	2	0	0
541	1	1	0	0
542	1	2	0	0
543	0	2	0	0
544	1	2	0	0
545	1	0	0	0
547	0	0	1	0
548	1	0	0	0
550	0	1	0	0
551	2	0	0	0
552	1	0	0	0
553	0	1	0	0
554	1	1	0	0
555	1	2	0	0
556	1	0	0	0
558	1	0	0	0
559	0	2	0	0
561	0	1	0	0
563	2	2	0	0
564	1	0	0	0
565	1	0	0	0
566	1	1	0	0
567	2	1	0	0
568	1	0	0	0
569	1	0	0	0
572	1	2	0	0
574	1	1	0	0
575	0	1	0	0
576	1	3	0	0
577	1	0	0	0
578	1	0	0	0
579	2	1	0	0
580	1	0	0	0
582	1	0	0	0
583	3	0	0	0
584	1	3	0	0
585	1	1	0	0
586	0	2	0	0
587	0	1	0	0
589	0	1	0	0
590	0	1	0	0
591	2	1	0	0
593	1	0	1	0
594	1	0	0	0
595	1	0	0	0
596	2	0	0	0
598	2	0	0	0
599	1	0	0	0
600	1	1	0	0
602	2	0	0	0
603	1	0	0	0
604	2	0	0	0
606	1	1	0	0
607	1	0	0	0
608	0	1	0	0
611	2	0	1	0
613	3	0	1	0
614	1	0	0	0
616	2	1	0	0
617	1	1	0	0
618	1	0	1	0
619	3	0	0	0
620	2	0	0	0
621	1	0	0	0
622	0	0	1	0
623	2	0	0	0
625	2	0	0	0
626	2	0	0	0
628	1	0	0	0
629	3	0	0	0
633	1	0	1	0
634	1	0	1	0
635	1	0	1	0
636	1	0	0	0
637	2	0	0	0
638	2	0	1	0
639	1	0	1	0
640	0	0	1	0
641	1	0	0	0
642	2	0	1	0
643	2	0	1	0
644	1	0	1	0
645	1	0	0	0
646	1	0	1	0
647	3	0	3	0
650	3	0	1	0
651	1	0	1	0
652	1	0	3	0
653	0	0	1	0
654	1	0	2	0
655	0	0	1	0
656	0	0	2	0
658	3	0	0	0
659	0	0	3	0
660	2	0	4	0
661	2	0	5	0
662	0	0	1	0
663	3	0	0	0
664	2	0	2	0
665	0	0	4	0
666	2	0	1	0
667	1	0	2	0
668	0	0	3	0
669	0	0	5	0
670	0	0	5	0
671	2	0	7	0
672	2	0	6	0
673	0	0	6	0
674	1	0	4	0
675	0	0	19	0
676	1	0	9	0
677	2	0	5	0
678	0	0	1	0
679	1	0	2	0
680	4	0	0	0
681	1	0	1	0
682	0	0	1	0
683	2	0	0	0
684	3	0	0	0
685	3	0	0	0
686	2	0	0	0
687	1	0	0	0
689	1	0	0	0
692	1	0	0	0
693	4	0	0	0
695	4	0	0	0
696	3	0	0	0
697	4	0	0	0
698	4	0	0	0
699	4	0	0	0
700	10	0	0	0
701	5	0	0	0
702	9	0	0	0
703	8	0	0	0
704	19	0	0	0
705	19	0	0	0
706	7	0	0	0
707	6	0	0	0
708	4	0	0	0
709	4	0	0	0
710	20	0	0	0
711	6	0	0	0
712	17	0	0	0
713	9	0	0	0
714	10	0	0	0
715	4	0	0	0
716	5	0	0	0
717	3	0	0	0
718	8	0	0	0
719	4	0	0	0
721	2	0	0	0
723	1	0	0	0
724	2	0	0	0
726	1	0	0	0
757	1	0	0	0

3.4.1 More statistics

weak_components_size$Kingdom <- factor(weak_components_size$Kingdom)
#weak_components_size


g <- ggplot(weak_components_size) +
  xlab("") +  # Eliminar el título del eje X
  ylab("Size of connected component") +  # Etiqueta del eje Y
  geom_jitter(aes(x = Kingdom, y = csize, color = Kingdom),
             size = 1) +  # Colorear puntos según 'Kingdom' y reducir el tamaño
  scale_y_continuous(breaks = seq(0, 640, by = 100)) +  # Escala del eje Y con saltos de 20
  theme_minimal() + # Tema minimalista con fondo blanco
  ggtitle("")  # Título del gráfico
  g

weak_components_size_max = weak_components_size %>%
  group_by(Organism) %>%
  summarise(csize = max(csize),Kingdom=first(Kingdom))
# Crear el gráfico de violín con puntos jitter
g <- ggplot(weak_components_size_max, aes(x = Kingdom, y = csize)) +
  geom_violin(aes(fill = Kingdom), trim = FALSE, alpha = 0.5) +  # Gráfico de violín con relleno por 'Kingdom' y sin recortar
  geom_jitter(aes(color = Kingdom), size = 1, width = 0.2) +  # Puntos con jitter para evitar solapamientos
  xlab("") +  # Eliminar el título del eje X
  ylab("Size of biggest connected component") +  
  scale_y_continuous(breaks = seq(0, 640, by = 100)) +  
  theme_minimal() +  # theme background white
  ggtitle("")  #
#Size of the largest weakly connected component by Kingdom \n (Violin Plot with Jittered Points)
# Mostrar el gráfico
g