Java, 应用系统的复杂网络分析

摘要: 大量研究表明, Java, 软件系统是一种人工复杂网络, 它的入度分布符合幂律, 然而出度却是对数正态分布.现有的这些研究都仅仅以, Java, 开发工具包, 如, JDK、log4j, 和, Tomcat, 这一类软件系统为研究对象. 除此之外, 所分析的数据类型也很有限, 只考虑了程序包与类的依赖关系, 忽略了很多有用的数据类型, 比如函数成员变量和函数临时变量.本文将这两类数据类型纳入了研究范畴, 拓展了类依赖关系. 不仅如此, 本文也将研究粒度细化至函数层面, 构建了函数依赖图.针对这两类依赖关系, 本文提出了将系统转化为加权有向网络图的理论方法.全面的实验结果显示, 本文所选取的, 10, 类, Java, 应用系统, 无论是出度还是入度绝大多数都符合幂律分布, 由此证明了所提出的理论方法, 验证了有向加权网络是否具有无标度特性在分析Java应用系统网络结构时是有效的.
- 复杂网络 /
- Java应用系统 /
- 幂律分布 /
- 类依赖图 /
- 函数依赖图
Abstract: A lot of empirical studies have demonstrated that Java software system is a kind of artificial complex network and its in-degree distribution obeys the power law, while out-degree distribution is lognormal. However, most experiment objects in these studies are Java development tools, such as JDK, log4j and Tomcat, and the type of data analyzed in dependence graph is limited, because they only consider some class dependence relationships and omit certain useful data types, like member variables and local variables. In this paper, we all useful dependence relationships between entities or modules on both class and function levels, and we further propose a novel method to transform a system network into a weighted directed graph. Comprehensive experiment results show that the in- and out-degree of 10 types of Java application systems mostly fit the power law distributions, and our proposed method to detect the scale-free feature of a weighted and directed network is effective in analyzing Java application systems.
- complex network /
- ava application systems /
- power law distribution /
- class dependence graph /
- function dependence graph

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Fig. 1 A sample of Java class binary file

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Fig. 2 (a) CDG network of focusns; (b) FDG network of focusns

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Fig. 3 In-degree distributions of CDG[3R] and CDG[5R] networks in all 10 types of systems (a) Blog and SNS systems; (b) ERP and CRM systems; (c) WebMail systems; (d) GIS systems; (e) Portal systems; (f) CMS systems; (g) Bug tracking systems; (h) LMS systems; (i) Wiki systems; (j) Forum systems

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Fig. 4 Out-degree distributions of CDG[3R] and CDG[5R] networks in all 10 types of systems (a) Blog and SNS systems; (b) ERP and CRM systems; (c) WebMail systems; (d) GIS systems; (e) Portal systems; (f) CMS systems; (g) Bug tracking systems; (h) LMS systems; (i) Wiki systems; (j) Forum systems

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Fig. 5 In- and out-degree distributions of FDG networks in all 10 types of systems (a) Blog and SNS systems; (b) ERP and CRM systems; (c) WebMail systems; (d) GIS systems; (e) Portal systems; (f) CMS systems; (g) Bug tracking systems; (h) LMS systems; (i) Wiki systems; (j) Forum systems

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Tab. 1 CDG and FDG networks for 10 types of Java application systems

Network	Description	\|V\|	\|E\|	\|V_f\|	\|E_f\|
GISToolkit	GIS system	470	2 467	468	1 488
OpenGTS	GIS system	357	2 474	67 04	7 122
OpenJUMP	GIS system	1 369	8 429	6 062	8 815
dotCMS	CMS system	2 412	13 801	2 382	6 680
infoGlue	CMS system	1 371	6 891	1 359	3 375
OpenCms	CMS system	1 572	12 288	1 558	6 452
eConf	LMS system	61	169	134	103
a-LMS	LMS system	440	1 861	1 988	1 759
OLMS	LMS system	130	358	141	97
JSPWiki	Wiki system	489	2 056	1 843	1 927
JAMWiki	Wiki system	150	744	762	770
FitNesse	Wiki system	672	2 789	1 957	1 764
jforum	Forum system	355	1 587	1 290	1 423
jGossip	Forum system	263	919	507	611
Yazd	Forum system	218	885	891	793
jPortlet	Portal system	133	555	318	273
OpenPortal	Portal system	84	151	87	92
Pluto	Portal system	351	1 189	821	706
GatorMail	WebMail system	110	324	269	197
OlivaMail	WebMail system	60	247	191	215
yawebmail	WebMail system	76	196	157	139
FocusSNS	Blog and SNS system	299	913	283	491
Pebble	Blog and SNS system	655	3 003	2 295	2 875
Roller	Blog and SNS system	513	2 843	2 536	3 314
ITracker	Bug tracking system	386	1 835	382	736
BugRat	Bug tracking system	74	383	364	513
Scarab	Bug tracking system	575	2 449	5 947	5 332
Hipergate	ERP and CRM system	643	2 517	3 181	3 366
SourceTap	ERP and CRM system	169	737	652	636
OpenCustomer	ERP and CRM system	398	2 019	1 151	1 392

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Tab. 2 The invocation number of the maximum node in each system

Network	R₁	R₂	R₃	R₄	R₅
GISToolkit	1	20	155	86	54
OpenGTS	3	0	391	335	60
OpenJUMP	1	79	394	64	179
dotCMS	3	0	3900	349	243
infoGlue	4	0	1850	58	199
OpenCms	0	107	1 894	292	1 162
eConf	0	1	2	5	14
a-LMS	1	0	309	52	2
OLMS	0	0	0	155	9
JSPWiki	1	57	126	52	73
JAMWiki	0	74	2	0	4
FitNesse	2	48	279	103	25
jforum	0	56	55	89	89
jGossip	1	0	105	18	2
Yazd	1	19	39	27	14
jPortlet	4	0	101	1	10
OpenPortal	0	0	8	1	6
Pluto	1	7	56	33	14
GatorMail	0	0	1	0	47
OlivaMail	0	1	1	26	27
yawebmail	1	1	4	0	6
FocusSNS	1	9	31	24	8
Pebble	0	32	86	132	147
Roller	13	0	98	104	0
ITracker	1	2	10	3	94
BugRat	0	0	250	51	101
Scarab	1	27	266	187	45
Hipergate	0	3	151	46	39
SourceTap	0	1	50	45	25
OpenCustomer	0	17	59	100	38

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Tab. 3 Value of α and xmin in all ten types of Java application networks

Network	CDG networks[5R]				CDG networks[3R]				FDG networks
Network	${\alpha}^{in}$	$x_{\min}^{in}$	${\alpha}^{out}$	$x_{\min}^{out}$	${\alpha}^{in}$	$x_{\min}^{in}$	${\alpha}^{out}$	$x_{\min}^{out}$	${\alpha}^{in}$	$x_{\min}^{in}$	${\alpha}^{out}$	$x_{\min}^{out}$
GISToolkit	2.01	6	4.23	39	1.96	3	2.72	8	1.80	1	3.38	14
OpenGTS	2.01	27	2.08	20	2.02	8	2.26	8	2.50	2	3.84	3
OpenJUMP	2.09	12	4.33	42	2.19	8	3.41	16	2.22	2	4.25	6
dotCMS	1.81	6	2.19	35	2.02	24	1.96	5	3.36	6	2.72	6
infoGlue	1.81	5	2.03	11	1.88	1	2.25	6	1.79	3	2.02	4
OpenCms	1.90	11	2.34	36	1.94	6	2.35	17	1.84	4	2.29	16
eConf	3.03	9	3.56	10	2.70	5	3.38	5	3.10	1	2.82	1
a-LMS	1.96	8	2.17	9	1.65	1	2.19	5	2.80	2	4.75	2
OLMS	1.85	2	2.25	6	2.51	1	2.38	1	2.59	1	4.89	1
JSPWiki	1.61	1	3.31	33	1.91	3	2.30	4	2.80	4	2.70	1
JAMWiki	1.90	10	2.57	23	1.63	1	2.47	13	2.26	2	4.62	2
FitNesse	1.99	6	3.20	18	1.78	1	4.03	16	2.66	2	2.87	1
jforum	2.15	32	3.92	34	1.78	1	2.92	6	2.80	5	5.00	4
jGossip	1.95	4	3.05	6	2.13	1	2.82	4	2.61	1	5.00	4
Yazd	1.87	7	1.96	6	1.86	1	2.26	5	2.30	1	5.00	3
jPortlet	2.35	12	2.32	8	2.12	4	2.63	5	2.40	1	2.61	1
OpenPortal	2.21	2	2.28	2	2.52	2	3.10	3	2.26	1	2.83	2
Pluto	2.47	8	2.66	11	2.41	5	2.48	4	2.92	2	2.67	1
GatorMail	2.00	3	3.00	5	2.10	1	2.45	2	2.68	1	3.49	1
OlivaMail	2.34	10	2.67	7	3.51	4	2.05	1	2.38	1	2.37	1
yawebmail	3.35	9	2.19	3	1.81	1	2.78	4	3.03	2	3.32	2
FocusSNS	1.71	1	2.57	7	1.90	1	5.00	11	2.75	15	4.58	8
Pebble	1.73	1	2.79	14	1.89	3	2.71	3	2.49	5	4.03	3
Roller	1.84	4	2.61	20	1.77	1	2.41	5	2.36	2	4.54	5
ITracker	2.94	83	2.57	15	2.37	18	2.10	2	2.31	1	2.36	3
BugRat	1.42	1	2.56	21	2.05	5	2.77	8	2.13	2	2.10	1
Scarab	2.32	37	2.62	41	2.56	29	2.44	21	2.30	1	4.25	1
Hipergate	2.19	17	2.59	24	2.07	5	2.72	15	2.39	2	3.43	3
SourceTap	1.64	1	2.11	8	1.62	2	2.37	5	2.45	1	2.68	1
OpenCustomer	1.94	4	5.00	27	2.12	3	4.13	10	2.19	1	2.31	1

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Tab. 4 p-values in all ten types of Java application networks

Network	CDG networks[5R]		CDG networks[3R]		FDG networks
Network	p-valueⁱⁿ	p-value^out	p-valueⁱⁿ	p-value^out	p-valueⁱⁿ	p-value^out
GISToolkit	0.0708	0.2084	0.637 6	0.001 2	0.344 4	0.1764
OpenGTS	0.6414	0.011 2	0.352 0	0.813 6	0.543 6	0.027 6
OpenJUMP	0.407 2	0.766 4	0.928 4	0.088 8	0.741 2	0.5608
dotCMS	0.034 4	0.001 2	0.664 0	0.008 0	0.234 0	0.168 0
infoGlue	0.218 8	0.175 6	0.794 0	0.041 6	0.326 0	0.0392
OpenCms	0.232 8	0.144 4	0.289 2	0.745 2	0.127 6	0.566 8
eConf	0.476 4	0.756 8	0.477 2	0.199 2	0.339 6	0.832 4
a-LMS	0.004 8	0.205 6	0.004 0	0.258 0	0.558 8	0.035 2
OLMS	0.020 8	0.055 6	0.342 0	0.666 4	0.382 8	0.497 2
JSPWiki	0.000 0	0.593 6	0.595 6	0.027 2	0.342 4	0.000 0
JAMWiki	0.297 6	0.902 8	0.000 4	0.195 2	0.548 8	0.365 6
FitNesse	0.027 6	0.255 2	0.019 2	0.917 6	0.461 6	0.0000
jforum	0.772 0	0.620 0	0.000 0	0.084 4	0.193 2	0.241 2
jGossip	0.305 2	0.059 6	0.001 6	0.860 8	0.079 6	0.692 8
Yazd	0.495 6	0.060 8	0.053 2	0.302 0	0.014 4	0.208 8
jPortlet	0.458 8	0.017 2	0.714 0	0.529 6	0.003 2	0.1716
OpenPortal	0.188 0	0.020 0	0.001 6	0.710 8	0.360 8	0.2524
Pluto	0.437 2	0.872 0	0.632 4	0.368 0	0.326 8	0.000 0
GatorMail	0.467 2	0.818 4	0.016 4	0.620 0	0.442 4	0.1440
OlivaMail	0.503 2	0.800 4	0.110 8	0.047 6	0.512 0	0.1420
yawebmail	0.658 0	0.665 6	0.004 8	0.562 0	0.549 2	0.0752
FocusSNS	0.001 6	0.042 8	0.080 4	0.939 6	0.695 6	0.7408
Pebble	0.000 0	0.613 6	0.643 2	0.001 6	0.264 0	0.012 4
Roller	0.045 6	0.353 2	0.000 4	0.666 8	0.916 0	0.026 8
ITracker	0.817 2	0.010 4	0.824 4	0.363 6	0.258 4	0.0416
BugRat	0.005 6	0.463 6	0.228 8	0.7728	0.4364	0.000 0
Scarab	0.307 6	0.229 2	0.0016	0.9808	0.0000	0.000 0
Hipergate	0.577 2	0.226 8	0.7416	0.2812	0.068 0	0.7228
SourceTap	0.528 4	0.001 2	0.7084	0.0448	0.606 0	0.0000
OpenCustomer	0.260 8	0.7868	0.5608	0.7300	0.3144	0.0000

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