Multidimensional analysis of complex networks

PhD dis­ser­ta­tion abstract

An Australian Virtual Social networkThe analy­sis of Com­plex Net­works turn out to be a very promis­ing field of research, tes­ti­fied by many research projects and works that span dif­fer­ent fields. Until recently, those analy­sis have been usu­ally focused on deeply char­ac­ter­ize a sin­gle aspect of the sys­tem, there­fore a study that con­sid­ers many infor­ma­tive axes along with a net­work evolve is lack­ing.
In this The­sis, we pro­pose a new mul­ti­di­men­sional analy­sis that is able to inspect net­works in the two most impor­tant dimen­sions of a sys­tem, namely space and time. In order to achieve this goal, we stud­ied them sin­gu­larly and inves­ti­gated how the vari­a­tion of the con­sti­tut­ing para­me­ters dri­ves changes to the net­work behav­iour as a whole.

By focus­ing on space dimen­sion, we were able to char­ac­ter­ize spa­tial alter­ation in terms of abstrac­tion lev­els. We pro­pose a novel algo­rithm that, by apply­ing a fuzzi­ness func­tion, can recon­struct net­works under dif­fer­ent level of details. We call this analy­sis tele­scopic as it recalls the mag­ni­fi­ca­tion and reduc­tion process of the lens.
Through this line of research we have suc­cess­fully ver­i­fied that sta­tis­ti­cal indi­ca­tors, that are fre­quently used in many com­plex net­works researches, depends strongly on the gran­u­lar­ity (i.e, the detail level) with which a sys­tem is described and on the class of net­works considered.

We keep fixed the space axes (that is, nodes’ coor­di­nates) and we iso­lated the dynam­ics behind net­works evo­lu­tion process.
In par­tic­u­lar, our goal is to detect new instincts that trig­ger online social net­works uti­liza­tion and spread the adop­tion of novel com­mu­ni­ties. We for­mal­ized this enhanced social net­work evo­lu­tion by adopt­ing new spe­cial nodes, called “sirens” that, thanks to their abil­ity to attract new links, were also able to con­struct effi­cient con­nec­tion pat­terns.
We both sim­u­late the dynam­ics of indi­vid­u­als and sirens by con­sid­er­ing three most known growth mod­els, namely ran­dom, pref­er­en­tial attach­ment and social.

Apply­ing this new frame­work to real and syn­thetic social net­works, we have shown that the sirens, even when used for a lim­ited period of time, effec­tively shrink the time needed to get a net­work in mature state. In order to pro­vide a con­crete con­text of our find­ings, we for­mal­ized the cost of set­ting up such enhance­ment and we pro­vided the best com­bi­na­tions of system’s para­me­ters, such as num­ber of sirens, time span of uti­liza­tion and attrac­tive­ness, which min­i­mize this cost.